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Like others before me HOG Trilinear Interpolation of Histogram Bins I am trying to understand and implement trilinear interpolation for HoG. Dalal's Thesis' here:

http://lear.inrialpes.fr/people/dalal/NavneetDalalThesis.pdf

The issue I am struggling to understand is that as I understand it, the task is of value re-destribution into bins rather than interpolation of known bin values. I am clear about the one dimensional case in the orientation dimension;

for example if I have a known pixel gradient orientation value of 75 and nearest bins of z1=60 and z2=80 (bin step size b=20), then the pixel value (gradient magnitude in this case, say w=16) will be distributed at a ratio of 1:3 into the adjacent bins (4 into the 60 bin and 12 into the 80 bin) right?

When it comes to the three dimensional case that requires spatial interpolation of the magnitude, I'm stumped. I fail to understand how the magnitude is redestributed to the appropriate bins. Any clear explanation for someone, who is admitedly slow, will be greatly appreciated.

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user2598073
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1 Answers1

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Histogram of Oriented Gradients as discussed by Navneet Dalal, discusses interpolation of the gradient magnitudes of the cells into orientation bins ( for 0 to 180 degrees we have 9 bins with a bin step size or bandwidth of 20 degrees)

A naive approach would be to just do this for every cell in the window/image but this would result in aliasing effects. In order to reduce aliasing it is discussed that the image should be partitioned into blocks (preferably overlapping) of n x n cells.
eg. for a 64 x 128 pixel image you could define the following:
1. Cell Size = 8x8 pixels
2. Block Size = 2x2 cells

this gives:
8x16 cells, or
4x8 NON-overlapping block's or
7x15 Blocks with a stride of 8 i.e 7x15 50% overlapping blocks

So instead of performing linear histogram interpolation of every cell on its own you would perform Trilinear interpoloation of cells in blocks i.e Interpolated trilinearly:
- Bilinearly into spatial cells (of the block)
- Linearly into orientation bins

Visualization of HoG Trilinear interpolation : http://www.ultraimg.com/d7km

ArmandNaudé
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