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opencv/modules/video/doc/motion_analysis_and_object_tracking.rst
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Motion Analysis and Object Tracking
===================================
.. highlight:: cpp
calcOpticalFlowPyrLK
------------------------
Calculates an optical flow for a sparse feature set using the iterative Lucas-Kanade method with pyramids.
.. ocv:function:: void calcOpticalFlowPyrLK( InputArray prevImg, InputArray nextImg, InputArray prevPts, InputOutputArray nextPts, OutputArray status, OutputArray err, Size winSize=Size(21,21), int maxLevel=3, TermCriteria criteria=TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 0.01), int flags=0, double minEigThreshold=1e-4 )
.. ocv:pyfunction:: cv2.calcOpticalFlowPyrLK(prevImg, nextImg, prevPts, nextPts[, status[, err[, winSize[, maxLevel[, criteria[, flags[, minEigThreshold]]]]]]]) -> nextPts, status, err
.. ocv:cfunction:: void cvCalcOpticalFlowPyrLK( const CvArr* prev, const CvArr* curr, CvArr* prev_pyr, CvArr* curr_pyr, const CvPoint2D32f* prev_features, CvPoint2D32f* curr_features, int count, CvSize win_size, int level, char* status, float* track_error, CvTermCriteria criteria, int flags )
:param prevImg: first 8-bit input image or pyramid constructed by :ocv:func:`buildOpticalFlowPyramid`.
:param nextImg: second input image or pyramid of the same size and the same type as ``prevImg``.
:param prevPts: vector of 2D points for which the flow needs to be found; point coordinates must be single-precision floating-point numbers.
:param nextPts: output vector of 2D points (with single-precision floating-point coordinates) containing the calculated new positions of input features in the second image; when ``OPTFLOW_USE_INITIAL_FLOW`` flag is passed, the vector must have the same size as in the input.
:param status: output status vector (of unsigned chars); each element of the vector is set to 1 if the flow for the corresponding features has been found, otherwise, it is set to 0.
:param err: output vector of errors; each element of the vector is set to an error for the corresponding feature, type of the error measure can be set in ``flags`` parameter; if the flow wasn't found then the error is not defined (use the ``status`` parameter to find such cases).
:param winSize: size of the search window at each pyramid level.
:param maxLevel: 0-based maximal pyramid level number; if set to 0, pyramids are not used (single level), if set to 1, two levels are used, and so on; if pyramids are passed to input then algorithm will use as many levels as pyramids have but no more than ``maxLevel``.
:param criteria: parameter, specifying the termination criteria of the iterative search algorithm (after the specified maximum number of iterations ``criteria.maxCount`` or when the search window moves by less than ``criteria.epsilon``.
:param flags: operation flags:
* **OPTFLOW_USE_INITIAL_FLOW** uses initial estimations, stored in ``nextPts``; if the flag is not set, then ``prevPts`` is copied to ``nextPts`` and is considered the initial estimate.
* **OPTFLOW_LK_GET_MIN_EIGENVALS** use minimum eigen values as an error measure (see ``minEigThreshold`` description); if the flag is not set, then L1 distance between patches around the original and a moved point, divided by number of pixels in a window, is used as a error measure.
:param minEigThreshold: the algorithm calculates the minimum eigen value of a 2x2 normal matrix of optical flow equations (this matrix is called a spatial gradient matrix in [Bouguet00]_), divided by number of pixels in a window; if this value is less than ``minEigThreshold``, then a corresponding feature is filtered out and its flow is not processed, so it allows to remove bad points and get a performance boost.
The function implements a sparse iterative version of the Lucas-Kanade optical flow in pyramids. See [Bouguet00]_. The function is parallelized with the TBB library.
.. note::
* An example using the Lucas-Kanade optical flow algorithm can be found at opencv_source_code/samples/cpp/lkdemo.cpp
* (Python) An example using the Lucas-Kanade optical flow algorithm can be found at opencv_source_code/samples/python2/lk_track.py
* (Python) An example using the Lucas-Kanade tracker for homography matching can be found at opencv_source_code/samples/python2/lk_homography.py
buildOpticalFlowPyramid
-----------------------
Constructs the image pyramid which can be passed to :ocv:func:`calcOpticalFlowPyrLK`.
.. ocv:function:: int buildOpticalFlowPyramid(InputArray img, OutputArrayOfArrays pyramid, Size winSize, int maxLevel, bool withDerivatives = true, int pyrBorder = BORDER_REFLECT_101, int derivBorder = BORDER_CONSTANT, bool tryReuseInputImage = true)
.. ocv:pyfunction:: cv2.buildOpticalFlowPyramid(img, winSize, maxLevel[, pyramid[, withDerivatives[, pyrBorder[, derivBorder[, tryReuseInputImage]]]]]) -> retval, pyramid
:param img: 8-bit input image.
:param pyramid: output pyramid.
:param winSize: window size of optical flow algorithm. Must be not less than ``winSize`` argument of :ocv:func:`calcOpticalFlowPyrLK`. It is needed to calculate required padding for pyramid levels.
:param maxLevel: 0-based maximal pyramid level number.
:param withDerivatives: set to precompute gradients for the every pyramid level. If pyramid is constructed without the gradients then :ocv:func:`calcOpticalFlowPyrLK` will calculate them internally.
:param pyrBorder: the border mode for pyramid layers.
:param derivBorder: the border mode for gradients.
:param tryReuseInputImage: put ROI of input image into the pyramid if possible. You can pass ``false`` to force data copying.
:return: number of levels in constructed pyramid. Can be less than ``maxLevel``.
calcOpticalFlowFarneback
----------------------------
Computes a dense optical flow using the Gunnar Farneback's algorithm.
.. ocv:function:: void calcOpticalFlowFarneback( InputArray prev, InputArray next, InputOutputArray flow, double pyr_scale, int levels, int winsize, int iterations, int poly_n, double poly_sigma, int flags )
.. ocv:cfunction:: void cvCalcOpticalFlowFarneback( const CvArr* prev, const CvArr* next, CvArr* flow, double pyr_scale, int levels, int winsize, int iterations, int poly_n, double poly_sigma, int flags )
.. ocv:pyfunction:: cv2.calcOpticalFlowFarneback(prev, next, flow, pyr_scale, levels, winsize, iterations, poly_n, poly_sigma, flags) -> flow
:param prev: first 8-bit single-channel input image.
:param next: second input image of the same size and the same type as ``prev``.
:param flow: computed flow image that has the same size as ``prev`` and type ``CV_32FC2``.
