Question

If the Gaussian filter is expressed as H(u, v) = e^(-D^2 (u,v)/2D 0^2),where D(u, v) is the distance from point(u, v), D0  is the distance defining cutoff frequency, then for what value of D(u, v) the filter is down to 0.607 of its maximum value?

(a) D(u, v) = D0

(b) D(u, v) = D0^2

(c) D(u, v) = D0^3

(d) D(u, v) = 0

The question was asked in an interview for internship.

The doubt is from Gaussain Lowpass and Sharpening Frequency Domain Filters topic in chapter Filtering in Frequency Domain of Digital Image Processing

Answer 1

The correct choice is (a) D(u, v) = D0

To explain: For the given Gaussian filter of 2-D image, the value D(u, v) = D0  gives the filter a down to 0.607 of its maximum value.