计算HOG功能

Question

I have one problem in the second step which is to accumulate weighted votes for gradient orientation over spatial cells.

Assuming the cell is 8*8 . Let me use two matrix GO[8][8]([1 9]) , GM[8][8] to represent the gradient orientation and gradient magnitude respectively. The gradient orientation ranges from 0 - 180 and there are 9 orientation bins.

According to my understanding of HOG, for every pixel in a cell, adding its gradient magnitude to its corresponding orientation bin. In this way, we can have the histogram for every cell.

But there is one sentence thats confusing me.

" To reduce aliasing, votes(gradient magnitude) are interpolated trilinearly between the neighbouring bin centers in both orientation and position. " ¹

Why interpolated? How to interpolate? Can someone explains more detailed? No reducing aliasing.

Thanks in advance.

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¹ This sentence is in Navneet Dalal's PHD thesis, p38, line 4.

Answer 1

Interpolation is a standard technique for computing histograms. The idea here is that each value is not simply placed into one bin, but is distributed between two neighboring bins (assuming a 1d histogram), based on how far away it is from the center of the original bin.

The purpose of this is to deal with situations when a small error in your measurement can cause a value to be placed into a different bin. This is a very good thing to do for any type of histogram, not just for HOGs, assuming you have the CPU cycles.

There is also bi-linear and tri-linear interpolation for 2d and 3d histograms, where each value is distributed between 4 and 8 neighboring bins respectively.