:param pyr_scale: parameter, specifying the image scale (<1) to build pyramids for each image; ``pyr_scale=0.5`` means a classical pyramid, where each next layer is twice smaller than the previous one.
:param levels: number of pyramid layers including the initial image; ``levels=1`` means that no extra layers are created and only the original images are used.
:param winsize: averaging window size; larger values increase the algorithm robustness to image noise and give more chances for fast motion detection, but yield more blurred motion field.
:param iterations: number of iterations the algorithm does at each pyramid level.
:param poly_n: size of the pixel neighborhood used to find polynomial expansion in each pixel; larger values mean that the image will be approximated with smoother surfaces, yielding more robust algorithm and more blurred motion field, typically ``poly_n`` =5 or 7.
:param poly_sigma: standard deviation of the Gaussian that is used to smooth derivatives used as a basis for the polynomial expansion; for ``poly_n=5``, you can set ``poly_sigma=1.1``, for ``poly_n=7``, a good value would be ``poly_sigma=1.5``.
:param flags: operation flags that can be a combination of the following:
* **OPTFLOW_USE_INITIAL_FLOW** uses the input ``flow`` as an initial flow approximation.
* **OPTFLOW_FARNEBACK_GAUSSIAN** uses the Gaussian :math:`\texttt{winsize}\times\texttt{winsize}` filter instead of a box filter of the same size for optical flow estimation; usually, this option gives z more accurate flow than with a box filter, at the cost of lower speed; normally, ``winsize`` for a Gaussian window should be set to a larger value to achieve the same level of robustness.
The function finds an optical flow for each ``prev`` pixel using the [Farneback2003]_ algorithm so that
.. math::
\texttt{prev} (y,x) \sim \texttt{next} ( y + \texttt{flow} (y,x)[1], x + \texttt{flow} (y,x)[0])
.. note::
* An example using the optical flow algorithm described by Gunnar Farneback can be found at opencv_source_code/samples/cpp/fback.cpp
* (Python) An example using the optical flow algorithm described by Gunnar Farneback can be found at opencv_source_code/samples/python2/opt_flow.py
estimateRigidTransform
--------------------------
Computes an optimal affine transformation between two 2D point sets.
.. ocv:function:: Mat estimateRigidTransform( InputArray src, InputArray dst, bool fullAffine )
.. ocv:pyfunction:: cv2.estimateRigidTransform(src, dst, fullAffine) -> retval
:param src: First input 2D point set stored in ``std::vector`` or ``Mat``, or an image stored in ``Mat``.
:param dst: Second input 2D point set of the same size and the same type as ``A``, or another image.
:param fullAffine: If true, the function finds an optimal affine transformation with no additional restrictions (6 degrees of freedom). Otherwise, the class of transformations to choose from is limited to combinations of translation, rotation, and uniform scaling (5 degrees of freedom).
The function finds an optimal affine transform *[A|b]* (a ``2 x 3`` floating-point matrix) that approximates best the affine transformation between:
*
Two point sets
*
Two raster images. In this case, the function first finds some features in the ``src`` image and finds the corresponding features in ``dst`` image. After that, the problem is reduced to the first case.
In case of point sets, the problem is formulated as follows: you need to find a 2x2 matrix *A* and 2x1 vector *b* so that:
.. math::
[A^*|b^*] = arg \min _{[A|b]} \sum _i \| \texttt{dst}[i] - A { \texttt{src}[i]}^T - b \| ^2
where ``src[i]`` and ``dst[i]`` are the i-th points in ``src`` and ``dst``, respectively
:math:`[A|b]` can be either arbitrary (when ``fullAffine=true`` ) or have a form of
.. math::
\begin{bmatrix} a_{11} & a_{12} & b_1 \\ -a_{12} & a_{11} & b_2 \end{bmatrix}
when ``fullAffine=false`` .
.. seealso::
:ocv:func:`getAffineTransform`,
:ocv:func:`getPerspectiveTransform`,
:ocv:func:`findHomography`
findTransformECC
------------------------
Finds the geometric transform (warp) between two images in terms of the ECC criterion [EP08]_.
.. ocv:function:: double findTransformECC( InputArray templateImage, InputArray inputImage, InputOutputArray warpMatrix, int motionType=MOTION_AFFINE, TermCriteria criteria=TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 50, 0.001))
.. ocv:pyfunction:: cv2.findTransformECC(templateImage, inputImage, warpMatrix[, motionType[, criteria]]) -> retval, warpMatrix
:param templateImage: single-channel template image; ``CV_8U`` or ``CV_32F`` array.
:param inputImage: single-channel input image which should be warped with the final ``warpMatrix`` in order to provide an image similar to ``templateImage``, same type as ``temlateImage``.
:param warpMatrix: floating-point :math:`2\times 3` or :math:`3\times 3` mapping matrix (warp).
:param motionType: parameter, specifying the type of motion:
* **MOTION_TRANSLATION** sets a translational motion model; ``warpMatrix`` is :math:`2\times 3` with the first :math:`2\times 2` part being the unity matrix and the rest two parameters being estimated.
* **MOTION_EUCLIDEAN** sets a Euclidean (rigid) transformation as motion model; three parameters are estimated; ``warpMatrix`` is :math:`2\times 3`.
* **MOTION_AFFINE** sets an affine motion model (DEFAULT); six parameters are estimated; ``warpMatrix`` is :math:`2\times 3`.
* **MOTION_HOMOGRAPHY** sets a homography as a motion model; eight parameters are estimated;``warpMatrix`` is :math:`3\times 3`.
:param criteria: parameter, specifying the termination criteria of the ECC algorithm; ``criteria.epsilon`` defines the threshold of the increment in the correlation coefficient between two iterations (a negative ``criteria.epsilon`` makes ``criteria.maxcount`` the only termination criterion). Default values are shown in the declaration above.
The function estimates the optimum transformation (``warpMatrix``) with respect to ECC criterion ([EP08]_), that is
.. math::
\texttt{warpMatrix} = \texttt{warpMatrix} = \arg\max_{W} \texttt{ECC}(\texttt{templateImage}(x,y),\texttt{inputImage}(x',y'))
where
.. math::
\begin{bmatrix} x' \\ y' \end{bmatrix} = W \cdot \begin{bmatrix} x \\ y \\ 1 \end{bmatrix}
(the equation holds with homogeneous coordinates for homography). It returns the final enhanced correlation coefficient, that is the correlation coefficient between the template image and the final warped input image. When a :math:`3\times 3` matrix is given with ``motionType`` =0, 1 or 2, the third row is ignored.
