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

modules/imgproc/doc/histograms.rst

@@ -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