The image gradient orientation and magnitude is calculated for each pixel in the image. The gradient filter kernels
in x- and y-direction are:
The gradient magnitude 
and orientation
is then calculated as:
In dependence on their orientation the calculated gradients are then assigned to a certain number of orientation bins.
The vote for the bin is a
function of the gradient magnitude. As Dalal and Triggs found out, a splitting of the orientation into 9 bins over
give the best results when using the HOG features
for human detection methods [Dal05]. In the VA example designs "HOG_9Bins_HistogramMax.va" and "HOG_9Bins_Histogram.va" we have implemented such binning.
In addition in the example "HOG_4Bins_HistogramMax.va" we perform a splitting into 4 bins over
. The assignment or weighting
of a certain orientation
to a bin (with orientation
) is done
via interpolation:
Here 
is the size of angle steps between the bins.
A single bin column 
of the Histogram of Oriented Gradients (each for a region of 8x8 pixels) is then calculated as:
The histograms for each cell of 8x8 pixels are then grouped in blocks of 2x2 cells size to cover local variances in luminance
or contrast. The blocks have an overlap of
.
Using the HOG descriptor for object recognition purposes, block normalization (algorithm see
[Dal05]) improves the performance by a factor of 
.
Block normalization is omitted in the current design examples. In the designs "HOG_4Bins_HistogramMax.va" and "HOG_9Bins_HistogramMax.va",
the maximum histogram orientation is
forwarded to DMA, whereas in "HOG_9Bins_Histogram.va" the complete Histogram of Oriented Gradients is sent to PC.
The designs introduced in the following can easily be adapted to the special purpose of the user. That is, a certain amount
and step size of the orientation binning or a block
normalization according to [Dal05] can be implemented in addition.
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