Question

If an image is expressed as the multiplication of illumination and reflectance component i.e. f(x, y)= i(x, y) * r(x, y), then Validate the statement “We can directly use the equation f(x, y)= i(x, y) * r(x, y) to operate separately on the frequency component of illumination and reflectance” .

(a) True

(b) False

I have been asked this question in a national level competition.

I'd like to ask this question from Homomorphic filtering topic in chapter Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

Correct option is (b) False

For explanation I would say: 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.