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

I am research about correlation kernel and I have some questions that need your help. Let see the pp. 3302-3303 in the paper:

Changyang Li, et al., Robust Model for Segmenting Images With/Without Intensity Inhomogeneities

The special kernel is defined as:

$$W(|y-x|)=\dfrac{\gamma}{1+\dfrac{1}{\sqrt{2\pi\omega^2}}e^{\dfrac{(y-x)^2}{2\omega^2}}}$$ where $\gamma$ is a normalizing weight obtained by:

$$\gamma=\left(\int \left( 1+\dfrac{1}{\sqrt{2\pi\omega^2}}e^{\dfrac{(y-x)^2}{2\omega^2}}\right)^{-1} \mathrm{d}y\right)^{-1}$$

and $\omega$ is a 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 benefit? To what kind of images apply the correlation kernel to? Thank you.

• I dont think its a highpass filter. Can u plz also attach the fft of both kernels. – learner Jul 16 '14 at 21:24
• How to plot fft of this data. Assume that G=fspecial('gaussian',round(2*sigma)*2 + 1,sigma); – John Jul 17 '14 at 4:22
• This filter isn't Spatially Invariant hence it doesn't have constant shape as you model it. – Royi May 11 '18 at 21:01