Unlike :ocv:func:`findHomography` and :ocv:func:`estimateRigidTransform`, the function :ocv:func:`findTransformECC` implements an area-based alignment that builds on intensity similarities. In essence, the function updates the initial transformation that roughly aligns the images. If this information is missing, the identity warp (unity matrix) should be given as input. Note that if images undergo strong displacements/rotations, an initial transformation that roughly aligns the images is necessary (e.g., a simple euclidean/similarity transform that allows for the images showing the same image content approximately). Use inverse warping in the second image to take an image close to the first one, i.e. use the flag ``WARP_INVERSE_MAP`` with :ocv:func:`warpAffine` or :ocv:func:`warpPerspective`. See also the OpenCV sample ``image_alignment.cpp`` that demonstrates the use of the function. Note that the function throws an exception if algorithm does not converges.
.. seealso::
:ocv:func:`estimateRigidTransform`,
:ocv:func:`findHomography`
updateMotionHistory
-----------------------
Updates the motion history image by a moving silhouette.
.. ocv:function:: void updateMotionHistory( InputArray silhouette, InputOutputArray mhi, double timestamp, double duration )
.. ocv:pyfunction:: cv2.updateMotionHistory(silhouette, mhi, timestamp, duration) -> mhi
.. ocv:cfunction:: void cvUpdateMotionHistory( const CvArr* silhouette, CvArr* mhi, double timestamp, double duration )
:param silhouette: Silhouette mask that has non-zero pixels where the motion occurs.
:param mhi: Motion history image that is updated by the function (single-channel, 32-bit floating-point).
:param timestamp: Current time in milliseconds or other units.
:param duration: Maximal duration of the motion track in the same units as ``timestamp`` .
The function updates the motion history image as follows:
.. math::
\texttt{mhi} (x,y)= \forkthree{\texttt{timestamp}}{if $\texttt{silhouette}(x,y) \ne 0$}{0}{if $\texttt{silhouette}(x,y) = 0$ and $\texttt{mhi} < (\texttt{timestamp} - \texttt{duration})$}{\texttt{mhi}(x,y)}{otherwise}
That is, MHI pixels where the motion occurs are set to the current ``timestamp`` , while the pixels where the motion happened last time a long time ago are cleared.
The function, together with
:ocv:func:`calcMotionGradient` and
:ocv:func:`calcGlobalOrientation` , implements a motion templates technique described in
[Davis97]_ and [Bradski00]_.
See also the OpenCV sample ``motempl.c`` that demonstrates the use of all the motion template functions.
calcMotionGradient
----------------------
Calculates a gradient orientation of a motion history image.
.. ocv:function:: void calcMotionGradient( InputArray mhi, OutputArray mask, OutputArray orientation, double delta1, double delta2, int apertureSize=3 )
.. ocv:pyfunction:: cv2.calcMotionGradient(mhi, delta1, delta2[, mask[, orientation[, apertureSize]]]) -> mask, orientation
.. ocv:cfunction:: void cvCalcMotionGradient( const CvArr* mhi, CvArr* mask, CvArr* orientation, double delta1, double delta2, int aperture_size=3 )
:param mhi: Motion history single-channel floating-point image.
:param mask: Output mask image that has the type ``CV_8UC1`` and the same size as ``mhi`` . Its non-zero elements mark pixels where the motion gradient data is correct.
:param orientation: Output motion gradient orientation image that has the same type and the same size as ``mhi`` . Each pixel of the image is a motion orientation, from 0 to 360 degrees.
:param delta1: Minimal (or maximal) allowed difference between ``mhi`` values within a pixel neighborhood.
:param delta2: Maximal (or minimal) allowed difference between ``mhi`` values within a pixel neighborhood. That is, the function finds the minimum ( :math:`m(x,y)` ) and maximum ( :math:`M(x,y)` ) ``mhi`` values over :math:`3 \times 3` neighborhood of each pixel and marks the motion orientation at :math:`(x, y)` as valid only if
.. math::
\min ( \texttt{delta1} , \texttt{delta2} ) \le M(x,y)-m(x,y) \le \max ( \texttt{delta1} , \texttt{delta2} ).
:param apertureSize: Aperture size of the :ocv:func:`Sobel` operator.
The function calculates a gradient orientation at each pixel
:math:`(x, y)` as:
.. math::
\texttt{orientation} (x,y)= \arctan{\frac{d\texttt{mhi}/dy}{d\texttt{mhi}/dx}}
In fact,
:ocv:func:`fastAtan2` and
:ocv:func:`phase` are used so that the computed angle is measured in degrees and covers the full range 0..360. Also, the ``mask`` is filled to indicate pixels where the computed angle is valid.
.. note::
* (Python) An example on how to perform a motion template technique can be found at opencv_source_code/samples/python2/motempl.py
calcGlobalOrientation
-------------------------
Calculates a global motion orientation in a selected region.
.. ocv:function:: double calcGlobalOrientation( InputArray orientation, InputArray mask, InputArray mhi, double timestamp, double duration )
.. ocv:pyfunction:: cv2.calcGlobalOrientation(orientation, mask, mhi, timestamp, duration) -> retval
.. ocv:cfunction:: double cvCalcGlobalOrientation( const CvArr* orientation, const CvArr* mask, const CvArr* mhi, double timestamp, double duration )
:param orientation: Motion gradient orientation image calculated by the function :ocv:func:`calcMotionGradient` .
:param mask: Mask image. It may be a conjunction of a valid gradient mask, also calculated by :ocv:func:`calcMotionGradient` , and the mask of a region whose direction needs to be calculated.
:param mhi: Motion history image calculated by :ocv:func:`updateMotionHistory` .
:param timestamp: Timestamp passed to :ocv:func:`updateMotionHistory` .
:param duration: Maximum duration of a motion track in milliseconds, passed to :ocv:func:`updateMotionHistory` .
The function calculates an average
motion direction in the selected region and returns the angle between
0 degrees and 360 degrees. The average direction is computed from
the weighted orientation histogram, where a recent motion has a larger
weight and the motion occurred in the past has a smaller weight, as recorded in ``mhi`` .
segmentMotion
-------------
Splits a motion history image into a few parts corresponding to separate independent motions (for example, left hand, right hand).
.. ocv:function:: void segmentMotion(InputArray mhi, OutputArray segmask, vector<Rect>& boundingRects, double timestamp, double segThresh)
.. ocv:pyfunction:: cv2.segmentMotion(mhi, timestamp, segThresh[, segmask]) -> segmask, boundingRects
.. ocv:cfunction:: CvSeq* cvSegmentMotion( const CvArr* mhi, CvArr* seg_mask, CvMemStorage* storage, double timestamp, double seg_thresh )
:param mhi: Motion history image.
