What is purpose of correlation kernel? IIs it high pass filter or low pass filter?

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I am research about correlation kernel and I have some questions that need your help. Let see the pp. 3302-3303 in the http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6517250&tag=1 The special kernel is defined that enter image description here where $\gamma$ is a normalizing weight obtained by enter image description here

and $\omega$ is Gaussian kernel

I implement it with support from Mr. Rayryeng. This is comparison of gaussian filter (right side)and correlation filter(left side). The gaussian looks like the low pass filter, whereas correlation kernel is as high pass filter. Could you help me explain the purpose of correlation kernel comparison with gaussian kernel? Which is beneifit? What kind of image to apply correlation kernel. Thank you

enter image description here

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matlabimage-processingsignal-processinggaussian
Hi there, you might get some help with this from math exchange math.stackexchange.com/questions – chiliNUT
@user8264 - ok, you didn't tell me that you were going to apply a Gaussian kernel in this fashion, so yes this does look like a high pass filter. Perhaps this is used because it is not as aggressive as a standard high pass filter using a Gaussian by doing 1 - hGauss for each of the coefficients. I honestly don't know why this kind of kernel would be used. As chiliNUT mentioned, perhaps carrying this over to Math SE may be fruitful. – rayryeng
Thank chiliNUT and rayryeng. I read that paper many time to see what is answer, and I read the its reference. But I did not find any information. Anyway, we can said it is high pass filter. I am do segmentation task. I think the filter result looks like low pass filter result with same kernel size. – John
This question has been cross-posted to Math: math.stackexchange.com/questions/869153/… – John1024

1 Answers

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Your implementation of the correlation filter looks off, it should tend to 0 for |x-y|->infinity and be decreasing in |x-y|.

Edit: according to wolfram alpha, with 2w^2=1 and setting gamma to 1 it looks like this:

enter image description here

It has the shape of a directional low-pass filter