converting cutoff frequency of lowpass filter for 2D images

Question

If we want to lowpass filter an image by 0.3xpi rad/sample by using h = fspecial('average', size), how shall we determine size parameter corresponding to 0.3xpi rad/sample in the following code?

lp_filter = fspecial('average', size);
img = imfilter(original,lp_filter,'replicate'); 

Answer 1

Filter size is the inverse of the cut-off. So, for a simple filter like average, if you had a size of 1 pixel (i.e. no averaging), the cut-off would be at pi rad/sample. So, the nearest integer to 0.3 pi rad/sample would be a size of 3 pixels.

The maths is a bit more complicated than that, but this is a useful rule of thumb in this case.