Exact_Pacthes about affnet HOT 8 CLOSED

I got it, thank you very much for your patient explanation.

from affnet.

Yes, you are right. But.

1. remember that sigma1 then is multiplied by coef. of the current octave. E.g. if octave is 2x downscaled. then coef is 2
2. Moreover, for description, there is "measurement region scale" mrScale, typically equal to 3sqrt(3) or 5:

http://cmp.felk.cvut.cz/~chum/papers/perdoch-cvpr09.pdf

from affnet.

remember that sigma1 then is multiplied by coef. of the current octave. E.g. if octave is 2x downscaled. then coef is 2

the coef is 1.0/2 or 2 ? for example, the content range covered by a pixel in one image from octave 2 is equal to the content range covered by 2*2 pixels in octave 1. So, the coef is should be equal to 1/2?

Moreover, for description, there is "measurement region scale" mrScale, typically equal to 3sqrt(3) or 5:

So, ( assume that 0 is the original image size, no downsampling), the measurement region scale in the octave N is larger N times than the one of 0th octave image, in terms of image content?

from affnet.

@yunyundong Lets do the example.

Say, on level 0 octave 0 we have feature location (x,y). Default init_sigma is 1.6, so is it our sigma.
Therefore ScaleSpaceAffinePatchExtractor, if no orientation/affine module is used, would output following LAF:

[mr_region_scale * sigma, 0, x;
0, mr_region_scale * sigma, y] =

[8.31, 0, x;
0, 8.31, y]

So our patch in term of image content would correspond to circle with diameter 2 * 8.31 = 16.62 px. Which is then resized to PS, 32x32 by default.

If we have level 0, octave 1 at feature location (x,y), then LAF would be:

[2 * mr_region_scale * sigma, 0, x;
0, 2 * mr_region_scale * sigma, y]

If we have level 1 or level 2, then radius would be a bit larger according to

from affnet.

I can get your example. What I want to say is as follows:
for level 0 in octave 0, the diameter is 2* 8.31=16.62 px
for level 0 in octave 1, the diameter is 2 * 3sqrt(3)*1.6 =16.62px (assume mr_region_sacle=3sqrt(3);)
Now, the image content covered by the region with diameter 16.0 pixel from level 0 in octave 1 is two larger than the image content covered by the region with diameter 16.62 . Because the octave is downsampled from octave 0 .
the coef 2 should be 1/2 so that the region from different octaves represent the same image content.

another example: a original image with size 6464 px, after downsample operation, it wil becom 3232 ->1616-> 88-> 44. Now , can I say the 44 image represent the same content range as the original 64*64 original image?

from affnet.

@yunyundong Yes, you can say it.
Regarding coefficient, I think, you are wrong. Inside the octave, it is always one. Octave is downsampled, we don`t need to account for it. But coefficient is 2 if you want to have go from "radius in octave image" to "radius in original image".

And yes, if you go other way round - to calculate "radius in octave" from "radius in original", then it is 1/2

from affnet.

In fact, I also suspect I am wrong. So, I am only curious that when the index of octave become larger, the region clipped to resample to ps*ps also becomes larger.

from affnet.

@yunyundong Yes, exactly.

from affnet.