opencv/modules/core/doc/basic_structures.rst

Basic Structures
================

.. highlight:: cpp

.. _DataType:

DataType
--------

Template "trait" class for other OpenCV primitive data types ::

    template<typename _Tp> class DataType
    {
        // value_type is always a synonym to _Tp.
        typedef _Tp value_type;

        // intermediate type used for operations on _Tp.
        // it is int for uchar, signed char, unsigned short, signed short, and int,
        // float for float, double for double, ...
        typedef <...> work_type;
        // in the case of multi-channel data, it is the data type of each channel
        typedef <...> channel_type;
        enum
        {
            // CV_8U ... CV_64F
            depth = DataDepth<channel_type>::value,
            // 1 ...
            channels = <...>,
            // '1u', '4i', '3f', '2d' etc.
            fmt=<...>,
            // CV_8UC3, CV_32FC2 ...
            type = CV_MAKETYPE(depth, channels)
        };
    };

The template class ``DataType`` is a descriptive class for OpenCV primitive data types and other types that comply with the following definition. A primitive OpenCV data type is one of ``unsigned char``, ``bool``, ``signed char``, ``unsigned short``, ``signed short``, ``int``, ``float``, ``double`` or a tuple of values of one of these types, where all the values in the tuple have the same type. Any primitive type from the list can be defined by an identifier in the form ``CV_<bit-depth>{U|S|F}C<number_of_channels>``, for example: ``uchar`` ~ ``CV_8UC1``, 3-element floating-point tuple ~ ``CV_32FC3``, and so on. A universal OpenCV structure, which is able to store a single instance of such a primitive data type, is
:ref:`Vec`. Multiple instances of such a type can be stored in a ``std::vector``,``Mat``,``Mat_``,``SparseMat``,``SparseMat_``, or any other container that is able to store
:ref:`Vec` instances.

The ``DataType`` class is basically used to provide a description of such primitive data types without adding any fields or methods to the corresponding classes (and it is actually impossible to add anything to primitive C/C++ data types). This technique is known in C++ as class traits. It is not ``DataType`` itself that is used, but its specialized versions, such as: ::

    template<> class DataType<uchar>
    {
        typedef uchar value_type;
        typedef int work_type;
        typedef uchar channel_type;
        enum { channel_type = CV_8U, channels = 1, fmt='u', type = CV_8U };
    };
    ...
    template<typename _Tp> DataType<std::complex<_Tp> >
    {
        typedef std::complex<_Tp> value_type;
        typedef std::complex<_Tp> work_type;
        typedef _Tp channel_type;
        // DataDepth is another helper trait class
        enum { depth = DataDepth<_Tp>::value, channels=2,
            fmt=(channels-1)*256+DataDepth<_Tp>::fmt,
            type=CV_MAKETYPE(depth, channels) };
    };
    ...

The main purpose of this class is to convert compilation-time type information to an OpenCV-compatible data type identifier, for example: ::

    // allocates a 30x40 floating-point matrix
    Mat A(30, 40, DataType<float>::type);

    Mat B = Mat_<std::complex<double> >(3, 3);
    // the statement below will print 6, 2 /*, that is depth == CV_64F, channels == 2 */
    cout << B.depth() << ", " << B.channels() << endl;


So, such traits are used to tell OpenCV which data type you are working with, even if such a type is not native to OpenCV (the matrix ``B`` intialization above is compiled because OpenCV defines the proper specialized template class ``DataType<complex<_Tp> >`` ). Also, this mechanism is useful (and used in OpenCV this way) for generic algorithms implementations.

Point\_
-------

Template class for 2D points ::

    template<typename _Tp> class Point_
    {
    public:
        typedef _Tp value_type;

        Point_();
        Point_(_Tp _x, _Tp _y);
        Point_(const Point_& pt);
        Point_(const CvPoint& pt);
        Point_(const CvPoint2D32f& pt);
        Point_(const Size_<_Tp>& sz);
        Point_(const Vec<_Tp, 2>& v);
        Point_& operator = (const Point_& pt);
        template<typename _Tp2> operator Point_<_Tp2>() const;
        operator CvPoint() const;
        operator CvPoint2D32f() const;
        operator Vec<_Tp, 2>() const;

        // computes dot-product (this->x*pt.x + this->y*pt.y)
        _Tp dot(const Point_& pt) const;
        // computes dot-product using double-precision arithmetics
        double ddot(const Point_& pt) const;
        // returns true if the point is inside the rectangle "r".
        bool inside(const Rect_<_Tp>& r) const;

        _Tp x, y;
    };

The class represents a 2D point, specified by its coordinates
:math:`x` and
:math:`y` .
Instance of the class is interchangeable with C structures, ``CvPoint`` and ``CvPoint2D32f`` . There is also a cast operator to convert point coordinates to the specified type. The conversion from floating-point coordinates to integer coordinates is done by rounding. Commonly, the conversion uses this
operation on each of the coordinates. Besides the class members listed in the declaration above, the following operations on points are implemented: ::

        pt1 = pt2 + pt3;
        pt1 = pt2 - pt3;
        pt1 = pt2 * a;
        pt1 = a * pt2;
        pt1 += pt2;
        pt1 -= pt2;
        pt1 *= a;
        double value = norm(pt); // L2 norm
        pt1 == pt2;
        pt1 != pt2;

For your convenience, the following type aliases are defined: ::

    typedef Point_<int> Point2i;
    typedef Point2i Point;
    typedef Point_<float> Point2f;
    typedef Point_<double> Point2d;

Here is a short example: ::

    Point2f a(0.3f, 0.f), b(0.f, 0.4f);
    Point pt = (a + b)*10.f;
    cout << pt.x << ", " << pt.y << endl;


Point3\_
--------

Template class for 3D points ::

    template<typename _Tp> class Point3_
    {
    public:
        typedef _Tp value_type;

        Point3_();
        Point3_(_Tp _x, _Tp _y, _Tp _z);
        Point3_(const Point3_& pt);
        explicit Point3_(const Point_<_Tp>& pt);
        Point3_(const CvPoint3D32f& pt);
        Point3_(const Vec<_Tp, 3>& v);
        Point3_& operator = (const Point3_& pt);
        template<typename _Tp2> operator Point3_<_Tp2>() const;
        operator CvPoint3D32f() const;
        operator Vec<_Tp, 3>() const;

        _Tp dot(const Point3_& pt) const;
        double ddot(const Point3_& pt) const;

        _Tp x, y, z;
    };


The class represents a 3D point specified by its coordinates
:math:`x`,:math:`y` and
:math:`z` .
Instance of the class is interchangeable with the C structure ``CvPoint2D32f`` . Similarly to ``Point_`` , the 3D points' coordinates can be converted to another type. The vector arithmetic and comparison operations are also supported.

The following type aliases are available: ::

    typedef Point3_<int> Point3i;
    typedef Point3_<float> Point3f;
    typedef Point3_<double> Point3d;


Size\_
------

Template class for specfying an image or rectangle size. ::

    template<typename _Tp> class Size_
    {
    public:
        typedef _Tp value_type;

        Size_();
        Size_(_Tp _width, _Tp _height);
        Size_(const Size_& sz);
        Size_(const CvSize& sz);
        Size_(const CvSize2D32f& sz);
        Size_(const Point_<_Tp>& pt);
        Size_& operator = (const Size_& sz);
        _Tp area() const;

        operator Size_<int>() const;
        operator Size_<float>() const;
        operator Size_<double>() const;
        operator CvSize() const;
        operator CvSize2D32f() const;

        _Tp width, height;
    };


The class ``Size_`` is similar to ``Point_``  except that the two members are called ``width`` and ``height`` instead of ``x`` and ``y`` . The structure can be converted to and from the old OpenCV structures
``CvSize`` and ``CvSize2D32f`` . The same set of arithmetic and comparison operations as for ``Point_`` is available.

OpenCV defines the following type aliases: ::

    typedef Size_<int> Size2i;
    typedef Size2i Size;
    typedef Size_<float> Size2f;


Rect\_
------

Template class for 2D rectangles ::

    template<typename _Tp> class Rect_
    {
    public:
        typedef _Tp value_type;

        Rect_();
        Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height);
        Rect_(const Rect_& r);
        Rect_(const CvRect& r);
        // (x, y) <- org, (width, height) <- sz
        Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz);
        // (x, y) <- min(pt1, pt2), (width, height) <- max(pt1, pt2) - (x, y)
        Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2);
        Rect_& operator = ( const Rect_& r );
        // returns Point_<_Tp>(x, y)
        Point_<_Tp> tl() const;
        // returns Point_<_Tp>(x+width, y+height)
        Point_<_Tp> br() const;

        // returns Size_<_Tp>(width, height)
        Size_<_Tp> size() const;
        // returns width*height
        _Tp area() const;

        operator Rect_<int>() const;
        operator Rect_<float>() const;
        operator Rect_<double>() const;
        operator CvRect() const;

        // x <= pt.x && pt.x < x + width &&
        // y <= pt.y && pt.y < y + height ? true : false
        bool contains(const Point_<_Tp>& pt) const;

        _Tp x, y, width, height;
    };


The rectangle is described by the coordinates of the top-left corner (which is the default interpretation of ``Rect_::x`` and ``Rect_::y`` in OpenCV; though, in your algorithms you may count ``x`` and ``y`` from the bottom-left corner), the rectangle width and height.

Another assumption OpenCV usually makes is that the top and left boundary of the rectangle are inclusive, while the right and bottom boundaries are not. For example, the method ``Rect_::contains`` returns ``true`` if

.. math::

    x  \leq pt.x < x+width,
          y  \leq pt.y < y+height

And virtually every loop over an image
ROI in OpenCV (where ROI is specified by ``Rect_<int>`` ) is implemented as: ::

    for(int y = roi.y; y < roi.y + rect.height; y++)
        for(int x = roi.x; x < roi.x + rect.width; x++)
        {
            // ...
        }


In addition to the class members, the following operations on rectangles are implemented:

*
    :math:`\texttt{rect} = \texttt{rect} \pm \texttt{point}`     (shifting a rectangle by a certain offset)

*
    :math:`\texttt{rect} = \texttt{rect} \pm \texttt{size}`     (expanding or shrinking a rectangle by a certain amount)

* ``rect += point, rect -= point, rect += size, rect -= size``     (augmenting operations)

* ``rect = rect1 & rect2``     (rectangle intersection)

* ``rect = rect1 | rect2``     (minimum area rectangle containing ``rect2``     and ``rect3``     )

* ``rect &= rect1, rect |= rect1``     (and the corresponding augmenting operations)

* ``rect == rect1, rect != rect1``     (rectangle comparison)

This is an example how the partial ordering on rectangles can be established (rect1
:math:`\subseteq` rect2): ::

    template<typename _Tp> inline bool
    operator <= (const Rect_<_Tp>& r1, const Rect_<_Tp>& r2)
    {
        return (r1 & r2) == r1;
    }


For your convenience, the following type alias is available: ::

    typedef Rect_<int> Rect;


.. _RotatedRect:

RotatedRect
-----------

Template class for rotated rectangles ::

    class RotatedRect
    {
    public:
        // constructors
        RotatedRect();
        RotatedRect(const Point2f& _center, const Size2f& _size, float _angle);
        RotatedRect(const CvBox2D& box);

        // returns minimal up-right rectangle that contains the rotated rectangle
        Rect boundingRect() const;
        // backward conversion to CvBox2D
        operator CvBox2D() const;

        // mass center of the rectangle
        Point2f center;
        // size
        Size2f size;
        // rotation angle in degrees
        float angle;
    };


The class ``RotatedRect`` replaces the old ``CvBox2D`` and is fully compatible with it.

