Patch Histogram Feature

This post will introduce a new feature for binary blobs like connected components in a text.

The feature is called patch histogram and it's the histogram of 3x3 patches of black and white pixels. We collect all 3x3 patches and count their frequency.

3x3 patch for a binary image contains $2^9 = 512$ different combinations. For each of these combinations, we assign a number. I wrote the implementation in Python and here is a lookup table that converts all possible 3x3 patches to their ids.

patch_histogram_dict = {}
for f in range(0, 512):
    i22 = f & 1
    i21 = (f >> 1) & 1
    i20 = (f >> 2) & 1
    i12 = (f >> 3) & 1
    i11 = (f >> 4) & 1
    i10 = (f >> 5) & 1
    i02 = (f >> 6) & 1
    i01 = (f >> 7) & 1
    i00 = (f >> 8) & 1
    patch_histogram_dict[ma(i00, i01, i02, i10, i11, i12, i20, i21, i22)] = f

I was looking a skeleton feature that can be applied to components after medial axis transform. However, we will use binarized connected component images directly in this version and take a look at skeletal version later.

Above, we used a function ma to convert a set of numbers to a tuple of tuples. It's simple as

def ma(i00, i01, i02, i10, i11, i12, i20, i21, i22):
    return ((i00, i01, i02),
            (i10, i11, i12),
            (i20, i21, i22))

The first step in feature generation is marking each pixel of the image with its id. Then a simple np.histogram call generates the histogram.

for i in range(1, rows - 1):
    for j in range(1, cols - 1):
        s = framed[(i-1):(i+2), (j-1):(j+2)]
        marks[i-1, j-1] = patch_dict[ma(s[0, 0], s[0, 1], s[0, 2],
                                        s[1, 0], s[1, 1], s[1, 2],
                                        s[2, 0], s[2, 1], s[2, 2])]

=framed= is a copy of the original image with a 1 pixel frame, so that boundary pixel are also counted without much checking. patch_dict is a parameter that the function receives. Its default value is the dictionary that we made above, but any kind of patch dictionaries can be used.

The feature is a call to numpy.histogram as follows

histogram = numpy.histogram(marked_points,

=marked~points~= are the result of above pixel counting loop. hist_range is the minimum and maximum value for the patch dictionary. density parameter is True, so that the histogram is normalized to 1 and feature become size invariant. bins is a parameter we can set freely, but by default it's equal to the range of elements.

The comparison can be done with standard histogram comparison methods, like EMD or Chi Square distance metrics.