:param segmask: Image where the found mask should be stored, single-channel, 32-bit floating-point.
:param boundingRects: Vector containing ROIs of motion connected components.
:param timestamp: Current time in milliseconds or other units.
:param segThresh: Segmentation threshold that is recommended to be equal to the interval between motion history "steps" or greater.
The function finds all of the motion segments and marks them in ``segmask`` with individual values (1,2,...). It also computes a vector with ROIs of motion connected components. After that the motion direction for every component can be calculated with :ocv:func:`calcGlobalOrientation` using the extracted mask of the particular component.
CamShift
--------
Finds an object center, size, and orientation.
.. ocv:function:: RotatedRect CamShift( InputArray probImage, Rect& window, TermCriteria criteria )
.. ocv:pyfunction:: cv2.CamShift(probImage, window, criteria) -> retval, window
.. ocv:cfunction:: int cvCamShift( const CvArr* prob_image, CvRect window, CvTermCriteria criteria, CvConnectedComp* comp, CvBox2D* box=NULL )
:param probImage: Back projection of the object histogram. See :ocv:func:`calcBackProject` .
:param window: Initial search window.
:param criteria: Stop criteria for the underlying :ocv:func:`meanShift` .
:returns: (in old interfaces) Number of iterations CAMSHIFT took to converge
The function implements the CAMSHIFT object tracking algorithm
[Bradski98]_.
First, it finds an object center using
:ocv:func:`meanShift` and then adjusts the window size and finds the optimal rotation. The function returns the rotated rectangle structure that includes the object position, size, and orientation. The next position of the search window can be obtained with ``RotatedRect::boundingRect()`` .
See the OpenCV sample ``camshiftdemo.c`` that tracks colored objects.
.. note::
* (Python) A sample explaining the camshift tracking algorithm can be found at opencv_source_code/samples/python2/camshift.py
meanShift
---------
Finds an object on a back projection image.
.. ocv:function:: int meanShift( InputArray probImage, Rect& window, TermCriteria criteria )
.. ocv:pyfunction:: cv2.meanShift(probImage, window, criteria) -> retval, window
.. ocv:cfunction:: int cvMeanShift( const CvArr* prob_image, CvRect window, CvTermCriteria criteria, CvConnectedComp* comp )
:param probImage: Back projection of the object histogram. See :ocv:func:`calcBackProject` for details.
:param window: Initial search window.
:param criteria: Stop criteria for the iterative search algorithm.
:returns: Number of iterations CAMSHIFT took to converge.
The function implements the iterative object search algorithm. It takes the input back projection of an object and the initial position. The mass center in ``window`` of the back projection image is computed and the search window center shifts to the mass center. The procedure is repeated until the specified number of iterations ``criteria.maxCount`` is done or until the window center shifts by less than ``criteria.epsilon`` . The algorithm is used inside
:ocv:func:`CamShift` and, unlike
:ocv:func:`CamShift` , the search window size or orientation do not change during the search. You can simply pass the output of
:ocv:func:`calcBackProject` to this function. But better results can be obtained if you pre-filter the back projection and remove the noise. For example, you can do this by retrieving connected components with
:ocv:func:`findContours` , throwing away contours with small area (
:ocv:func:`contourArea` ), and rendering the remaining contours with
:ocv:func:`drawContours` .
.. note::
* A mean-shift tracking sample can be found at opencv_source_code/samples/cpp/camshiftdemo.cpp
KalmanFilter
------------
.. ocv:class:: KalmanFilter
Kalman filter class.
The class implements a standard Kalman filter
http://en.wikipedia.org/wiki/Kalman_filter, [Welch95]_. However, you can modify ``transitionMatrix``, ``controlMatrix``, and ``measurementMatrix`` to get an extended Kalman filter functionality. See the OpenCV sample ``kalman.cpp`` .
.. note::
* An example using the standard Kalman filter can be found at opencv_source_code/samples/cpp/kalman.cpp
KalmanFilter::KalmanFilter
--------------------------
The constructors.
.. ocv:function:: KalmanFilter::KalmanFilter()
.. ocv:function:: KalmanFilter::KalmanFilter(int dynamParams, int measureParams, int controlParams=0, int type=CV_32F)
.. ocv:pyfunction:: cv2.KalmanFilter([dynamParams, measureParams[, controlParams[, type]]]) -> <KalmanFilter object>
.. ocv:cfunction:: CvKalman* cvCreateKalman( int dynam_params, int measure_params, int control_params=0 )
The full constructor.
:param dynamParams: Dimensionality of the state.
:param measureParams: Dimensionality of the measurement.
:param controlParams: Dimensionality of the control vector.
:param type: Type of the created matrices that should be ``CV_32F`` or ``CV_64F``.
.. note:: In C API when ``CvKalman* kalmanFilter`` structure is not needed anymore, it should be released with ``cvReleaseKalman(&kalmanFilter)``
KalmanFilter::init
------------------
Re-initializes Kalman filter. The previous content is destroyed.
.. ocv:function:: void KalmanFilter::init(int dynamParams, int measureParams, int controlParams=0, int type=CV_32F)
:param dynamParams: Dimensionalityensionality of the state.
:param measureParams: Dimensionality of the measurement.
:param controlParams: Dimensionality of the control vector.
:param type: Type of the created matrices that should be ``CV_32F`` or ``CV_64F``.
KalmanFilter::predict
---------------------
Computes a predicted state.
.. ocv:function:: const Mat& KalmanFilter::predict(const Mat& control=Mat())
.. ocv:pyfunction:: cv2.KalmanFilter.predict([control]) -> retval
.. ocv:cfunction:: const CvMat* cvKalmanPredict( CvKalman* kalman, const CvMat* control=NULL)
:param control: The optional input control
KalmanFilter::correct
---------------------
Updates the predicted state from the measurement.
.. ocv:function:: const Mat& KalmanFilter::correct(const Mat& measurement)
.. ocv:pyfunction:: cv2.KalmanFilter.correct(measurement) -> retval
.. ocv:cfunction:: const CvMat* cvKalmanCorrect( CvKalman* kalman, const CvMat* measurement )
:param measurement: The measured system parameters
BackgroundSubtractor
--------------------
.. ocv:class:: BackgroundSubtractor : public Algorithm
Base class for background/foreground segmentation. ::
class BackgroundSubtractor : public Algorithm
{
public:
virtual ~BackgroundSubtractor();
virtual void apply(InputArray image, OutputArray fgmask, double learningRate=0);
virtual void getBackgroundImage(OutputArray backgroundImage) const;
};
The class is only used to define the common interface for the whole family of background/foreground segmentation algorithms.