TermCriteria
------------

.. c:type:: TermCriteria

Template class defining termination criteria for iterative algorithms ::

    class TermCriteria
    {
    public:
        enum { COUNT=1, MAX_ITER=COUNT, EPS=2 };

        // constructors
        TermCriteria();
        // type can be MAX_ITER, EPS or MAX_ITER+EPS.
        // type = MAX_ITER means that only the number of iterations does matter;
        // type = EPS means that only the required precision (epsilon) does matter
        //    (though, most algorithms limit the number of iterations anyway)
        // type = MAX_ITER + EPS means that algorithm stops when
        // either the specified number of iterations is made,
        // or when the specified accuracy is achieved - whatever happens first.
        TermCriteria(int _type, int _maxCount, double _epsilon);
        TermCriteria(const CvTermCriteria& criteria);
        operator CvTermCriteria() const;

        int type;
        int maxCount;
        double epsilon;
    };


The class ``TermCriteria`` replaces the old ``CvTermCriteria`` and is fully compatible with it.

.. _Matx:

Matx
----

Template class for small matrices ::

    template<typename T, int m, int n> class Matx
    {
    public:
        typedef T value_type;
        enum { depth = DataDepth<T>::value, channels = m*n,
               type = CV_MAKETYPE(depth, channels) };

        // various methods
        ...

        Tp val[m*n];
    };

    typedef Matx<float, 1, 2> Matx12f;
    typedef Matx<double, 1, 2> Matx12d;
    ...
    typedef Matx<float, 1, 6> Matx16f;
    typedef Matx<double, 1, 6> Matx16d;

    typedef Matx<float, 2, 1> Matx21f;
    typedef Matx<double, 2, 1> Matx21d;
    ...
    typedef Matx<float, 6, 1> Matx61f;
    typedef Matx<double, 6, 1> Matx61d;

    typedef Matx<float, 2, 2> Matx22f;
    typedef Matx<double, 2, 2> Matx22d;
    ...
    typedef Matx<float, 6, 6> Matx66f;
    typedef Matx<double, 6, 6> Matx66d;


The class represents small matrices, whose type and size are known at compilation time. If you need a more flexible type, use
:ref:`Mat` . The elements of the matrix ``M`` are accessible using the ``M(i,j)`` notation, and most of the common matrix operations (see also
:ref:`MatrixExpressions` ) are available. If you need to do an operation on ``Matx`` that is not implemented, it is easy to convert the matrix to
:ref:`Mat` and backwards. ::

    Matx33f m(1, 2, 3,
              4, 5, 6,
              7, 8, 9);
    cout << sum(Mat(m*m.t())) << endl;


.. _Vec:

Vec
---

Template class for short numerical vectors ::

    template<typename T, int cn> class Vec : public Matx<T, cn, 1>
    {
    public:
        typedef T value_type;
        enum { depth = DataDepth<T>::value, channels = cn,
               type = CV_MAKETYPE(depth, channels) };

        // various methods ...
    };

    typedef Vec<uchar, 2> Vec2b;
    typedef Vec<uchar, 3> Vec3b;
    typedef Vec<uchar, 4> Vec4b;

    typedef Vec<short, 2> Vec2s;
    typedef Vec<short, 3> Vec3s;
    typedef Vec<short, 4> Vec4s;

    typedef Vec<int, 2> Vec2i;
    typedef Vec<int, 3> Vec3i;
    typedef Vec<int, 4> Vec4i;

    typedef Vec<float, 2> Vec2f;
    typedef Vec<float, 3> Vec3f;
    typedef Vec<float, 4> Vec4f;
    typedef Vec<float, 6> Vec6f;

    typedef Vec<double, 2> Vec2d;
    typedef Vec<double, 3> Vec3d;
    typedef Vec<double, 4> Vec4d;
    typedef Vec<double, 6> Vec6d;

``Vec`` is a partial case of ``Matx`` . It is possible to convert ``Vec<T,2>`` to/from ``Point_``,``Vec<T,3>`` to/from ``Point3_`` , and ``Vec<T,4>`` to ``CvScalar`` or :ref:`Scalar`. The elements of ``Vec`` are accessed using ``operator[]``. All the expected vector operations are implemented too:

*
    :math:`\texttt{v1} = \texttt{v2} \pm \texttt{v3}`,    :math:`\texttt{v1} = \texttt{v2} * \alpha`,    :math:`\texttt{v1} = \alpha * \texttt{v2}`     (plus the corresponding augmenting operations; note that these operations apply
    to each computed vector component)

* ``v1 == v2, v1 != v2`` * ``norm(v1)``     (:math:`L_2`-norm)

The ``Vec`` class is commonly used to describe pixel types of multi-channel arrays. See ``Mat_`` for details.

.. _Scalar:

Scalar\_
--------

Template class for a 4-element vector ::

    template<typename _Tp> class Scalar_ : public Vec<_Tp, 4>
    {
    public:
        Scalar_();
        Scalar_(_Tp v0, _Tp v1, _Tp v2=0, _Tp v3=0);
        Scalar_(const CvScalar& s);
        Scalar_(_Tp v0);
        static Scalar_<_Tp> all(_Tp v0);
        operator CvScalar() const;

        template<typename T2> operator Scalar_<T2>() const;

        Scalar_<_Tp> mul(const Scalar_<_Tp>& t, double scale=1 ) const;
        template<typename T2> void convertTo(T2* buf, int channels, int unroll_to=0) const;
    };

    typedef Scalar_<double> Scalar;


The template class ``Scalar_`` and its double-precision instantiation ``Scalar`` represent a 4-element vector. Being derived from ``Vec<_Tp, 4>`` , they can be used as typical 4-element vectors, but in addition they can be converted to/from ``CvScalar`` . The type ``Scalar`` is widely used in OpenCV for passing pixel values and it is a drop-in replacement for
``CvScalar`` that was used for the same purpose in the earlier versions of OpenCV.

.. _Range:

Range
-----

Template class specifying a continuous subsequence (a.k.a. slice) of a sequence. ::

    class Range
    {
    public:
        Range();
        Range(int _start, int _end);
        Range(const CvSlice& slice);
        int size() const;
        bool empty() const;
        static Range all();
        operator CvSlice() const;

        int start, end;
    };


The class is used to specify a row or column span in a matrix (
:ref:`Mat` ) and for many other purposes. ``Range(a,b)`` is basically the same as ``a:b`` in Matlab or ``a..b`` in Python. As in Python, ``start`` is an inclusive left boundary of the range and ``end`` is an exclusive right boundary of the range. Such a half-opened interval is usually denoted as
:math:`[start,end)` .

The static method ``Range::all()`` returns a special variable that means "the whole sequence" or "the whole range", just like " ``:`` " in Matlab or " ``...`` " in Python. All the methods and functions in OpenCV that take ``Range`` support this special ``Range::all()`` value. But, of course, in case of your own custom processing, you will probably have to check and handle it explicitly: ::

    void my_function(..., const Range& r, ....)
    {
        if(r == Range::all()) {
            // process all the data
        }
        else {
            // process [r.start, r.end)
        }
    }


.. _Ptr:

Ptr
---

Template class for smart reference-counting pointers ::

    template<typename _Tp> class Ptr
    {
    public:
        // default constructor
        Ptr();
        // constructor that wraps the object pointer
        Ptr(_Tp* _obj);
        // destructor: calls release()
        ~Ptr();
        // copy constructor; increments ptr's reference counter
        Ptr(const Ptr& ptr);
        // assignment operator; decrements own reference counter
        // (with release()) and increments ptr's reference counter
        Ptr& operator = (const Ptr& ptr);
        // increments reference counter
        void addref();
        // decrements reference counter; when it becomes 0,
        // delete_obj() is called
        void release();
        // user-specified custom object deletion operation.
        // by default, "delete obj;" is called
        void delete_obj();
        // returns true if obj == 0;
        bool empty() const;

        // provide access to the object fields and methods
        _Tp* operator -> ();
        const _Tp* operator -> () const;

        // return the underlying object pointer;
        // thanks to the methods, the Ptr<_Tp> can be
        // used instead of _Tp*
        operator _Tp* ();
        operator const _Tp*() const;
    protected:
        // the encapsulated object pointer
        _Tp* obj;
        // the associated reference counter
        int* refcount;
    };


The ``Ptr<_Tp>`` class is a template class that wraps pointers of the corresponding type. It is similar to ``shared_ptr`` that is part of the Boost library (
http://www.boost.org/doc/libs/1_40_0/libs/smart_ptr/shared_ptr.htm
) and also part of the `C++0x <http://en.wikipedia.org/wiki/C++0x>`_
standard.

By using this class you can get the following capabilities:

*
    Default constructor, copy constructor, and assignment operator for an arbitrary C++ class or a C structure. For some objects, like files, windows, mutexes, sockets, and others, copy constructor or assignment operator are difficult to define. For some other objects, like complex classifiers in OpenCV, copy constructors are absent and not easy to implement. Finally, some of complex OpenCV and your own data structures may have been written in C. However, copy constructors and default constructors can simplify programming a lot; besides, they are often required (for example, by STL containers). By wrapping a pointer to such a complex object ``TObj``     to ``Ptr<TObj>`` , you will automatically get all of the necessary constructors and the assignment operator.

*
    All the above-mentioned operations running very fast, regardless of the data size, that is like "O(1)" operations. Indeed, while some structures, like ``std::vector`` ,   provide a copy constructor and an assignment operator, the operations may take a considerable amount of time if the data structures are big. But if the structures are put into ``Ptr<>``     , the overhead becomes small and independent of the data size.

*
    Automatic destruction, even for C structures. See the example below with ``FILE*``     .

*
    Heterogeneous collections of objects. The standard STL and most other C++ and OpenCV containers can only store objects of the same type and the same size. The classical solution to store objects of different types in the same container is to store pointers to the base class ``base_class_t*``     instead but when you loose the automatic memory management. Again, by using ``Ptr<base_class_t>()``     instead of the raw pointers, you can solve the problem.

The ``Ptr`` class treats the wrapped object as a black box. The reference counter is allocated and managed separately. The only thing the pointer class needs to know about the object is how to deallocate it. This knowledge is incapsulated in the ``Ptr::delete_obj()`` method that is called when the reference counter becomes 0. If the object is a C++ class instance, no additional coding is needed, because the default implementation of this method calls ``delete obj;`` .
However, if the object is deallocated in a different way, then the specialized method should be created. For example, if you want to wrap ``FILE`` , the ``delete_obj`` may be implemented as follows: ::

    template<> inline void Ptr<FILE>::delete_obj()
    {
        fclose(obj); // no need to clear the pointer afterwards,
                     // it is done externally.
    }
    ...

    // now use it:
    Ptr<FILE> f(fopen("myfile.txt", "r"));
    if(f.empty())
        throw ...;
    fprintf(f, ....);
    ...
    // the file will be closed automatically by the Ptr<FILE> destructor.


**Note**

The reference increment/decrement operations are implemented as atomic operations, and therefore it is normally safe to use the classes in multi-threaded applications. The same is true for
:ref:`Mat` and other C++ OpenCV classes that operate on the reference counters.

.. _Mat:

Mat
---

.. c:type:: Mat

OpenCV C++ n-dimensional dense array class. ::

    class CV_EXPORTS Mat
    {
    public:
        // ... a lot of methods ...
        ...

