Question

In Homomorphic filtering which of the following operations is used to convert input image to discrete Fourier transformed function?

(a) Logarithmic operation

(b) Exponential operation

(c) Negative transformation

(d) None of the mentioned

I got this question in exam.

My doubt is from Homomorphic filtering topic in chapter Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

The correct answer is (a) Logarithmic operation

The explanation is: For an image is expressed as the multiplication of illumination and reflectance component i.e. f(x, y) = i(x, y) * r(x, y), the equation can’t be used directly to operate separately on the frequency component of illumination and reflectance because the Fourier transform of the product of two function is not separable. So, the logarithmic operation is used.I{z(x,y)}=I{ln⁡(f(x,y)) }=I{ln⁡(i(x,y)) }+I{ln⁡(r(x,y))}.