:param arrays:Source arrays. They all should have the same depth, ``CV_8U`` or ``CV_32F`` , and the same size. Each of them can have an arbitrary number of channels.
:param channels:List of the ``dims`` channels used to compute the histogram. The first array channels are numerated from 0 to ``arrays[0].channels()-1`` , the second array channels are counted from ``arrays[0].channels()`` to ``arrays[0].channels() + arrays[1].channels()-1`` etc.
:param mask:Optional mask. If the matrix is not empty, it must be an 8-bit array of the same size as ``arrays[i]`` . The non-zero mask elements mark the array elements counted in the histogram.
:param ranges:Array of the ``dims`` arrays of the histogram bin boundaries in each dimension. When the histogram is uniform ( ``uniform`` =true), then for each dimension ``i`` it is enough to specify the lower (inclusive) boundary :math:`L_0` of the 0-th histogram bin and the upper (exclusive) boundary :math:`U_{\texttt{histSize}[i]-1}` for the last histogram bin ``histSize[i]-1`` . That is, in case of a uniform histogram each of ``ranges[i]`` is an array of 2 elements. When the histogram is not uniform ( ``uniform=false`` ), then each of ``ranges[i]`` contains ``histSize[i]+1`` elements: :math:`L_0, U_0=L_1, U_1=L_2, ..., U_{\texttt{histSize[i]}-2}=L_{\texttt{histSize[i]}-1}, U_{\texttt{histSize[i]}-1}` . The array elements, that are not between :math:`L_0` and :math:`U_{\texttt{histSize[i]}-1}` , are not counted in the histogram.
:param accumulate:Accumulation flag. If it is set, the histogram is not cleared in the beginning when it is allocated. This feature enables you to compute a single histogram from several sets of arrays, or to update the histogram in time.
:param arrays:Source arrays. They all should have the same depth, ``CV_8U`` or ``CV_32F`` , and the same size. Each of them can have an arbitrary number of channels.
:param channels:The list of channels that are used to compute the back projection. The number of channels must match the histogram dimensionality. The first array channels are numerated from 0 to ``arrays[0].channels()-1`` , the second array channels are counted from ``arrays[0].channels()`` to ``arrays[0].channels() + arrays[1].channels()-1`` and so on.
The functions ``calcBackProject`` calculate the back project of the histogram. That is, similarly to ``calcHist`` , at each location ``(x, y)`` the function collects the values from the selected channels in the input images and finds the corresponding histogram bin. But instead of incrementing it, the function reads the bin value, scales it by ``scale`` , and stores in ``backProject(x,y)`` . In terms of statistics, the function computes probability of each element value in respect with the empirical probability distribution represented by the histogram. See how, for example, you can find and track a bright-colored object in a scene:
Before tracking, show the object to the camera so that it covers almost the whole frame. Calculate a hue histogram. The histogram may have strong maximums, corresponding to the dominant colors in the object.
When tracking, calculate a back projection of a hue plane of each input video frame using that pre-computed histogram. Threshold the back projection to suppress weak colors. It may also make sense to suppress pixels with non-sufficient color saturation and too dark or too bright pixels.
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
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`` .
The function computes the earth mover distance and/or a lower boundary of the distance between the two weighted point configurations. One of the applications described in :ref:`RubnerSept98` is multi-dimensional histogram comparison for image retrieval. EMD is a transportation problem that is solved using some modification of a simplex algorithm, thus the complexity is exponential in the worst case, though, on average it is much faster. In the case of a real metric the lower boundary can be calculated even faster (using linear-time algorithm) and it can be used to determine roughly whether the two signatures are far enough so that they cannot relate to the same object.