        /*! includes several bit-fields:
             - the magic signature
             - continuity flag
             - depth
             - number of channels
         */
        int flags;
        //! the array dimensionality, >= 2
        int dims;
        //! the number of rows and columns or (-1, -1) when the array has more than 2 dimensions
        int rows, cols;
        //! pointer to the data
        uchar* data;

        //! pointer to the reference counter;
        // when array points to user-allocated data, the pointer is NULL
        int* refcount;

        // other members
        ...
    };


The class ``Mat`` represents an n-dimensional dense numerical single-channel or multi-channel array. It can be used to store real or complex-valued vectors and matrices, grayscale or color images, voxel volumes, vector fields, point clouds, tensors, histograms (though, very high-dimensional histograms may be better stored in a ``SparseMat`` ). The data layout of array
:math:`M` is defined by the array ``M.step[]`` , so that the address of element
:math:`(i_0,...,i_{M.dims-1})` , where
:math:`0\leq i_k<M.size[k]` is computed as:

.. math::

    addr(M_{i_0,...,i_{M.dims-1}}) = M.data + M.step[0]*i_0 + M.step[1]*i_1 + ... + M.step[M.dims-1]*i_{M.dims-1}

In the case of 2-dimensional array, the above formula is reduced to:

.. math::

    addr(M_{i,j}) = M.data + M.step[0]*i + M.step[1]*j

Note that ``M.step[i] >= M.step[i+1]`` (in fact, ``M.step[i] >= M.step[i+1]*M.size[i+1]`` ), that is, 2-dimensional matrices are stored row-by-row, 3-dimensional matrices are stored plane-by-plane, and so on. ``M.step[M.dims-1]`` is minimal and always equal to the element size ``M.elemSize()`` .

So, the data layout in ``Mat`` is fully compatible with ``CvMat``,``IplImage`` and ``CvMatND`` types from OpenCV 1.x, as well as with the majority of dense array types from the standard toolkits and SDKs, such as Numpy (ndarray), Win32 (independent device bitmaps), and others, that is any other array that uses "steps", a.k.a. "strides", to compute the position of a pixel. Due to this compatibility, it is possible to make a ``Mat`` header for user-allocated data and process it in-place using OpenCV functions.

There are many different ways to create a ``Mat`` object. Here are some popular ones:

*
    
    Use the ``create(nrows, ncols, type)``   method or the similar ``Mat(nrows, ncols, type[, fillValue])``     constructor. A new array of the specified size and specifed type is allocated. ``type``     has the same meaning as in
    :func:`cvCreateMat`     method.
    For example, ``CV_8UC1``     means a 8-bit single-channel array, ``CV_32FC2``     means a 2-channel (complex) floating-point array, and so on:

    ::

        // make a 7x7 complex matrix filled with 1+3j.
        Mat M(7,7,CV_32FC2,Scalar(1,3));
        // and now turn M to a 100x60 15-channel 8-bit matrix.
        // The old content will be deallocated
        M.create(100,60,CV_8UC(15));

    ..

    As noted in the introduction to this chapter, ``create()``      allocates only a new array when the current array shape or type are different from the specified ones.

*
    
    Similarly to above, create a multi-dimensional array:

    ::

        // create a 100x100x100 8-bit array
        int sz[] = {100, 100, 100};
        Mat bigCube(3, sz, CV_8U, Scalar::all(0));

    ..

    Note that it passes the number of dimensions =1 to the ``Mat``     constructor but the created array will be 2-dimensional with the number of columns set to 1. That is why ``Mat::dims``     is always >= 2 (can also be 0 when the array is empty).

*
    
    Use a copy constructor or assignment operator, where on the right side it can be an array or expression (see below). Again, as noted in the introduction, array assignment is O(1) operation because it only copies the header and increases the reference counter. ``Mat::clone()``     method can be used to get a full (a.k.a. deep) copy of the array when you need it.

*
    
    Construct a header for a part of another array. It can be a single row, single column, several rows, several columns, rectangular region in the array (called a minor in algebra) or a diagonal. Such operations are also O(1), because the new header will reference the same data. You can actually modify a part of the array using this feature, for example:

    ::

        // add 5-th row, multiplied by 3 to the 3rd row
        M.row(3) = M.row(3) + M.row(5)*3;

        // now copy 7-th column to the 1-st column
        // M.col(1) = M.col(7); // this will not work
        Mat M1 = M.col(1);
        M.col(7).copyTo(M1);

        // create new 320x240 image
        Mat img(Size(320,240),CV_8UC3);
        // select a roi
        Mat roi(img, Rect(10,10,100,100));
        // fill the ROI with (0,255,0) (which is green in RGB space);
        // the original 320x240 image will be modified
        roi = Scalar(0,255,0);

    ..

    Thanks to the additional ``datastart``     and ``dataend``     members, it is possible to compute a relative sub-array position in the main *"container"* array using ``locateROI()``:

    ::

        Mat A = Mat::eye(10, 10, CV_32S);
        // extracts A columns, 1 (inclusive) to 3 (exclusive).
        Mat B = A(Range::all(), Range(1, 3));
        // extracts B rows, 5 (inclusive) to 9 (exclusive).
        // that is, C ~ A(Range(5, 9), Range(1, 3))
        Mat C = B(Range(5, 9), Range::all());
        Size size; Point ofs;
        C.locateROI(size, ofs);
        // size will be (width=10,height=10) and the ofs will be (x=1, y=5)

    ..

    As in the case of whole matrices, if you need a deep copy, use the ``clone()``     method of the extracted sub-matrices.

*
    
    Make a header for user-allocated data. It can be useful to do the following:

    #.
        Process "foreign" data using OpenCV (for example, when you implement a DirectShow* filter or a processing module for ``gstreamer``, and so on). For example:

        ::

            void process_video_frame(const unsigned char* pixels,
                                     int width, int height, int step)
            {
                Mat img(height, width, CV_8UC3, pixels, step);
                GaussianBlur(img, img, Size(7,7), 1.5, 1.5);
            }

        ..

    #.
        Quickly initialize small matrices and/or get a super-fast element access.

        ::

            double m[3][3] = {{a, b, c}, {d, e, f}, {g, h, i}};
            Mat M = Mat(3, 3, CV_64F, m).inv();

        ..

        Partial yet very common cases of this *user-allocated data* case are conversions from ``CvMat``     and ``IplImage`` to ``Mat``. For this purpose, there are special constructors taking pointers to ``CvMat``     or ``IplImage`` and the optional flag indicating whether to copy the data or not.

        Backward conversion from ``Mat`` to ``CvMat`` or ``IplImage`` is provided via cast operators ``Mat::operator CvMat() const`` and ``Mat::operator IplImage()``. The operators do NOT copy the data.

    ::

        IplImage* img = cvLoadImage("greatwave.jpg", 1);
        Mat mtx(img); // convert IplImage* -> Mat
        CvMat oldmat = mtx; // convert Mat -> CvMat
        CV_Assert(oldmat.cols == img->width && oldmat.rows == img->height &&
            oldmat.data.ptr == (uchar*)img->imageData && oldmat.step == img->widthStep);

    ..

*
    
    Use MATLAB-style array initializers, ``zeros(), ones(), eye()``     , for example:

    ::

        // create a double-precision identity martix and add it to M.
        M += Mat::eye(M.rows, M.cols, CV_64F);

    ..

*
    
    Use a comma-separated initializer:

    ::

        // create a 3x3 double-precision identity matrix
        Mat M = (Mat_<double>(3,3) << 1, 0, 0, 0, 1, 0, 0, 0, 1);

    ..

    Here you first call a constructor of the ``Mat_``     class (that will be described further) with the proper parameters, and then you just put ``<<``     operator followed by comma-separated values that can be constants, variables, expressions, and so on. Also, note the extra parentheses required to avoid compilation errors.

Once the array is created, it is automatically managed via a reference-counting mechanism. If the array header is built on top of user-allocated data, you should handle the data by yourself.
The array data is deallocated when no one points to it. If you want to release the data pointed by a array header before the array destructor is called, use ``Mat::release()`` .

The next important thing to learn about the array class is element access. This manual already described how to compute an address of each array element. Normally, it is not needed to use the formula directly in your code. If you know the array element type (which can be retrieved using the method ``Mat::type()`` ), you can access the element
:math:`M_{ij}` of a 2-dimensional array as: ::

    M.at<double>(i,j) += 1.f;


assuming that M is a double-precision floating-point array. There are several variants of the method ``at`` for a different number of dimensions.

If you need to process a whole row of a 2D array, the most efficient way is to get the pointer to the row first, and then just use plain C operator ``[]`` : ::

    // compute sum of positive matrix elements
    // (assuming that M isa double-precision matrix)
    double sum=0;
    for(int i = 0; i < M.rows; i++)
    {
        const double* Mi = M.ptr<double>(i);
        for(int j = 0; j < M.cols; j++)
            sum += std::max(Mi[j], 0.);
    }


Some operations, like the one above, do not actually depend on the array shape. They just process elements of an array one by one (or elements from multiple arrays that have the same coordinates, for example, array addition). Such operations are called element-wise. It makes sense to check whether all the input/output arrays are continuous, that is, have no gaps in the end of each row. If yes, process them as a single long row: ::

    // compute sum of positive matrix elements, optimized variant
    double sum=0;
    int cols = M.cols, rows = M.rows;
    if(M.isContinuous())
    {
        cols *= rows;
        rows = 1;
    }
    for(int i = 0; i < rows; i++)
    {
        const double* Mi = M.ptr<double>(i);
        for(int j = 0; j < cols; j++)
            sum += std::max(Mi[j], 0.);
    }


In case of the continuous matrix, the outer loop body is executed just once. So, the overhead is smaller, which is especially noticeable in case of small matrices.

Finally, there are STL-style iterators that are smart enough to skip gaps between successive rows: ::

    // compute sum of positive matrix elements, iterator-based variant
    double sum=0;
    MatConstIterator_<double> it = M.begin<double>(), it_end = M.end<double>();
    for(; it != it_end; ++it)
        sum += std::max(*it, 0.);


The matrix iterators are random-access iterators, so they can be passed to any STL algorithm, including ``std::sort()`` .

.. _MatrixExpressions:

Matrix Expressions
------------------

This is a list of implemented matrix operations that can be combined in arbitrary complex expressions
(here
*A*,*B*
stand for matrices ( ``Mat`` ),
*s*
for a scalar ( ``Scalar`` ),
:math:`\alpha` for a real-valued scalar ( ``double`` )):

*
    addition, subtraction, negation:
    :math:`A \pm B,\;A \pm s,\;s \pm A,\;-A` *
    scaling:
    :math:`A*\alpha`,    :math:`A*\alpha` *
    per-element multiplication and division:
    :math:`A.mul(B), A/B, \alpha/A` *
    matrix multiplication:
    :math:`A*B` *
    transposition:
    :math:`A.t() \sim A^t` *
    matrix inversion and pseudo-inversion, solving linear systems and least-squares problems:

    :math:`A.inv([method]) \sim A^{-1}, A.inv([method])*B \sim X:\,AX=B`
    
*
    comparison:
    :math:`A\gtreqqless B,\;A \ne B,\;A \gtreqqless \alpha,\;A \ne \alpha`. The result of comparison is an 8-bit single channel mask whose elements are set to 255 (if the particular element or pair of elements satisfy the condition) or 0.

*
    bitwise logical operations: ``A & B, A & s, A | B, A | s, A textasciicircum B, A textasciicircum s, ~ A`` *
    element-wise minimum and maximum:
    :math:`min(A, B), min(A, \alpha), max(A, B), max(A, \alpha)` *
    element-wise absolute value:
    :math:`abs(A)` *
    cross-product, dot-product:
    :math:`A.cross(B), A.dot(B)` *
    any function of matrix or matrices and scalars that returns a matrix or a scalar, such as

    :func:`norm`,    :func:`mean`,    :func:`sum`,    :func:`countNonZero`,    :func:`trace`,
    :func:`determinant`,    :func:`repeat`  , and others.

*
    matrix initializers ( ``eye(), zeros(), ones()``     ), matrix comma-separated initializers, matrix constructors and operators that extract sub-matrices (see :ref:`Mat`     description).

*
    ``Mat_<destination_type>()`` constructors to cast the result to the proper type.

Note, however, that comma-separated initializers and probably some other operations may require additional explicit ``Mat()`` or ``Mat_<T>()`` constuctor calls to resolve a possible ambiguity.

Below is the formal description of the ``Mat`` methods.