BackgroundSubtractor::apply
--------------------------------
Computes a foreground mask.
.. ocv:function:: void BackgroundSubtractor::apply(InputArray image, OutputArray fgmask, double learningRate=-1)
.. ocv:pyfunction:: cv2.BackgroundSubtractor.apply(image[, fgmask[, learningRate]]) -> fgmask
:param image: Next video frame.
:param fgmask: The output foreground mask as an 8-bit binary image.
:param learningRate: The value between 0 and 1 that indicates how fast the background model is learnt. Negative parameter value makes the algorithm to use some automatically chosen learning rate. 0 means that the background model is not updated at all, 1 means that the background model is completely reinitialized from the last frame.
BackgroundSubtractor::getBackgroundImage
----------------------------------------
Computes a background image.
.. ocv:function:: void BackgroundSubtractor::getBackgroundImage(OutputArray backgroundImage) const
:param backgroundImage: The output background image.
.. note:: Sometimes the background image can be very blurry, as it contain the average background statistics.
BackgroundSubtractorMOG
-----------------------
.. ocv:class:: BackgroundSubtractorMOG : public BackgroundSubtractor
Gaussian Mixture-based Background/Foreground Segmentation Algorithm.
The class implements the algorithm described in [KB2001]_.
createBackgroundSubtractorMOG
------------------------------------------------
Creates mixture-of-gaussian background subtractor
.. ocv:function:: Ptr<BackgroundSubtractorMOG> createBackgroundSubtractorMOG(int history=200, int nmixtures=5, double backgroundRatio=0.7, double noiseSigma=0)
.. ocv:pyfunction:: cv2.createBackgroundSubtractorMOG([history[, nmixtures[, backgroundRatio[, noiseSigma]]]]) -> retval
:param history: Length of the history.
:param nmixtures: Number of Gaussian mixtures.
:param backgroundRatio: Background ratio.
:param noiseSigma: Noise strength (standard deviation of the brightness or each color channel). 0 means some automatic value.
BackgroundSubtractorMOG2
------------------------
Gaussian Mixture-based Background/Foreground Segmentation Algorithm.
.. ocv:class:: BackgroundSubtractorMOG2 : public BackgroundSubtractor
The class implements the Gaussian mixture model background subtraction described in [Zivkovic2004]_ and [Zivkovic2006]_ .
createBackgroundSubtractorMOG2
--------------------------------------------------
Creates MOG2 Background Subtractor
.. ocv:function:: Ptr<BackgroundSubtractorMOG2> createBackgroundSubtractorMOG2( int history=500, double varThreshold=16, bool detectShadows=true )
:param history: Length of the history.
:param varThreshold: Threshold on the squared Mahalanobis distance between the pixel and the model to decide whether a pixel is well described by the background model. This parameter does not affect the background update.
:param detectShadows: If true, the algorithm will detect shadows and mark them. It decreases the speed a bit, so if you do not need this feature, set the parameter to false.
BackgroundSubtractorMOG2::getHistory
--------------------------------------
Returns the number of last frames that affect the background model
.. ocv:function:: int BackgroundSubtractorMOG2::getHistory() const
BackgroundSubtractorMOG2::setHistory
--------------------------------------
Sets the number of last frames that affect the background model
.. ocv:function:: void BackgroundSubtractorMOG2::setHistory(int history)
BackgroundSubtractorMOG2::getNMixtures
--------------------------------------
Returns the number of gaussian components in the background model
.. ocv:function:: int BackgroundSubtractorMOG2::getNMixtures() const
BackgroundSubtractorMOG2::setNMixtures
--------------------------------------
Sets the number of gaussian components in the background model. The model needs to be reinitalized to reserve memory.
.. ocv:function:: void BackgroundSubtractorMOG2::setNMixtures(int nmixtures)
BackgroundSubtractorMOG2::getBackgroundRatio
---------------------------------------------
Returns the "background ratio" parameter of the algorithm
.. ocv:function:: double BackgroundSubtractorMOG2::getBackgroundRatio() const
If a foreground pixel keeps semi-constant value for about ``backgroundRatio*history`` frames, it's considered background and added to the model as a center of a new component. It corresponds to ``TB`` parameter in the paper.
BackgroundSubtractorMOG2::setBackgroundRatio
---------------------------------------------
Sets the "background ratio" parameter of the algorithm
.. ocv:function:: void BackgroundSubtractorMOG2::setBackgroundRatio(double ratio)
BackgroundSubtractorMOG2::getVarThreshold
---------------------------------------------
Returns the variance threshold for the pixel-model match
.. ocv:function:: double BackgroundSubtractorMOG2::getVarThreshold() const
The main threshold on the squared Mahalanobis distance to decide if the sample is well described by the background model or not. Related to Cthr from the paper.
BackgroundSubtractorMOG2::setVarThreshold
---------------------------------------------
Sets the variance threshold for the pixel-model match
.. ocv:function:: void BackgroundSubtractorMOG2::setVarThreshold(double varThreshold)
BackgroundSubtractorMOG2::getVarThresholdGen
---------------------------------------------
Returns the variance threshold for the pixel-model match used for new mixture component generation
.. ocv:function:: double BackgroundSubtractorMOG2::getVarThresholdGen() const
Threshold for the squared Mahalanobis distance that helps decide when a sample is close to the existing components (corresponds to ``Tg`` in the paper). If a pixel is not close to any component, it is considered foreground or added as a new component. ``3 sigma => Tg=3*3=9`` is default. A smaller ``Tg`` value generates more components. A higher ``Tg`` value may result in a small number of components but they can grow too large.
BackgroundSubtractorMOG2::setVarThresholdGen
---------------------------------------------
Sets the variance threshold for the pixel-model match used for new mixture component generation
.. ocv:function:: void BackgroundSubtractorMOG2::setVarThresholdGen(double varThresholdGen)
BackgroundSubtractorMOG2::getVarInit
---------------------------------------------
Returns the initial variance of each gaussian component
.. ocv:function:: double BackgroundSubtractorMOG2::getVarInit() const
BackgroundSubtractorMOG2::setVarInit
---------------------------------------------
Sets the initial variance of each gaussian component
.. ocv:function:: void BackgroundSubtractorMOG2::setVarInit(double varInit)
BackgroundSubtractorMOG2::getComplexityReductionThreshold
----------------------------------------------------------
Returns the complexity reduction threshold
.. ocv:function:: double BackgroundSubtractorMOG2::getComplexityReductionThreshold() const
This parameter defines the number of samples needed to accept to prove the component exists. ``CT=0.05`` is a default value for all the samples. By setting ``CT=0`` you get an algorithm very similar to the standard Stauffer&Grimson algorithm.
