How to Obtain Mathematically High Frequency and Low Frequency Component Separately Using Bilateral Filter? I have asked this question before in the sense that what does a high frequency and low frequency component signify in a image and i got satisfactory answers now i want to know that how i can get high frequency and low frequency component separately from the image. 

I mean what changes i have to make in the equations of bilateral filters and its implementation in matlab so that i can get both high frequency and low frequency component of that image. 

Because in my experiment i need both the high frequency and low frequency component of a image.

Bilateral filters takes a weighted sum of the pixels in a local neighborhood; the weights 
depend on both the spatial distance and the intensity distance.

The value of a pixel assigned is given as 

$$
      BF[I_p] = \frac{1}{W_p} \sum_{\substack{ q\in S }} G_{\sigma_s}(\parallel p-q \parallel) G_{\sigma_r}(\mid I_p - I_q\mid) I_q
      $$

Do I have to make changes to this equation of bilateral filter to get high frequency and low frequency components separately .

What component does this equation signify is it the high frequency component or low frequency component ?
One you have convolved your original image with the gaussian kernel (of appropriately chosen variance), then simply subtract the original image from the result of the convolution. This will give you the image with only the high frequency components of your original.