.. index:: Mat::Mat

.. _Mat::Mat:

Mat::Mat
------------
.. c:function:: (1) Mat::Mat()

.. c:function:: (2) Mat::Mat(int rows, int cols, int type)

.. c:function:: (3) Mat::Mat(Size size, int type)

.. c:function:: (4) Mat::Mat(int rows, int cols, int type, const Scalar& s)

.. c:function:: (5) Mat::Mat(Size size, int type, const Scalar& s)

.. c:function:: (6) Mat::Mat(const Mat& m)

.. c:function:: (7) Mat::Mat(int rows, int cols, int type, void* data, size_t step=AUTO_STEP)

.. c:function:: (8) Mat::Mat(Size size, int type, void* data, size_t step=AUTO_STEP)

.. c:function:: (9) Mat::Mat(const Mat& m, const Range& rowRange, const Range& colRange)

.. c:function:: (10) Mat::Mat(const Mat& m, const Rect& roi)

.. c:function:: (11) Mat::Mat(const CvMat* m, bool copyData=false)

.. c:function:: (12) Mat::Mat(const IplImage* img, bool copyData=false)

.. c:function:: (13) template<typename T, int n> explicit Mat::Mat(const Vec<T, n>& vec, bool copyData=true)

.. c:function:: (14) template<typename T, int m, int n> explicit Mat::Mat(const Matx<T, m, n>& vec, bool copyData=true)

.. c:function:: (15) template<typename T> explicit Mat::Mat(const vector<T>& vec, bool copyData=false)

.. c:function:: (16) Mat::Mat(const MatExpr& expr)

.. c:function:: (17) Mat::Mat(int ndims, const int* sizes, int type)

.. c:function:: (18) Mat::Mat(int ndims, const int* sizes, int type, const Scalar& s)

.. c:function:: (19) Mat::Mat(int ndims, const int* sizes, int type, void* data, const size_t* steps=0)

.. c:function:: (20) Mat::Mat(const Mat& m, const Range* ranges)

    Provides various array constructors.

    :param ndims: Array dimensionality.

    :param rows: The number of rows in a 2D array.

    :param cols: The number of columns in a 2D array.

    :param size: 2D array size:  ``Size(cols, rows)`` . Note that in the  ``Size()``  constructor, the number of rows and the number of columns go in the reverse order.

    :param sizes: Array of integers specifying an n-dimensional array shape.

    :param type: Array type. Use  ``CV_8UC1, ..., CV_64FC4``  to create 1-4 channel matrices, or  ``CV_8UC(n), ..., CV_64FC(n)``  to create multi-channel (up to  ``CV_MAX_CN``  channels) matrices.

    :param s: An optional value to initialize each matrix element with. To set all the matrix elements to the particular value after the construction, use the assignment operator  ``Mat::operator=(const Scalar& value)`` .

    :param data: Pointer to the user data. Matrix constructors that take  ``data``  and  ``step``  parameters do not allocate matrix data. Instead, they just initialize the matrix header that points to the specified data, which means that no data is copied. This operation is very efficient and can be used to process external data using OpenCV functions. The external data is not automatically deallocated, so you should take care of it.

    :param step: The number of bytes each matrix row occupies. The value should include the padding bytes in the end of each row, if any. If the parameter is missing (set to  ``AUTO_STEP`` ), no padding is assumed and the actual step is calculated as  ``cols*elemSize()`` . See  :ref:`Mat::elemSize` ().

    :param steps: The array of  ``ndims-1``  steps in case of a multi-dimensional array (the last step is always set to the element size). If not specified, the matrix is assumed to be continuous.

    :param m: The array that (in whole or partly) is assigned to the constructed matrix. No data is copied by these constructors. Instead, the header pointing to  ``m``  data, or its sub-array, is constructed and associated with it. The reference counter, if any, is incremented. That is, when you modify the matrix formed using such a constructor, you also modify the corresponding elements of  ``m`` . If you want to have an independent copy of the sub-array, use  ``Mat::clone()`` .

    :param img: Pointer to the old-style  ``IplImage``  image structure. By default, the data is shared between the original image and the new matrix. But when  ``copyData``  is set, the full copy of the image data is created.

    :param vec: STL vector whose elements form the matrix. The matrix has a single column and the number of rows equal to the number of vector elements. Type of the matrix matches the type of vector elements. The constructor can handle arbitrary types, for which there is a properly declared  :ref:`DataType` . This means that the vector elements must be primitive numbers or uni-type numerical tuples of numbers. Mixed-type structures are not supported. Beware that the corresponding constructor is explicit. Meaning that STL vectors are not automatically converted to  ``Mat``  instances, you should write  ``Mat(vec)``  explicitly. Note that unless you copied the data into the matrix ( ``copyData=true`` ), no new elements should be added to the vector because it can potentially yield vector data reallocation, and, thus, the matrix data pointer will become invalid.

    :param copyData: Flag to specify whether the underlying data of the STL vector, or the old-style  ``CvMat``  or  ``IplImage``,  should be copied to (``true``) or shared with (``false``) the newly constructed matrix. When the data is copied, the allocated buffer will be managed using  ``Mat`` 's reference counting mechanism. While the data is shared, the reference counter is NULL, and you should not deallocate the data until the matrix is not destructed.

    :param rowRange: The range of the  ``m`` 's rows to take. As usual, the range start is inclusive and the range end is exclusive. Use  ``Range::all()``  to take all the rows.

    :param colRange: The range of the  ``m`` 's columns to take. Use  ``Range::all()``  to take all the columns.

    :param ranges: The array of selected ranges of  ``m``  along each dimensionality.

    :param expr: Matrix expression. See  :ref:`MatrixExpressions`.

These are various constructors that form a matrix. As noticed in the :ref:`AutomaticAllocation`,
often the default constructor is enough, and the proper matrix will be allocated by an OpenCV function. The constructed matrix can further be assigned to another matrix or matrix expression, in which case the old content is de-referenced, or be allocated with
:ref:`Mat::create` .

.. index:: Mat::Mat

Mat::~Mat
------------
.. cpp:function:: Mat::~Mat()

    Provides a matrix destructor.

The matrix destructor calls
:ref:`Mat::release` .

.. index:: Mat::operator =

Mat::operator =
-------------------
.. cpp:function:: Mat& Mat::operator = (const Mat& m)

.. cpp:function:: Mat& Mat::operator = (const MatExpr_Base& expr)

.. cpp:function:: Mat& operator = (const Scalar& s)

    Provides matrix assignment operators.

    :param m: The assigned, right-hand-side matrix. Matrix assignment is O(1) operation, that is, no data is copied. Instead, the data is shared and the reference counter, if any, is incremented. Before assigning new data, the old data is de-referenced via  :ref:`Mat::release` .

    :param expr: The assigned matrix expression object. As opposite to the first form of assignment operation, the second form can reuse already allocated matrix if it has the right size and type to fit the matrix expression result. It is automatically handled by the real function that the matrix expressions is expanded to. For example,  ``C=A+B``  is expanded to  ``add(A, B, C)`` , and  :func:`add`  takes care of automatic  ``C``  reallocation.

    :param s: The scalar assigned to each matrix element. The matrix size or type is not changed.

These are available assignment operators. Since they all are very different, make sure to read the operator parameters description.

.. index:: Mat::operator MatExpr

Mat::operator MatExpr
-------------------------
.. cpp:function:: Mat::operator MatExpr_<Mat, Mat>() const

    Provides a ``Mat`` -to- ``MatExpr`` cast operator.

The cast operator should not be called explicitly. It is used internally by the
:ref:`MatrixExpressions` engine.

.. index:: Mat::row

.. _Mat::row:

Mat::row
------------
.. cpp:function:: Mat Mat::row(int i) const

    Creates a matrix header for the specified matrix row.

    :param i: A 0-based row index.

The method makes a new header for the specified matrix row and returns it. This is an O(1) operation, regardless of the matrix size. The underlying data of the new matrix is shared with the original matrix. Here is the example of one of the classical basic matrix processing operations, ``axpy``, used by LU and many other algorithms: ::

    inline void matrix_axpy(Mat& A, int i, int j, double alpha)
    {
        A.row(i) += A.row(j)*alpha;
    }


**Warning**

In the current implementation the following code does not work as expected: ::

    Mat A;
    ...
    A.row(i) = A.row(j); // will not work


This is because ``A.row(i)`` forms a temporary header, which is further assigned to another header. Remember that each of these operations is O(1), that is, no data is copied. Thus, the above assignment will have absolutely no effect, while you may have expected the j-th row to be copied to the i-th row. To achieve that, you should either turn this simple assignment into an expression, or use
:ref:`Mat::copyTo` method: ::

    Mat A;
    ...
    // works, but looks a bit obscure.
    A.row(i) = A.row(j) + 0;

    // this is a bit longe, but the recommended method.
    Mat Ai = A.row(i); M.row(j).copyTo(Ai);


.. index:: Mat::col

.. _Mat::col:

Mat::col
------------
.. cpp:function:: Mat Mat::col(int j) const

    Creates a matrix header for the specified matrix column.

    :param j: A 0-based column index.

The method makes a new header for the specified matrix column and returns it. This is an O(1) operation, regardless of the matrix size. The underlying data of the new matrix is shared with the original matrix. See also the
:ref:`Mat::row` description.

.. index:: Mat::rowRange

.. _Mat::rowRange:

Mat::rowRange
-----------------
.. cpp:function:: Mat Mat::rowRange(int startrow, int endrow) const

.. cpp:function:: Mat Mat::rowRange(const Range& r) const

    Creates a matrix header for the specified row span.

    :param startrow: A 0-based start index of the row span.

    :param endrow: A 0-based ending index of the row span.

    :param r: The  :func:`Range`  structure containing both the start and the end indices.

The method makes a new header for the specified row span of the matrix. Similarly to
:func:`Mat::row` and
:func:`Mat::col` , this is an O(1) operation.

.. index:: Mat::colRange

.. _Mat::colRange:

Mat::colRange
-----------------
.. cpp:function:: Mat Mat::colRange(int startcol, int endcol) const

.. cpp:function:: Mat Mat::colRange(const Range& r) const

    Creates a matrix header for the specified row span.

    :param startcol: A 0-based start index of the column span.

    :param endcol: A 0-based ending index of the column span.

    :param r: The  :func:`Range`  structure containing both the start and the end indices.

The method makes a new header for the specified column span of the matrix. Similarly to
:func:`Mat::row` and
:func:`Mat::col` , this is an O(1) operation.

.. index:: Mat::diag

.. _Mat::diag:

Mat::diag
-------------
.. cpp:function:: Mat Mat::diag(int d) const

.. cpp:function:: static Mat Mat::diag(const Mat& matD)

    Extracts a diagonal from a matrix, or creates a diagonal matrix.

    :param d: Index of the diagonal, with the following values:

        * **d=0** the main diagonal

        * **d>0** a diagonal from the lower half. For example,  ``d=1``  means the diagonal is set immediately below the main one.

        * **d<0** a diagonal from the upper half. For example,  ``d=1``  means the diagonal is set immediately above the main one.

    :param matD: A single-column matrix that forms the diagonal matrix.

The method makes a new header for the specified matrix diagonal. The new matrix is represented as a single-column matrix. Similarly to
:func:`Mat::row` and
:func:`Mat::col` , this is an O(1) operation.

.. index:: Mat::clone

.. _Mat::clone:

Mat::clone
--------------
.. cpp:function:: Mat Mat::clone() const

    Creates a full copy of the array and the underlying data.

The method creates a full copy of the array. The original ``step[]`` are not taken into account. That is, the array copy is a continuous array occupying ``total()*elemSize()`` bytes.

.. index:: Mat::copyTo

.. _Mat::copyTo:

Mat::copyTo
---------------
.. cpp:function:: void Mat::copyTo( Mat& m ) const
.. cpp:function:: void Mat::copyTo( Mat& m, const Mat& mask ) const

    Copies the matrix to another one.

