HOMOMORPHIC FILTERING IN IMAGE PROCESSING AND ITSAPPLICATIONS
Image processing in humans
Image processing in computer
WHAT IS IMAGE PROCESSING?Image processing is a form of signal processing for which the input is an image, such as photographs or frames of videos and the output can either be an image or a set of characteristics or parameters related to the image.
Principle:HomomorphicFiltering:Homomorphic filtering is a generalized technique for image enhancement and/or 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,z)=i(x,y,z).r(x,y,z)  =>   g(x,y,z)=ln(f(x,y,z))   =>   g(x,y,z)=ln(i(x,y,z))+ln(r(x,y,z))
Then taking DFT:          F(g(x,y,z))=F(ln(i(x,y,z)))+F(ln(r(x,y,z)))Then we will apply it to a filter. 	we will get F(s(x,y,z)) as o/p Then inverse DFT(IDFT) of filter output is taken.	we will get,	 s(x,y,z)=I'(x,y,z)+r’(x,y,z)Then we will take exponential to get enhanched image	s’(x,y,z)=I‘’(x,y,z).r’’(x,y,z)
I‘’(x,y,z), r’’(x,y,z) are the illumination and reflectance of the ‘’enhanced'' image.    The illumination component tends to vary  slowly across the image. The reflectance tends                   to vary rapidly. Therefore, by applying a frequency domain filter we can reduce intensity variation across the image while highlighting detail.
Homomorphic filtering
Filtering in the Frequency Domain :Lowpass FilterHighpass Filter
Typical operations:Image masking 
Image re-touching, Cleaning & Cloning 
Colorization 
Specialized Services 
Photo Restoration 
Removing objects, backgrounds, persons etc. 

Image Processing