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Added documenation of the Earth Mover Distance (C++ interface, ticket #696)

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Ilya Lysenkov 2011-06-08 10:08:24 +00:00
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commit 1e945dc984
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modules/imgproc/doc/histograms.rst
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@ -201,7 +201,30 @@ The function returns
:math:`d(H_1, H_2)` .
While the function works well with 1-, 2-, 3-dimensional dense histograms, it may not be suitable for high-dimensional sparse histograms. In such histograms, because of aliasing and sampling problems, the coordinates of non-zero histogram bins can slightly shift. To compare such histograms or more general sparse configurations of weighted points, consider using the
:cpp:func:`calcEMD` function.
:cpp:func:`EMD` function.
.. index:: EMD
EMD
------
.. cpp:function:: float EMD( InputArray signature1, InputArray signature2, int distType, InputArray cost=noArray(), float* lowerBound=0, OutputArray flow=noArray() )
Computes the "minimal work" distance between two weighted point configurations.
:param signature1: The first signature, a :math:`\texttt{size1}\times \texttt{dims}+1` floating-point matrix. Each row stores the point weight followed by the point coordinates. The matrix is allowed to have a single column (weights only) if the user-defined cost matrix is used.
:param signature2: The second signature of the same format as ``signature1`` , though the number of rows may be different. The total weights may be different, in this case an extra "dummy" point is added to either ``signature1`` or ``signature2`` .
:param distType: Used metric. ``CV_DIST_L1, CV_DIST_L2`` , and ``CV_DIST_C`` stand for one of the standard metrics; ``CV_DIST_USER`` means that a pre-calculated cost matrix ``cost`` is used.
:param cost: The user-defined :math:`\texttt{size1}\times \texttt{size2}` cost matrix. Also, if a cost matrix is used, lower boundary ``lowerBound`` can not be calculated, because it needs a metric function.
:param lowerBound: Optional input/output parameter: lower boundary of distance between the two signatures that is a distance between mass centers. The lower boundary may not be calculated if the user-defined cost matrix is used, the total weights of point configurations are not equal, or if the signatures consist of weights only (i.e. the signature matrices have a single column). The user **must** initialize ``*lowerBound`` . If the calculated distance between mass centers is greater or equal to ``*lowerBound`` (it means that the signatures are far enough) the function does not calculate EMD. In any case ``*lowerBound`` is set to the calculated distance between mass centers on return. Thus, if user wants to calculate both distance between mass centers and EMD, ``*lowerBound`` should be set to 0.
:param flow: The resultant :math:`\texttt{size1} \times \texttt{size2}` flow matrix: :math:`\texttt{flow}_{i,j}` is a flow from :math:`i` th point of ``signature1`` to :math:`j` th point of ``signature2`` .
.. index:: equalizeHist