    :param m: The destination matrix. If it does not have a proper size or type before the operation, it is reallocated.

    :param mask: The operation mask. Its non-zero elements indicate which matrix elements need to be copied.

The method copies the matrix data to another matrix. Before copying the data, the method invokes ::

    m.create(this->size(), this->type);


so that the destination matrix is reallocated if needed. While ``m.copyTo(m);`` works flawlessly, the function does not handle the case of a partial overlap between the source and the destination matrices.

When the operation mask is specified, and the ``Mat::create`` call shown above reallocated the matrix, the newly allocated matrix is initialized with all 0's before copying the data.

.. index:: Mat::convertTo

.. _Mat::convertTo:

Mat::convertTo
------------------
.. cpp:function:: void Mat::convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const

    Converts an array to another datatype with optional scaling.

    :param m: The destination matrix. If it does not have a proper size or type before the operation, it is reallocated.

    :param rtype: The desired destination matrix type, or rather, the depth (since the number of channels are the same as the source has). If  ``rtype``  is negative, the destination matrix will have the same type as the source.

    :param alpha: The optional scale factor.

    :param beta: The optional delta added to the scaled values.

The method converts source pixel values to the target datatype. ``saturate_cast<>`` is applied at the end to avoid possible overflows:

.. math::

    m(x,y) = saturate \_ cast<rType>( \alpha (*this)(x,y) +  \beta )

.. index:: Mat::assignTo

Mat::assignTo
-----------------
.. cpp:function:: void Mat::assignTo( Mat& m, int type=-1 ) const

    Provides a functional form of ``convertTo``.

    :param m: The destination array.

    :param type: The desired destination array depth (or -1 if it should be the same as the source type).

This is an internally used method called by the
:ref:`MatrixExpressions` engine.

.. index:: Mat::setTo

Mat::setTo
--------------
.. c:function:: Mat& Mat::setTo(const Scalar& s, const Mat& mask=Mat())

    Sets all or some of the array elements to the specified value.

    :param s: Assigned scalar converted to the actual array type.

    :param mask: Operation mask of the same size as  ``*this``. This is an advanced variant of the ``Mat::operator=(const Scalar& s)`` operator.

.. index:: Mat::reshape

Mat::reshape
----------------
.. cpp:function:: Mat Mat::reshape(int cn, int rows=0) const

    Changes the 2D matrix's shape and/or the number of channels without copying the data.

    :param cn: The new number of channels. If the parameter is 0, the number of channels remains the same.

    :param rows: The new number of rows. If the parameter is 0, the number of rows remains the same.

The method makes a new matrix header for ``*this`` elements. The new matrix may have different size and/or different number of channels. Any combination is possible, as long as:

*
    No extra elements is included into the new matrix and no elements are excluded. Consequently, the product ``rows*cols*channels()``     must stay the same after the transformation.

*
    No data is copied. That is, this is an O(1) operation. Consequently, if you change the number of rows, or the operation changes the indices of elements' row  in some other way, the matrix must be continuous. See
    :func:`Mat::isContinuous`     .

For example, if there is a set of 3D points stored as an STL vector, and you want to represent the points as a ``3xN`` matrix, do the following: ::

    std::vector<Point3f> vec;
    ...

    Mat pointMat = Mat(vec). // convert vector to Mat, O(1) operation
                      reshape(1). // make Nx3 1-channel matrix out of Nx1 3-channel.
                                  // Also, an O(1) operation
                         t(); // finally, transpose the Nx3 matrix.
                              // This involves copying all the elements


.. index:: Mat::t

Mat::t
----------
.. cpp:function:: MatExpr Mat::t() const

    Transposes a matrix.

The method performs matrix transposition by means of matrix expressions. It does not perform the actual transposition but returns a temporary "matrix transposition" object that can be further used as a part of more complex matrix expressions or be assigned to a matrix: ::

    Mat A1 = A + Mat::eye(A.size(), A.type)*lambda;
    Mat C = A1.t()*A1; // compute (A + lambda*I)^t * (A + lamda*I)


.. index:: Mat::inv

Mat::inv
------------
.. cpp:function:: MatExpr Mat::inv(int method=DECOMP_LU) const

    Inverses a matrix.

    :param method: The matrix inversion method. Possible values are the following:

        * **DECOMP_LU** LU decomposition. The matrix must be non-singular.

        * **DECOMP_CHOLESKY** Cholesky  :math:`LL^T`  decomposition, for symmetrical positively defined matrices only. This type is about twice faster than LU on big matrices.

        * **DECOMP_SVD** SVD decomposition.  If the matrix is singular or even non-square, the pseudo inversion is computed.

The method performs matrix inversion by means of matrix expressions. This means that a temporary "matrix inversion" object is returned by the method and can further be used as a part of more complex matrix expression or be assigned to a matrix.

.. index:: Mat::mul

Mat::mul
------------
.. cpp:function:: MatExpr Mat::mul(const Mat& m, double scale=1) const

.. cpp:function:: MatExpr Mat::mul(const MatExpr& m, double scale=1) const

    Performs an element-wise multiplication or division of the two matrices.

    :param m: Another matrix of the same type and the same size as  ``*this`` , or a matrix expression.

    :param scale: Optional scale factor.

The method returns a temporary object encoding per-element array multiplication, with optional scale. Note that this is not a matrix multiplication that corresponds to a simpler "*" operator.

Here is an example: ::

    Mat C = A.mul(5/B); // equivalent to divide(A, B, C, 5)


.. index:: Mat::cross

Mat::cross
--------------
.. cpp:function:: Mat Mat::cross(const Mat& m) const

    Computes a cross-product of two 3-element vectors.

    :param m: Another cross-product operand.

The method computes a cross-product of two 3-element vectors. The vectors must be 3-elements floating-point vectors of the same shape and the same size. The result is another 3-element vector of the same shape and the same type as operands.

.. index:: Mat::dot

Mat::dot
------------
.. cpp:function:: double Mat::dot(const Mat& m) const

    Computes a dot-product of two vectors.

    :param m: Another dot-product operand.

The method computes a dot-product of two matrices. If the matrices are not single-column or single-row vectors, the top-to-bottom left-to-right scan ordering is used to treat them as 1D vectors. The vectors must have the same size and the same type. If the matrices have more than one channel, the dot products from all the channels are summed together.

.. index:: Mat::zeros

Mat::zeros
--------------
.. cpp:function:: static MatExpr Mat::zeros(int rows, int cols, int type)
.. cpp:function:: static MatExpr Mat::zeros(Size size, int type)
.. cpp:function:: static MatExpr Mat::zeros(int ndims, const int* sizes, int type)

    Returns a zero array of the specified size and type.

    :param ndims: Array dimensionality.

    :param rows: The number of rows.

    :param cols: The number of columns.

    :param size: Alternative matrix size specification:  ``Size(cols, rows)``     
	
	:param sizes: An array of integers specifying the array shape.

    :param type: Created matrix type.

The method returns a Matlab-style zero array initializer. It can be used to quickly form a constant array and use it as a function parameter, as a part of matrix expression, or as a matrix initializer. ::

    Mat A;
    A = Mat::zeros(3, 3, CV_32F);


Note that in the sample above a new matrix will be allocated only if ``A`` is not a 3x3 floating-point matrix. Otherwise, the existing matrix ``A`` will be filled with 0's.

.. index:: Mat::ones

Mat::ones
-------------
.. cpp:function:: static MatExpr Mat::ones(int rows, int cols, int type)
.. cpp:function:: static MatExpr Mat::ones(Size size, int type)
.. cpp:function:: static MatExpr Mat::ones(int ndims, const int* sizes, int type)

    Returns an array of all 1's of the specified size and type.

    :param ndims: Array dimensionality.

    :param rows: The number of rows.

    :param cols: The number of columns.

    :param size: Alternative matrix size specification:  ``Size(cols, rows)``     
	
	:param sizes: An array of integers specifying the array shape.

    :param type: Created matrix type.

The method returns a Matlab-style 1's array initializer, similarly to
:func:`Mat::zeros` . Note that using this method you can initialize an array with an arbitrary value, using the following Matlab idiom: ::

    Mat A = Mat::ones(100, 100, CV_8U)*3; // make 100x100 matrix filled with 3.


The above operation does not form a 100x100 matrix of 1's and then multiply it by 3. Instead, it will just remember the scale factor (3 in this case) and use it when actually invoking the matrix initializer.

.. index:: Mat::eye

Mat::eye
------------
.. cpp:function:: static MatExpr Mat::eye(int rows, int cols, int type)
.. cpp:function:: static MatExpr Mat::eye(Size size, int type)

    Returns an identity matrix of the specified size and type.

    :param rows: The number of rows.

    :param cols: The number of columns.

    :param size: Alternative matrix size specification:  ``Size(cols, rows)`` .     
	
	:param type: Created matrix type.

The method returns a Matlab-style identity matrix initializer, similarly to
:func:`Mat::zeros` . Similarly to ``Mat::ones`` , you can use a scale operation to create a scaled identity matrix efficiently: ::

    // make a 4x4 diagonal matrix with 0.1's on the diagonal.
    Mat A = Mat::eye(4, 4, CV_32F)*0.1;


.. index:: Mat::create

.. _Mat::create:

Mat::create
---------------
.. cpp:function:: void Mat::create(int rows, int cols, int type)
.. cpp:function:: void Mat::create(Size size, int type)
.. cpp:function:: void Mat::create(int ndims, const int* sizes, int type)

    Allocates new array data if needed.

    :param ndims: New array dimensionality.

    :param rows: New number of rows.

    :param cols: New number of columns.

    :param size: Alternative new matrix size specification:  ``Size(cols, rows)``     
	
	:param sizes: An array of integers specifying the new array shape.

    :param type: New matrix type.

This is one of the key ``Mat`` methods. Most new-style OpenCV functions and methods that produce arrays call this method for each output array. The method uses the following algorithm:

#.
    If the current array shape and the type match the new ones, return immediately.

#.
    Otherwise, de-reference the previous data by calling
    :func:`Mat::release` #.
    initialize the new header

#.
    Allocate the new data of ``total()*elemSize()``     bytes.

#.
    Allocate the new, associated with the data, reference counter and set it to 1.

Such a scheme makes the memory management robust and efficient at the same time and helps avoid extra typing for you. This means that usually there is no need to explicitly allocate output arrays. That is, instead of writing: ::

    Mat color;
    ...
    Mat gray(color.rows, color.cols, color.depth());
    cvtColor(color, gray, CV_BGR2GRAY);


you can simply write: ::

    Mat color;
    ...
    Mat gray;
    cvtColor(color, gray, CV_BGR2GRAY);


because ``cvtColor`` , as well as the most of OpenCV functions, calls ``Mat::create()`` for the output array internally.

.. index:: Mat::addref

.. _Mat::addref:

Mat::addref
---------------
.. cpp:function:: void Mat::addref()

    Increments the reference counter.

The method increments the reference counter associated with the matrix data. If the matrix header points to an external data set (see
:func:`Mat::Mat` ), the reference counter is NULL, and the method has no effect in this case. Normally, to avoid memory leaks, the method should not be called explicitly. It is called implicitly by the matrix assignment operator. The reference counter increment is an atomic operation on the platforms that support it. Thus, it is safe to operate on the same matrices asynchronously in different threads.

.. index:: Mat::release

.. _Mat::release:

Mat::release
----------------
.. cpp:function:: void Mat::release()

    Decrements the reference counter and deallocates the matrix if needed.

The method decrements the reference counter associated with the matrix data. When the reference counter reaches 0, the matrix data is deallocated and the data and the reference counter pointers are set to NULL's. If the matrix header points to an external data set (see
:func:`Mat::Mat` ), the reference counter is NULL, and the method has no effect in this case.

