homomorphic filtering

Homomorphic Filtering 

Homomorphic filtering is a generalized technique for nonlinear image enhancement and correction. It 

simultaneously normalizes the brightness across an image and increases contrast. 

An image can be expressed as the product of illumination and reflectance: 

f( x, y ) = i( x, y )⋅r( x, y ) 

When the illumination is uniform, i( x,y ) is considered to be a constant and the image is considered to 

the reflectance of the object. However, the lighting condition is usually unequal. The illumination component 

tends to vary slowly and its frequency fastens on low part in the frequency domain; the reflectance tends to 

vary rapidly and its frequency is in high part. If two components can be operated separately, the illumination 

problem will be solved and the image will be enhanced. Hence, the log transform is used to equation (1): 

ln f( x, y )= lni( x, y )+lnr( x,y ) -(2) 

Then Fourier transform is used to equation (2), which makes the succedent operation is in frequency 

domain.