Image Processing

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:

Homomorphic Filtering:• 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 images’(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 :

Highpass Filter

Lowpass Filter

Typical operations:

Image masking Image re-touching, Cleaning & Cloning Colorization Specialized Services Photo Restoration Removing objects, backgrounds, persons etc. Portraitize, Glamorize, Adding Motion Effects.

Applications:

Astronomical applicationMedical applications• MRI, CT, Microscopy• Ultrasound imaging3D image processingDefenceSecurityPasswords

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