This method can be called manually to force the matrix data deallocation. But since this method is automatically called in the destructor, or by any other method that changes the data pointer, it is usually not needed. The reference counter decrement and check for 0 is an atomic operation on the platforms that support it. Thus, it is safe to operate on the same matrices asynchronously in different threads.

.. index:: Mat::resize

.. _Mat::resize:

Mat::resize
---------------
.. cpp:function:: void Mat::resize( size_t sz ) const

    Changes the number of matrix rows.

    :param sz: The new number of rows.

The method changes the number of matrix rows. If the matrix is reallocated, the first ``min(Mat::rows, sz)`` rows are preserved. The method emulates the corresponding method of the STL vector class.

.. index:: Mat::push_back

.. _Mat::push_back:

Mat::push_back
--------------
.. c:function:: template<typename T> void Mat::push_back(const T& elem)
.. c:function:: template<typename T> void Mat::push_back(const Mat_<T>& elem)

    Adds elements to the bottom of the matrix.

    :param elem: Added element(s).

The methods add one or more elements to the bottom of the matrix. They emulate the corresponding method of the STL vector class. When ``elem`` is ``Mat`` , its type and the number of columns must be the same as in the container matrix.

.. index:: Mat::pop_back

.. _Mat::pop_back:

Mat::pop_back
-------------
.. c:function:: template<typename T> void Mat::pop_back(size_t nelems=1)

    Removes elements from the bottom of the matrix.

    :param nelems: The number of removed rows. If it is greater than the total number of rows, an exception is thrown.

The method removes one or more rows from the bottom of the matrix.

.. index:: Mat::locateROI

.. _Mat::locateROI:

Mat::locateROI
------------------
.. cpp:function:: void Mat::locateROI( Size& wholeSize, Point& ofs ) const

    Locates the matrix header within a parent matrix.

    :param wholeSize: An output parameter that contains the size of the whole matrix, which contains ``*this`` is a part.

    :param ofs: An output parameter that contains an offset of  ``*this``  inside the whole matrix.

After you extracted a submatrix from a matrix using
:func:`Mat::row`,:func:`Mat::col`,:func:`Mat::rowRange`,:func:`Mat::colRange` , and others, the resultant submatrix will point just to the part of the original big matrix. However, each submatrix contains some information (represented by ``datastart`` and ``dataend`` fields) that helps reconstruct the original matrix size and the position of the extracted submatrix within the original matrix. The method ``locateROI`` does exactly that.

.. index:: Mat::adjustROI

.. _Mat::adjustROI:

Mat::adjustROI
------------------
.. cpp:function:: Mat& Mat::adjustROI( int dtop, int dbottom, int dleft, int dright )

    Adjusts a submatrix size and position within the parent matrix.

    :param dtop: The shift of the top submatrix boundary upwards.

    :param dbottom: The shift of the bottom submatrix boundary downwards.

    :param dleft: The shift of the left submatrix boundary to the left.

    :param dright: The shift of the right submatrix boundary to the right.

The method is complimentary to 
:func:`Mat::locateROI` . Indeed, the typical use of these functions is to determine the submatrix position within the parent matrix and then shift the position somehow. Typically, it can be required for filtering operations when pixels outside of the ROI should be taken into account. When all the method parameters are positive, the ROI needs to grow in all directions by the specified amount, for example: ::

    A.adjustROI(2, 2, 2, 2);


In this example, the matrix size is increased by 4 elements in each direction. The matrix is shifted by 2 elements to the left and 2 elements up, which brings in all the necessary pixels for the filtering with 5x5 kernel.

It is your responsibility to make sure ``adjustROI`` does not cross the parent matrix boundary. If it does, the function signals an error.

The function is used internally by the OpenCV filtering functions, like
:func:`filter2D` , morphological operations, and so on.

See Also
:func:`copyMakeBorder` 

.. index:: Mat::operator()

.. _Mat::operator ():

Mat::operator()
-------------------
.. cpp:function:: Mat Mat::operator()( Range rowRange, Range colRange ) const

.. cpp:function:: Mat Mat::operator()( const Rect& roi ) const

.. cpp:function:: Mat Mat::operator()( const Ranges* ranges ) const

    Extracts a rectangular submatrix.

    :param rowRange: The start and the end row of the extracted submatrix. The upper boundary is not included. To select all the rows, use `Range::all()``.    
	
	:param colRange: The start and the end column of the extracted submatrix. The upper boundary is not included. To select all the columns, use  ``Range::all()`` .    
	
	:param roi: The extracted submatrix specified as a rectangle.

    :param ranges: The array of selected ranges along each array dimension.

The operators make a new header for the specified sub-array of ``*this`` . They are the most generalized forms of
:func:`Mat::row`,:func:`Mat::col`,:func:`Mat::rowRange`, and
:func:`Mat::colRange` . For example, ``A(Range(0, 10), Range::all())`` is equivalent to ``A.rowRange(0, 10)`` . Similarly to all of the above, the operators are O(1) operations, that is, no matrix data is copied.

.. index:: Mat::operator CvMat

Mat::operator CvMat
-----------------------
.. cpp:function:: Mat::operator CvMat(void) const

    Creates the ``CvMat`` header for the matrix.

The operator creates the ``CvMat`` header for the matrix without copying the underlying data. The reference counter is not taken into account by this operation. Thus, you should make sure than the original matrix is not deallocated while the ``CvMat`` header is used. The operator is useful for intermixing the new and the old OpenCV API's, for example: ::

    Mat img(Size(320, 240), CV_8UC3);
    ...

    CvMat cvimg = img;
    mycvOldFunc( &cvimg, ...);


where ``mycvOldFunc`` is a function written to work with OpenCV 1.x data structures.

.. index:: Mat::operator IplImage

Mat::operator IplImage
--------------------------
.. cpp:function:: Mat::operator IplImage(void) const

    Creates the ``IplImage`` header for the matrix.

The operator creates the ``IplImage`` header for the matrix without copying the underlying data. You should make sure than the original matrix is not deallocated while the ``IplImage`` header is used. Similarly to ``Mat::operator CvMat`` , the operator is useful for intermixing the new and the old OpenCV API's.

.. index:: Mat::total

.. _Mat::total:

Mat::total
--------------
.. cpp:function:: size_t Mat::total(void) const

    Returns the total number of array elements.

The method returns the number of array elements (a number of pixels if the array represents an image).

.. index:: Mat::isContinuous

.. _Mat::isContinuous:

Mat::isContinuous
---------------------
.. cpp:function:: bool Mat::isContinuous(void) const

    Reports whether the matrix is continuous or not.

The method returns ``true`` if the matrix elements are stored continuously - without gaps in the end of each row. Otherwise, it returns ``false``. Obviously, ``1x1`` or ``1xN`` matrices are always continuous. Matrices created with
:func:`Mat::create` are always continuous. But if you extract a part of the matrix using
:func:`Mat::col`,:func:`Mat::diag` , and so on, or constructed a matrix header for externally allocated data, such matrices may no longer have this property.

The continuity flag is stored as a bit in the ``Mat::flags`` field and is computed automatically when you construct a matrix header. Thus, the continuity check is a very fast operation, though it could be, in theory, done as following: ::

    // alternative implementation of Mat::isContinuous()
    bool myCheckMatContinuity(const Mat& m)
    {
        //return (m.flags & Mat::CONTINUOUS_FLAG) != 0;
        return m.rows == 1 || m.step == m.cols*m.elemSize();
    }


The method is used in quite a few of OpenCV functions. The point is that element-wise operations (such as arithmetic and logical operations, math functions, alpha blending, color space transformations, and others) do not depend on the image geometry. Thus, if all the input and output arrays are continuous, the functions can process them as very long single-row vectors. Here is the example of how an alpha-blending function can be implemented. ::

    template<typename T>
    void alphaBlendRGBA(const Mat& src1, const Mat& src2, Mat& dst)
    {
        const float alpha_scale = (float)std::numeric_limits<T>::max(),
                    inv_scale = 1.f/alpha_scale;

        CV_Assert( src1.type() == src2.type() &&
                   src1.type() == CV_MAKETYPE(DataType<T>::depth, 4) &&
                   src1.size() == src2.size());
        Size size = src1.size();
        dst.create(size, src1.type());

        // here is the idiom: check the arrays for continuity and,
        // if this is the case,
        // treat the arrays as 1D vectors
        if( src1.isContinuous() && src2.isContinuous() && dst.isContinuous() )
        {
            size.width *= size.height;
            size.height = 1;
        }
        size.width *= 4;

        for( int i = 0; i < size.height; i++ )
        {
            // when the arrays are continuous,
            // the outer loop is executed only once
            const T* ptr1 = src1.ptr<T>(i);
            const T* ptr2 = src2.ptr<T>(i);
            T* dptr = dst.ptr<T>(i);

            for( int j = 0; j < size.width; j += 4 )
            {
                float alpha = ptr1[j+3]*inv_scale, beta = ptr2[j+3]*inv_scale;
                dptr[j] = saturate_cast<T>(ptr1[j]*alpha + ptr2[j]*beta);
                dptr[j+1] = saturate_cast<T>(ptr1[j+1]*alpha + ptr2[j+1]*beta);
                dptr[j+2] = saturate_cast<T>(ptr1[j+2]*alpha + ptr2[j+2]*beta);
                dptr[j+3] = saturate_cast<T>((1 - (1-alpha)*(1-beta))*alpha_scale);
            }
        }
    }


This trick, while being very simple, can boost performance of a simple element-operation by 10-20 percents, especially if the image is rather small and the operation is quite simple.

Also, note that there is another OpenCV idiom in this function: a call of
:func:`Mat::create` for the destination array instead of checking that it already has the proper size and type. And while the newly allocated arrays are always continuous, we still check the destination array, because
:func:`create` does not always allocate a new matrix.

.. index:: Mat::elemSize

.. _Mat::elemSize:

Mat::elemSize
-----------------
.. cpp:function:: size_t Mat::elemSize(void) const

    Returns  the matrix element size in bytes.

The method returns the matrix element size in bytes. For example, if the matrix type is ``CV_16SC3`` , the method returns ``3*sizeof(short)`` or 6.

.. index:: Mat::elemSize1

.. _Mat::elemSize1:

Mat::elemSize1
------------------
.. cpp:function:: size_t Mat::elemSize1(void) const

    Returns the size of each matrix element channel in bytes.

The method returns the matrix element channel size in bytes, that is, it ignores the number of channels. For example, if the matrix type is ``CV_16SC3`` , the method returns ``sizeof(short)`` or 2.

.. index:: Mat::type

.. _Mat::type:

Mat::type
-------------
.. cpp:function:: int Mat::type(void) const

    Returns a matrix element type.

The method returns a matrix element type. This is an id, compatible with the ``CvMat`` type system, like ``CV_16SC3`` or 16-bit signed 3-channel array, and so on.

.. index:: Mat::depth

.. _Mat::depth:

Mat::depth
--------------
.. cpp:function:: int Mat::depth(void) const

    Returns the matrix element depth.

The method returns the matrix element depth id (the type of each individual channel). For example, for a 16-bit signed 3-channel array, the method returns ``CV_16S`` . A complete list of matrix types:

* ``CV_8U``     - 8-bit unsigned integers ( ``0..255``     )

* ``CV_8S``     - 8-bit signed integers ( ``-128..127``     )

* ``CV_16U``     - 16-bit unsigned integers ( ``0..65535``     )

* ``CV_16S``     - 16-bit signed integers ( ``-32768..32767``     )

* ``CV_32S``     - 32-bit signed integers ( ``-2147483648..2147483647``     )

* ``CV_32F``     - 32-bit floating-point numbers ( ``-FLT_MAX..FLT_MAX, INF, NAN``     )

* ``CV_64F``     - 64-bit floating-point numbers ( ``-DBL_MAX..DBL_MAX, INF, NAN``     )

.. index:: Mat::channels

.. _Mat::channels:

Mat::channels
-----------------
.. cpp:function:: int Mat::channels(void) const

    Returns a matrix element depth.