BackgroundSubtractorMOG2::setComplexityReductionThreshold
----------------------------------------------------------
Sets the complexity reduction threshold
.. ocv:function:: void BackgroundSubtractorMOG2::setComplexityReductionThreshold(double ct)
BackgroundSubtractorMOG2::getDetectShadows
---------------------------------------------
Returns the shadow detection flag
.. ocv:function:: bool BackgroundSubtractorMOG2::getDetectShadows() const
If true, the algorithm detects shadows and marks them. See createBackgroundSubtractorMOG2 for details.
BackgroundSubtractorMOG2::setDetectShadows
---------------------------------------------
Enables or disables shadow detection
.. ocv:function:: void BackgroundSubtractorMOG2::setDetectShadows(bool detectShadows)
BackgroundSubtractorMOG2::getShadowValue
---------------------------------------------
Returns the shadow value
.. ocv:function:: int BackgroundSubtractorMOG2::getShadowValue() const
Shadow value is the value used to mark shadows in the foreground mask. Default value is 127. Value 0 in the mask always means background, 255 means foreground.
BackgroundSubtractorMOG2::setShadowValue
---------------------------------------------
Sets the shadow value
.. ocv:function:: void BackgroundSubtractorMOG2::setShadowValue(int value)
BackgroundSubtractorMOG2::getShadowThreshold
---------------------------------------------
Returns the shadow threshold
.. ocv:function:: double BackgroundSubtractorMOG2::getShadowThreshold() const
A shadow is detected if pixel is a darker version of the background. The shadow threshold (``Tau`` in the paper) is a threshold defining how much darker the shadow can be. ``Tau= 0.5`` means that if a pixel is more than twice darker then it is not shadow. See Prati, Mikic, Trivedi and Cucchiarra, *Detecting Moving Shadows...*, IEEE PAMI,2003.
BackgroundSubtractorMOG2::setShadowThreshold
---------------------------------------------
Sets the shadow threshold
.. ocv:function:: void BackgroundSubtractorMOG2::setShadowThreshold(double threshold)
BackgroundSubtractorKNN
------------------------
K-nearest neigbours - based Background/Foreground Segmentation Algorithm.
.. ocv:class:: BackgroundSubtractorKNN : public BackgroundSubtractor
The class implements the K-nearest neigbours background subtraction described in [Zivkovic2006]_ . Very efficient if number of foreground pixels is low.
createBackgroundSubtractorKNN
--------------------------------------------------
Creates KNN Background Subtractor
.. ocv:function:: Ptr<BackgroundSubtractorKNN> createBackgroundSubtractorKNN( int history=500, double dist2Threshold=400.0, bool detectShadows=true )
:param history: Length of the history.
:param dist2Threshold: Threshold on the squared distance between the pixel and the sample to decide whether a pixel is close to that sample. This parameter does not affect the background update.
:param detectShadows: If true, the algorithm will detect shadows and mark them. It decreases the speed a bit, so if you do not need this feature, set the parameter to false.
BackgroundSubtractorKNN::getHistory
--------------------------------------
Returns the number of last frames that affect the background model
.. ocv:function:: int BackgroundSubtractorKNN::getHistory() const
BackgroundSubtractorKNN::setHistory
--------------------------------------
Sets the number of last frames that affect the background model
.. ocv:function:: void BackgroundSubtractorKNN::setHistory(int history)
BackgroundSubtractorKNN::getNSamples
--------------------------------------
Returns the number of data samples in the background model
.. ocv:function:: int BackgroundSubtractorKNN::getNSamples() const
BackgroundSubtractorKNN::setNSamples
--------------------------------------
Sets the number of data samples in the background model. The model needs to be reinitalized to reserve memory.
.. ocv:function:: void BackgroundSubtractorKNN::setNSamples(int nN)
BackgroundSubtractorKNN::getDist2Threshold
---------------------------------------------
Returns the threshold on the squared distance between the pixel and the sample
.. ocv:function:: double BackgroundSubtractorKNN::getDist2Threshold() const
The threshold on the squared distance between the pixel and the sample to decide whether a pixel is close to a data sample.
BackgroundSubtractorKNN::setDist2Threshold
---------------------------------------------
Sets the threshold on the squared distance
.. ocv:function:: void BackgroundSubtractorKNN::setDist2Threshold(double dist2Threshold)
BackgroundSubtractorKNN::getkNNSamples
---------------------------------------------
Returns the k in the kNN. K is the number of samples that need to be within dist2Threshold in order to decide that that pixel is matching the kNN background model.
.. ocv:function:: int BackgroundSubtractorKNN::getkNNSamples() const
BackgroundSubtractorKNN::setkNNSamples
---------------------------------------------
Sets the k in the kNN. How many nearest neigbours need to match.
.. ocv:function:: void BackgroundSubtractorKNN::setkNNSamples(int nKNN)
BackgroundSubtractorKNN::getDetectShadows
---------------------------------------------
Returns the shadow detection flag
.. ocv:function:: bool BackgroundSubtractorKNN::getDetectShadows() const
If true, the algorithm detects shadows and marks them. See createBackgroundSubtractorKNN for details.
BackgroundSubtractorKNN::setDetectShadows
---------------------------------------------
Enables or disables shadow detection
.. ocv:function:: void BackgroundSubtractorKNN::setDetectShadows(bool detectShadows)
BackgroundSubtractorKNN::getShadowValue
---------------------------------------------
Returns the shadow value
.. ocv:function:: int BackgroundSubtractorKNN::getShadowValue() const
Shadow value is the value used to mark shadows in the foreground mask. Default value is 127. Value 0 in the mask always means background, 255 means foreground.
BackgroundSubtractorKNN::setShadowValue
---------------------------------------------
Sets the shadow value
.. ocv:function:: void BackgroundSubtractorKNN::setShadowValue(int value)
BackgroundSubtractorKNN::getShadowThreshold
---------------------------------------------
Returns the shadow threshold
.. ocv:function:: double BackgroundSubtractorKNN::getShadowThreshold() const
A shadow is detected if pixel is a darker version of the background. The shadow threshold (``Tau`` in the paper) is a threshold defining how much darker the shadow can be. ``Tau= 0.5`` means that if a pixel is more than twice darker then it is not shadow. See Prati, Mikic, Trivedi and Cucchiarra, *Detecting Moving Shadows...*, IEEE PAMI,2003.
