HOG - What's the point of blocks?

[Flix]

Hi,

I don't understand the point of separating the image into overlapping blocks of the HOG descriptor.

Let's assume we devided an image into 3x3 cells and have already calculated the gradient histograms \(h_1, ..., h_9\) for each cell. Now we further devide the image into overlapping blocks of 2x2 cells. This should look something like this, cells are black boxes, blocks are colored boxes:

hog.png (4.58 KiB) 1645 mal betrachtet

The resulting descriptors now is:

\((b_1, b_2, b_3, b_4) = (h_1, h_2, h_4, h_5, h_2, h_3, h_5, h_6, h_4, h_5, h_7, h_8, h_5, h_6, h_8, h_9)\)

If I got that right, I don't understand why it is useful to have every histogram appear in the descriptor multiple times.

Thanks in advance for any advice.

[lustiz]

Well, you do not just concatenate those cells, but you normalize within each block. The benefit is invariance to illumination and contrast.

[Flix]

Somehow I overlooked that part. So basically for my example the descriptor would be calculated like this (for L2-norm):

\(b_1 = [h_1; h_2; h_4; h_5]\)
\(b_1^{normed} = \frac{b_1}{\sqrt{|b_1|^2 + e}}\)
\(...\)
\(descriptor = [b_1^{normed}; ...; b_4^{normed}]\)

[lustiz]

Each cell contibutes multiple times, namly once for each normalization as part of the various blocks. So take your first one, but normalize all the h's w.r.t. to the block they came from.