The method returns the number of matrix channels.

.. index:: Mat::step1

.. _Mat::step1:

Mat::step1
--------------
.. cpp:function:: size_t Mat::step1(void) const

    Returns a normalized step.

The method returns a matrix step divided by
:func:`Mat::elemSize1()` . It can be useful to quickly access an arbitrary matrix element.

.. index:: Mat::size

.. _Mat::size:

Mat::size
-------------
.. cpp:function:: Size Mat::size(void) const

    Returns a matrix size.

The method returns a matrix size: ``Size(cols, rows)`` .

.. index:: Mat::empty

.. _Mat::empty:

Mat::empty
--------------
.. cpp:function:: bool Mat::empty(void) const

    Returns ``true`` if the array has no elemens.

The method returns ``true`` if ``Mat::total()`` is 0 or if ``Mat::data`` is NULL. Because of ``pop_back()`` and ``resize()`` methods ``M.total() == 0`` does not imply that ``M.data == NULL`` .

.. index:: Mat::ptr

.. _Mat::ptr:

Mat::ptr
------------
.. c:function:: uchar* Mat::ptr(int i=0)

.. c:function:: const uchar* Mat::ptr(int i=0) const

.. c:function:: template<typename _Tp> _Tp* Mat::ptr(int i=0)

.. c:function:: template<typename _Tp> const _Tp* Mat::ptr(int i=0) const

    Returns a pointer to the specified matrix row.

    :param i: A 0-based row index.

The methods return ``uchar*`` or typed pointer to the specified matrix row. See the sample in
:func:`Mat::isContinuous` () to know how to use these methods.

.. index:: Mat::at

.. _Mat::at:

Mat::at
-----------
.. c:function:: template<typename T> T& Mat::at(int i) const

.. c:function:: template<typename T> const T& Mat::at(int i) const

.. c:function:: template<typename T> T& Mat::at(int i, int j)

.. c:function:: template<typename T> const T& Mat::at(int i, int j) const

.. c:function:: template<typename T> T& Mat::at(Point pt)

.. c:function:: template<typename T> const T& Mat::at(Point pt) const

.. c:function:: template<typename T> T& Mat::at(int i, int j, int k)

.. c:function:: template<typename T> const T& Mat::at(int i, int j, int k) const

.. c:function:: template<typename T> T& Mat::at(const int* idx)

.. c:function:: template<typename T> const T& Mat::at(const int* idx) const

    Returns a reference to the specified array element.

    :param i, j, k: Indices along the dimensions 0, 1, and 2, respectively.

    :param pt: An element position specified as  ``Point(j,i)`` .    
	
	:param idx: An array of  ``Mat::dims``  indices.

The template methods return a reference to the specified array element. For the sake of higher performance, the index range checks are only performed in the Debug configuration.

Note that the variants with a single index (i) can be used to access elements of single-row or single-column 2-dimensional arrays. That is, if, for example, ``A`` is a ``1 x N`` floating-point matrix and ``B`` is an ``M x 1`` integer matrix, you can simply write ``A.at<float>(k+4)`` and ``B.at<int>(2*i+1)`` instead of ``A.at<float>(0,k+4)`` and ``B.at<int>(2*i+1,0)`` , respectively.

Here is an example of initialization of a Hilbert matrix: ::

    Mat H(100, 100, CV_64F);
    for(int i = 0; i < H.rows; i++)
        for(int j = 0; j < H.cols; j++)
            H.at<double>(i,j)=1./(i+j+1);


.. index:: Mat::begin

.. _Mat::begin:

Mat::begin
--------------
.. c:function:: template<typename _Tp> MatIterator_<_Tp> Mat::begin() template<typename _Tp> MatConstIterator_<_Tp> Mat::begin() const

    Returns the matrix iterator and sets it to the first matrix element..

The methods return the matrix read-only or read-write iterators. The use of matrix iterators is very similar to the use of bi-directional STL iterators. Here is the alpha blending function rewritten using the matrix iterators: ::

    template<typename T>
    void alphaBlendRGBA(const Mat& src1, const Mat& src2, Mat& dst)
    {
        typedef Vec<T, 4> VT;

        const float alpha_scale = (float)std::numeric_limits<T>::max(),
                    inv_scale = 1.f/alpha_scale;

        CV_Assert( src1.type() == src2.type() &&
                   src1.type() == DataType<VT>::type &&
                   src1.size() == src2.size());
        Size size = src1.size();
        dst.create(size, src1.type());

        MatConstIterator_<VT> it1 = src1.begin<VT>(), it1_end = src1.end<VT>();
        MatConstIterator_<VT> it2 = src2.begin<VT>();
        MatIterator_<VT> dst_it = dst.begin<VT>();

        for( ; it1 != it1_end; ++it1, ++it2, ++dst_it )
        {
            VT pix1 = *it1, pix2 = *it2;
            float alpha = pix1[3]*inv_scale, beta = pix2[3]*inv_scale;
            *dst_it = VT(saturate_cast<T>(pix1[0]*alpha + pix2[0]*beta),
                         saturate_cast<T>(pix1[1]*alpha + pix2[1]*beta),
                         saturate_cast<T>(pix1[2]*alpha + pix2[2]*beta),
                         saturate_cast<T>((1 - (1-alpha)*(1-beta))*alpha_scale));
        }
    }


.. index:: Mat::end

.. _Mat::end:

Mat::end
------------
.. c:function:: template<typename _Tp> MatIterator_<_Tp> Mat::end() template<typename _Tp> MatConstIterator_<_Tp> Mat::end() const

    Returns the matrix iterator and sets it to the after-last matrix element.

The methods return the matrix read-only or read-write iterators, set to the point following the last matrix element.

Mat\_
-----

Template matrix class derived from
:ref:`Mat` ::

    template<typename _Tp> class Mat_ : public Mat
    {
    public:
        // ... some specific methods
        //         and
        // no new extra fields
    };


The class ``Mat_<_Tp>`` is a "thin" template wrapper on top of the ``Mat`` class. It does not have any extra data fields. Nor this class nor ``Mat`` has any virtual methods. Thus, references or pointers to these two classes can be freely but carefully converted one to another. For example: ::

    // create a 100x100 8-bit matrix
    Mat M(100,100,CV_8U);
    // this will be compiled fine. no any data conversion will be done.
    Mat_<float>& M1 = (Mat_<float>&)M;
    // the program is likely to crash at the statement below
    M1(99,99) = 1.f;


While ``Mat`` is sufficient in most cases, ``Mat_`` can be more convenient if you use a lot of element access operations and if you know matrix type at the compilation time. Note that ``Mat::at<_Tp>(int y, int x)`` and ``Mat_<_Tp>::operator ()(int y, int x)`` do absolutely the same and run at the same speed, but the latter is certainly shorter: ::

    Mat_<double> M(20,20);
    for(int i = 0; i < M.rows; i++)
        for(int j = 0; j < M.cols; j++)
            M(i,j) = 1./(i+j+1);
    Mat E, V;
    eigen(M,E,V);
    cout << E.at<double>(0,0)/E.at<double>(M.rows-1,0);


To use ``Mat_`` for multi-channel images/matrices, pass ``Vec`` as a ``Mat_`` parameter: ::

    // allocate a 320x240 color image and fill it with green (in RGB space)
    Mat_<Vec3b> img(240, 320, Vec3b(0,255,0));
    // now draw a diagonal white line
    for(int i = 0; i < 100; i++)
        img(i,i)=Vec3b(255,255,255);
    // and now scramble the 2nd (red) channel of each pixel
    for(int i = 0; i < img.rows; i++)
        for(int j = 0; j < img.cols; j++)
            img(i,j)[2] ^= (uchar)(i ^ j);


.. _NAryMatIterator:

NAryMatIterator
---------------

n-ary multi-dimensional array iterator ::

    class CV_EXPORTS NAryMatIterator
    {
    public:
        //! the default constructor
        NAryMatIterator();
        //! the full constructor taking arbitrary number of n-dim matrices
        NAryMatIterator(const Mat** arrays, Mat* planes, int narrays=-1);
        //! the separate iterator initialization method
        void init(const Mat** arrays, Mat* planes, int narrays=-1);

        //! proceeds to the next plane of every iterated matrix
        NAryMatIterator& operator ++();
        //! proceeds to the next plane of every iterated matrix (postfix increment operator)
        NAryMatIterator operator ++(int);

        ...
        int nplanes; // the total number of planes
    };


The class is used for implementation of unary, binary, and, generally, n-ary element-wise operations on multi-dimensional arrays. Some of the arguments of  n-ary function may be continuous arrays, some may be not. It is possible to use conventional
``MatIterator`` 's for each array but it can be a big overhead to increment all of the iterators after each small operations. In this case consider using ``NAryMatIterator`` . Using it, you can iterate though several matrices simultaneously as long as they have the same geometry (dimensionality and all the dimension sizes are the same). On each iteration ``it.planes[0]``,``it.planes[1]`` , ... will be the slices of the corresponding matrices.

Here is an example of how you can compute a normalized and thresholded 3D color histogram: ::

    void computeNormalizedColorHist(const Mat& image, Mat& hist, int N, double minProb)
    {
        const int histSize[] = {N, N, N};

        // make sure that the histogram has a proper size and type
        hist.create(3, histSize, CV_32F);

        // and clear it
        hist = Scalar(0);

        // the loop below assumes that the image
        // is a 8-bit 3-channel. check it.
        CV_Assert(image.type() == CV_8UC3);
        MatConstIterator_<Vec3b> it = image.begin<Vec3b>(),
                                 it_end = image.end<Vec3b>();
        for( ; it != it_end; ++it )
        {
            const Vec3b& pix = *it;
            hist.at<float>(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f;
        }

        minProb *= image.rows*image.cols;
        Mat plane;
        NAryMatIterator it(&hist, &plane, 1);
        double s = 0;
        // iterate through the matrix. on each iteration
        // it.planes[*] (of type Mat) will be set to the current plane.
        for(int p = 0; p < it.nplanes; p++, ++it)
        {
            threshold(it.planes[0], it.planes[0], minProb, 0, THRESH_TOZERO);
            s += sum(it.planes[0])[0];
        }

        s = 1./s;
        it = NAryMatIterator(&hist, &plane, 1);
        for(int p = 0; p < it.nplanes; p++, ++it)
            it.planes[0] *= s;
    }


.. _SparseMat:

SparseMat
---------

Sparse n-dimensional array. ::

    class SparseMat
    {
    public:
        typedef SparseMatIterator iterator;
        typedef SparseMatConstIterator const_iterator;

        // internal structure - sparse matrix header
        struct Hdr
        {
            ...
        };

        // sparse matrix node - element of a hash table
        struct Node
        {
            size_t hashval;
            size_t next;
            int idx[CV_MAX_DIM];
        };

        ////////// constructors and destructor //////////
        // default constructor
        SparseMat();
        // creates matrix of the specified size and type
        SparseMat(int dims, const int* _sizes, int _type);
        // copy constructor
        SparseMat(const SparseMat& m);
        // converts dense array to the sparse form,
        // if try1d is true and matrix is a single-column matrix (Nx1),
        // then the sparse matrix will be 1-dimensional.
        SparseMat(const Mat& m, bool try1d=false);
        // converts an old-style sparse matrix to the new style.
        // all the data is copied so that "m" can be safely
        // deleted after the conversion
        SparseMat(const CvSparseMat* m);
        // destructor
        ~SparseMat();

        ///////// assignment operations ///////////

        // this is an O(1) operation; no data is copied
        SparseMat& operator = (const SparseMat& m);
        // (equivalent to the corresponding constructor with try1d=false)
        SparseMat& operator = (const Mat& m);