BackgroundSubtractorKNN::setShadowThreshold
---------------------------------------------
Sets the shadow threshold
.. ocv:function:: void BackgroundSubtractorKNN::setShadowThreshold(double threshold)
BackgroundSubtractorGMG
------------------------
Background Subtractor module based on the algorithm given in [Gold2012]_.
.. ocv:class:: BackgroundSubtractorGMG : public BackgroundSubtractor
createBackgroundSubtractorGMG
-----------------------------------
Creates a GMG Background Subtractor
.. ocv:function:: Ptr<BackgroundSubtractorGMG> createBackgroundSubtractorGMG(int initializationFrames=120, double decisionThreshold=0.8)
.. ocv:pyfunction:: cv2.createBackgroundSubtractorGMG([, initializationFrames[, decisionThreshold]]) -> retval
:param initializationFrames: number of frames used to initialize the background models.
:param decisionThreshold: Threshold value, above which it is marked foreground, else background.
BackgroundSubtractorGMG::getNumFrames
---------------------------------------
Returns the number of frames used to initialize background model.
.. ocv:function:: int BackgroundSubtractorGMG::getNumFrames() const
BackgroundSubtractorGMG::setNumFrames
---------------------------------------
Sets the number of frames used to initialize background model.
.. ocv:function:: void BackgroundSubtractorGMG::setNumFrames(int nframes)
BackgroundSubtractorGMG::getDefaultLearningRate
--------------------------------------------------
Returns the learning rate of the algorithm. It lies between 0.0 and 1.0. It determines how quickly features are "forgotten" from histograms.
.. ocv:function:: double BackgroundSubtractorGMG::getDefaultLearningRate() const
BackgroundSubtractorGMG::setDefaultLearningRate
--------------------------------------------------
Sets the learning rate of the algorithm.
.. ocv:function:: void BackgroundSubtractorGMG::setDefaultLearningRate(double lr)
BackgroundSubtractorGMG::getDecisionThreshold
--------------------------------------------------
Returns the value of decision threshold. Decision value is the value above which pixel is determined to be FG.
.. ocv:function:: double BackgroundSubtractorGMG::getDecisionThreshold() const
BackgroundSubtractorGMG::setDecisionThreshold
--------------------------------------------------
Sets the value of decision threshold.
.. ocv:function:: void BackgroundSubtractorGMG::setDecisionThreshold(double thresh)
BackgroundSubtractorGMG::getMaxFeatures
--------------------------------------------------
Returns total number of distinct colors to maintain in histogram.
.. ocv:function:: int BackgroundSubtractorGMG::getMaxFeatures() const
BackgroundSubtractorGMG::setMaxFeatures
--------------------------------------------------
Sets total number of distinct colors to maintain in histogram.
.. ocv:function:: void BackgroundSubtractorGMG::setMaxFeatures(int maxFeatures)
BackgroundSubtractorGMG::getQuantizationLevels
--------------------------------------------------
Returns the parameter used for quantization of color-space. It is the number of discrete levels in each channel to be used in histograms.
.. ocv:function:: int BackgroundSubtractorGMG::getQuantizationLevels() const
BackgroundSubtractorGMG::setQuantizationLevels
--------------------------------------------------
Sets the parameter used for quantization of color-space
.. ocv:function:: void BackgroundSubtractorGMG::setQuantizationLevels(int nlevels)
BackgroundSubtractorGMG::getSmoothingRadius
--------------------------------------------------
Returns the kernel radius used for morphological operations
.. ocv:function:: int BackgroundSubtractorGMG::getSmoothingRadius() const
BackgroundSubtractorGMG::setSmoothingRadius
--------------------------------------------------
Sets the kernel radius used for morphological operations
.. ocv:function:: void BackgroundSubtractorGMG::setSmoothingRadius(int radius)
BackgroundSubtractorGMG::getUpdateBackgroundModel
--------------------------------------------------
Returns the status of background model update
.. ocv:function:: bool BackgroundSubtractorGMG::getUpdateBackgroundModel() const
BackgroundSubtractorGMG::setUpdateBackgroundModel
--------------------------------------------------
Sets the status of background model update
.. ocv:function:: void BackgroundSubtractorGMG::setUpdateBackgroundModel(bool update)
BackgroundSubtractorGMG::getMinVal
--------------------------------------------------
Returns the minimum value taken on by pixels in image sequence. Usually 0.
.. ocv:function:: double BackgroundSubtractorGMG::getMinVal() const
BackgroundSubtractorGMG::setMinVal
--------------------------------------------------
Sets the minimum value taken on by pixels in image sequence.
.. ocv:function:: void BackgroundSubtractorGMG::setMinVal(double val)
BackgroundSubtractorGMG::getMaxVal
--------------------------------------------------
Returns the maximum value taken on by pixels in image sequence. e.g. 1.0 or 255.
.. ocv:function:: double BackgroundSubtractorGMG::getMaxVal() const
BackgroundSubtractorGMG::setMaxVal
--------------------------------------------------
Sets the maximum value taken on by pixels in image sequence.
.. ocv:function:: void BackgroundSubtractorGMG::setMaxVal(double val)
BackgroundSubtractorGMG::getBackgroundPrior
--------------------------------------------------
Returns the prior probability that each individual pixel is a background pixel.
.. ocv:function:: double BackgroundSubtractorGMG::getBackgroundPrior() const
BackgroundSubtractorGMG::setBackgroundPrior
--------------------------------------------------
Sets the prior probability that each individual pixel is a background pixel.
.. ocv:function:: void BackgroundSubtractorGMG::setBackgroundPrior(double bgprior)
calcOpticalFlowSF
-----------------
Calculate an optical flow using "SimpleFlow" algorithm.
.. ocv:function:: void calcOpticalFlowSF( InputArray from, InputArray to, OutputArray flow, int layers, int averaging_block_size, int max_flow )
.. ocv:function:: calcOpticalFlowSF( InputArray from, InputArray to, OutputArray flow, int layers, int averaging_block_size, int max_flow, double sigma_dist, double sigma_color, int postprocess_window, double sigma_dist_fix, double sigma_color_fix, double occ_thr, int upscale_averaging_radius, double upscale_sigma_dist, double upscale_sigma_color, double speed_up_thr )
:param prev: First 8-bit 3-channel image.
:param next: Second 8-bit 3-channel image of the same size as ``prev``
:param flow: computed flow image that has the same size as ``prev`` and type ``CV_32FC2``
:param layers: Number of layers
:param averaging_block_size: Size of block through which we sum up when calculate cost function for pixel
:param max_flow: maximal flow that we search at each level
:param sigma_dist: vector smooth spatial sigma parameter
:param sigma_color: vector smooth color sigma parameter
:param postprocess_window: window size for postprocess cross bilateral filter
:param sigma_dist_fix: spatial sigma for postprocess cross bilateralf filter
:param sigma_color_fix: color sigma for postprocess cross bilateral filter
:param occ_thr: threshold for detecting occlusions
:param upscale_averaging_radius: window size for bilateral upscale operation
:param upscale_sigma_dist: spatial sigma for bilateral upscale operation
:param upscale_sigma_color: color sigma for bilateral upscale operation
:param speed_up_thr: threshold to detect point with irregular flow - where flow should be recalculated after upscale
See [Tao2012]_. And site of project - http://graphics.berkeley.edu/papers/Tao-SAN-2012-05/.
.. note::
* An example using the simpleFlow algorithm can be found at opencv_source_code/samples/cpp/simpleflow_demo.cpp
createOptFlow_DualTVL1
----------------------
"Dual TV L1" Optical Flow Algorithm.
.. ocv:function:: Ptr<DenseOpticalFlow> createOptFlow_DualTVL1()
The class implements the "Dual TV L1" optical flow algorithm described in [Zach2007]_ and [Javier2012]_ .
Here are important members of the class that control the algorithm, which you can set after constructing the class instance:
.. ocv:member:: double tau
Time step of the numerical scheme.
.. ocv:member:: double lambda
Weight parameter for the data term, attachment parameter. This is the most relevant parameter, which determines the smoothness of the output. The smaller this parameter is, the smoother the solutions we obtain. It depends on the range of motions of the images, so its value should be adapted to each image sequence.
.. ocv:member:: double theta
Weight parameter for (u - v)^2, tightness parameter. It serves as a link between the attachment and the regularization terms. In theory, it should have a small value in order to maintain both parts in correspondence. The method is stable for a large range of values of this parameter.
.. ocv:member:: int nscales
Number of scales used to create the pyramid of images.
.. ocv:member:: int warps
Number of warpings per scale. Represents the number of times that I1(x+u0) and grad( I1(x+u0) ) are computed per scale. This is a parameter that assures the stability of the method. It also affects the running time, so it is a compromise between speed and accuracy.
.. ocv:member:: double epsilon
Stopping criterion threshold used in the numerical scheme, which is a trade-off between precision and running time. A small value will yield more accurate solutions at the expense of a slower convergence.
.. ocv:member:: int iterations
Stopping criterion iterations number used in the numerical scheme.
DenseOpticalFlow::calc
--------------------------
Calculates an optical flow.
.. ocv:function:: void DenseOpticalFlow::calc(InputArray I0, InputArray I1, InputOutputArray flow)
:param prev: first 8-bit single-channel input image.
:param next: second input image of the same size and the same type as ``prev`` .
:param flow: computed flow image that has the same size as ``prev`` and type ``CV_32FC2`` .
DenseOpticalFlow::collectGarbage
--------------------------------
Releases all inner buffers.
.. ocv:function:: void DenseOpticalFlow::collectGarbage()
.. [Bouguet00] Jean-Yves Bouguet. Pyramidal Implementation of the Lucas Kanade Feature Tracker.
.. [Bradski98] Bradski, G.R. "Computer Vision Face Tracking for Use in a Perceptual User Interface", Intel, 1998
.. [Bradski00] Davis, J.W. and Bradski, G.R. “Motion Segmentation and Pose Recognition with Motion History Gradients”, WACV00, 2000
.. [Davis97] Davis, J.W. and Bobick, A.F. “The Representation and Recognition of Action Using Temporal Templates”, CVPR97, 1997
.. [EP08] Evangelidis, G.D. and Psarakis E.Z. "Parametric Image Alignment using Enhanced Correlation Coefficient Maximization", IEEE Transactions on PAMI, vol. 32, no. 10, 2008
.. [Farneback2003] Gunnar Farneback, Two-frame motion estimation based on polynomial expansion, Lecture Notes in Computer Science, 2003, (2749), , 363-370.
.. [Horn81] Berthold K.P. Horn and Brian G. Schunck. Determining Optical Flow. Artificial Intelligence, 17, pp. 185-203, 1981.
.. [KB2001] P. KadewTraKuPong and R. Bowden. "An improved adaptive background mixture model for real-time tracking with shadow detection", Proc. 2nd European Workshop on Advanced Video-Based Surveillance Systems, 2001: http://personal.ee.surrey.ac.uk/Personal/R.Bowden/publications/avbs01/avbs01.pdf
.. [Javier2012] Javier Sanchez, Enric Meinhardt-Llopis and Gabriele Facciolo. "TV-L1 Optical Flow Estimation".
.. [Lucas81] Lucas, B., and Kanade, T. An Iterative Image Registration Technique with an Application to Stereo Vision, Proc. of 7th International Joint Conference on Artificial Intelligence (IJCAI), pp. 674-679.
.. [Welch95] Greg Welch and Gary Bishop “An Introduction to the Kalman Filter”, 1995
.. [Tao2012] Michael Tao, Jiamin Bai, Pushmeet Kohli and Sylvain Paris. SimpleFlow: A Non-iterative, Sublinear Optical Flow Algorithm. Computer Graphics Forum (Eurographics 2012)
.. [Zach2007] C. Zach, T. Pock and H. Bischof. "A Duality Based Approach for Realtime TV-L1 Optical Flow", In Proceedings of Pattern Recognition (DAGM), Heidelberg, Germany, pp. 214-223, 2007
.. [Zivkovic2004] Z. Zivkovic. "Improved adaptive Gausian mixture model for background subtraction", International Conference Pattern Recognition, UK, August, 2004, http://www.zoranz.net/Publications/zivkovic2004ICPR.pdf. The code is very fast and performs also shadow detection. Number of Gausssian components is adapted per pixel.
.. [Zivkovic2006] Z.Zivkovic, F. van der Heijden. "Efficient Adaptive Density Estimation per Image Pixel for the Task of Background Subtraction", Pattern Recognition Letters, vol. 27, no. 7, pages 773-780, 2006.
.. [Gold2012] Andrew B. Godbehere, Akihiro Matsukawa, Ken Goldberg, "Visual Tracking of Human Visitors under Variable-Lighting Conditions for a Responsive Audio Art Installation", American Control Conference, Montreal, June 2012.
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