        // creates a full copy of the matrix
        SparseMat clone() const;

        // copy all the data to the destination matrix.
        // the destination will be reallocated if needed.
        void copyTo( SparseMat& m ) const;
        // converts 1D or 2D sparse matrix to dense 2D matrix.
        // If the sparse matrix is 1D, the result will
        // be a single-column matrix.
        void copyTo( Mat& m ) const;
        // converts arbitrary sparse matrix to dense matrix.
        // multiplies all the matrix elements by the specified scalar
        void convertTo( SparseMat& m, int rtype, double alpha=1 ) const;
        // converts sparse matrix to dense matrix with optional type conversion and scaling.
        // When rtype=-1, the destination element type will be the same
        // as the sparse matrix element type.
        // Otherwise, rtype will specify the depth and
        // the number of channels will remain the same as in the sparse matrix
        void convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const;

        // not used now
        void assignTo( SparseMat& m, int type=-1 ) const;

        // reallocates sparse matrix. If it was already of the proper size and type,
        // it is simply cleared with clear(), otherwise,
        // the old matrix is released (using release()) and the new one is allocated.
        void create(int dims, const int* _sizes, int _type);
        // sets all the matrix elements to 0, which means clearing the hash table.
        void clear();
        // manually increases reference counter to the header.
        void addref();
        // decreses the header reference counter when it reaches 0.
        // the header and all the underlying data are deallocated.
        void release();

        // converts sparse matrix to the old-style representation.
        // all the elements are copied.
        operator CvSparseMat*() const;
        // size of each element in bytes
        // (the matrix nodes will be bigger because of
        //  element indices and other SparseMat::Node elements).
        size_t elemSize() const;
        // elemSize()/channels()
        size_t elemSize1() const;

        // the same is in Mat
        int type() const;
        int depth() const;
        int channels() const;

        // returns the array of sizes and 0 if the matrix is not allocated
        const int* size() const;
        // returns i-th size (or 0)
        int size(int i) const;
        // returns the matrix dimensionality
        int dims() const;
        // returns the number of non-zero elements
        size_t nzcount() const;

        // compute element hash value from the element indices:
        // 1D case
        size_t hash(int i0) const;
        // 2D case
        size_t hash(int i0, int i1) const;
        // 3D case
        size_t hash(int i0, int i1, int i2) const;
        // n-D case
        size_t hash(const int* idx) const;

        // low-level element-access functions,
        // special variants for 1D, 2D, 3D cases, and the generic one for n-D case.
        //
        // return pointer to the matrix element.
        //  if the element is there (it is non-zero), the pointer to it is returned
        //  if it is not there and createMissing=false, NULL pointer is returned
        //  if it is not there and createMissing=true, the new element
        //    is created and initialized with 0. Pointer to it is returned.
        //  If the optional hashval pointer is not NULL, the element hash value is
        //  not computed but *hashval is taken instead.
        uchar* ptr(int i0, bool createMissing, size_t* hashval=0);
        uchar* ptr(int i0, int i1, bool createMissing, size_t* hashval=0);
        uchar* ptr(int i0, int i1, int i2, bool createMissing, size_t* hashval=0);
        uchar* ptr(const int* idx, bool createMissing, size_t* hashval=0);

        // higher-level element access functions:
        // ref<_Tp>(i0,...[,hashval]) - equivalent to *(_Tp*)ptr(i0,...true[,hashval]).
        //    always return valid reference to the element.
        //    If it does not exist, it is created.
        // find<_Tp>(i0,...[,hashval]) - equivalent to (_const Tp*)ptr(i0,...false[,hashval]).
        //    return pointer to the element or NULL pointer if the element is not there.
        // value<_Tp>(i0,...[,hashval]) - equivalent to
        //    { const _Tp* p = find<_Tp>(i0,...[,hashval]); return p ? *p : _Tp(); }
        //    that is, 0 is returned when the element is not there.
        // note that _Tp must match the actual matrix type -
        // the functions do not do any on-fly type conversion

        // 1D case
        template<typename _Tp> _Tp& ref(int i0, size_t* hashval=0);
        template<typename _Tp> _Tp value(int i0, size_t* hashval=0) const;
        template<typename _Tp> const _Tp* find(int i0, size_t* hashval=0) const;

        // 2D case
        template<typename _Tp> _Tp& ref(int i0, int i1, size_t* hashval=0);
        template<typename _Tp> _Tp value(int i0, int i1, size_t* hashval=0) const;
        template<typename _Tp> const _Tp* find(int i0, int i1, size_t* hashval=0) const;

        // 3D case
        template<typename _Tp> _Tp& ref(int i0, int i1, int i2, size_t* hashval=0);
        template<typename _Tp> _Tp value(int i0, int i1, int i2, size_t* hashval=0) const;
        template<typename _Tp> const _Tp* find(int i0, int i1, int i2, size_t* hashval=0) const;

        // n-D case
        template<typename _Tp> _Tp& ref(const int* idx, size_t* hashval=0);
        template<typename _Tp> _Tp value(const int* idx, size_t* hashval=0) const;
        template<typename _Tp> const _Tp* find(const int* idx, size_t* hashval=0) const;

        // erase the specified matrix element.
        // when there is no such an element, the methods do nothing
        void erase(int i0, int i1, size_t* hashval=0);
        void erase(int i0, int i1, int i2, size_t* hashval=0);
        void erase(const int* idx, size_t* hashval=0);

        // return the matrix iterators,
        //   pointing to the first sparse matrix element,
        SparseMatIterator begin();
        SparseMatConstIterator begin() const;
        //   ... or to the point after the last sparse matrix element
        SparseMatIterator end();
        SparseMatConstIterator end() const;

        // and the template forms of the above methods.
        // _Tp must match the actual matrix type.
        template<typename _Tp> SparseMatIterator_<_Tp> begin();
        template<typename _Tp> SparseMatConstIterator_<_Tp> begin() const;
        template<typename _Tp> SparseMatIterator_<_Tp> end();
        template<typename _Tp> SparseMatConstIterator_<_Tp> end() const;

        // return value stored in the sparse martix node
        template<typename _Tp> _Tp& value(Node* n);
        template<typename _Tp> const _Tp& value(const Node* n) const;

        ////////////// some internally used methods ///////////////
        ...

        // pointer to the sparse matrix header
        Hdr* hdr;
    };


The class ``SparseMat`` represents multi-dimensional sparse numerical arrays. Such a sparse array can store elements of any type that
:ref:`Mat` can store. *Sparse* means that only non-zero elements are stored (though, as a result of operations on a sparse matrix, some of its stored elements can actually become 0. It is up to you to detect such elements and delete them using ``SparseMat::erase`` ). The non-zero elements are stored in a hash table that grows when it is filled so that the search time is O(1) in average (regardless of whether element is there or not). Elements can be accessed using the following methods:

*
    Query operations ( ``SparseMat::ptr``     and the higher-level ``SparseMat::ref``,    ``SparseMat::value``     and ``SparseMat::find``     ), for example:

    ::

            const int dims = 5;
            int size[] = {10, 10, 10, 10, 10};
            SparseMat sparse_mat(dims, size, CV_32F);
            for(int i = 0; i < 1000; i++)
            {
                int idx[dims];
                for(int k = 0; k < dims; k++)
                    idx[k] = rand()
                sparse_mat.ref<float>(idx) += 1.f;
            }

    ..

*
    Sparse matrix iterators. They are similar to ``MatIterator`` but different from :ref:`NAryMatIterator`.     That is, the iteration loop is familiar to STL users:

    ::

            // prints elements of a sparse floating-point matrix
            // and the sum of elements.
            SparseMatConstIterator_<float>
                it = sparse_mat.begin<float>(),
                it_end = sparse_mat.end<float>();
            double s = 0;
            int dims = sparse_mat.dims();
            for(; it != it_end; ++it)
            {
                // print element indices and the element value
                const Node* n = it.node();
                printf("(")
                for(int i = 0; i < dims; i++)
                    printf("
                printf(":
                s += *it;
            }
            printf("Element sum is

    ..

    If you run this loop, you will notice that elements are not enumerated in a logical order (lexicographical, and so on). They come in the same order as they are stored in the hash table (semi-randomly). You may collect pointers to the nodes and sort them to get the proper ordering. Note, however, that pointers to the nodes may become invalid when you add more elements to the matrix. This may happen due to possible buffer reallocation.

*
    Combination of the above 2 methods when you need to process 2 or more sparse matrices simultaneously. For example, this is how you can compute unnormalized cross-correlation of the 2 floating-point sparse matrices:

    ::

            double cross_corr(const SparseMat& a, const SparseMat& b)
            {
                const SparseMat *_a = &a, *_b = &b;
                // if b contains less elements than a,
                // it is faster to iterate through b
                if(_a->nzcount() > _b->nzcount())
                    std::swap(_a, _b);
                SparseMatConstIterator_<float> it = _a->begin<float>(),
                                               it_end = _a->end<float>();
                double ccorr = 0;
                for(; it != it_end; ++it)
                {
                    // take the next element from the first matrix
                    float avalue = *it;
                    const Node* anode = it.node();
                    // and try to find an element with the same index in the second matrix.
                    // since the hash value depends only on the element index,
                    // reuse the hash value stored in the node
                    float bvalue = _b->value<float>(anode->idx,&anode->hashval);
                    ccorr += avalue*bvalue;
                }
                return ccorr;
            }

    ..

SparseMat\_
-----------

Template sparse n-dimensional array class derived from
:ref:`SparseMat` ::

    template<typename _Tp> class SparseMat_ : public SparseMat
    {
    public:
        typedef SparseMatIterator_<_Tp> iterator;
        typedef SparseMatConstIterator_<_Tp> const_iterator;

        // constructors;
        // the created matrix will have data type = DataType<_Tp>::type
        SparseMat_();
        SparseMat_(int dims, const int* _sizes);
        SparseMat_(const SparseMat& m);
        SparseMat_(const SparseMat_& m);
        SparseMat_(const Mat& m);
        SparseMat_(const CvSparseMat* m);
        // assignment operators; data type conversion is done when necessary
        SparseMat_& operator = (const SparseMat& m);
        SparseMat_& operator = (const SparseMat_& m);
        SparseMat_& operator = (const Mat& m);

        // equivalent to the correspoding parent class methods
        SparseMat_ clone() const;
        void create(int dims, const int* _sizes);
        operator CvSparseMat*() const;

        // overriden methods that do extra checks for the data type
        int type() const;
        int depth() const;
        int channels() const;

        // more convenient element access operations.
        // ref() is retained (but <_Tp> specification is not needed anymore);
        // operator () is equivalent to SparseMat::value<_Tp>
        _Tp& ref(int i0, size_t* hashval=0);
        _Tp operator()(int i0, size_t* hashval=0) const;
        _Tp& ref(int i0, int i1, size_t* hashval=0);
        _Tp operator()(int i0, int i1, size_t* hashval=0) const;
        _Tp& ref(int i0, int i1, int i2, size_t* hashval=0);
        _Tp operator()(int i0, int i1, int i2, size_t* hashval=0) const;
        _Tp& ref(const int* idx, size_t* hashval=0);
        _Tp operator()(const int* idx, size_t* hashval=0) const;

        // iterators
        SparseMatIterator_<_Tp> begin();
        SparseMatConstIterator_<_Tp> begin() const;
        SparseMatIterator_<_Tp> end();
        SparseMatConstIterator_<_Tp> end() const;
    };
    
``SparseMat_`` is a thin wrapper on top of :ref:`SparseMat`  created in the same way as ``Mat_`` .
It simplifies notation of some operations. ::

    int sz[] = {10, 20, 30};
    SparseMat_<double> M(3, sz);
    ...
    M.ref(1, 2, 3) = M(4, 5, 6) + M(7, 8, 9);