Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Digital Image
Processing
Contrast Enhancement: Part II
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Histogram Processing
Histogram : is the discrete function h(rk)=nk , where rk is the kth
gray level in the range of [0, L-1] and nk is the number of pixels
having gray level rk.
Normalized histogram : is p(rk)=nk/n, for k=0,1,…,L-1 and p(rk)
can be considered to give an estimate of the probability of
occurrence of ray level rk.
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Histogram Equalization
Histogram equalization : is a method which increases the
dynamic range of the gray-levels in a low-contrast image to cover
full range of gray-levels.
How-to-Do: is achieved by having a transformation function
which is the Cumulative Distribution Function (CDF) of a given
PDF of gray-levels in a given image.
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Histogram Equalization
Histogram equalization :
calculated by:
the new intensity value of pixel x is
 cdf  x   min cdf

I  x   round 
  L  1 
 1  min cdf

Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Histogram Equalization
Histogram equalization :
levels is uniform.
the probability function of the output
Note : the transformation function is simply the CDF.
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Histogram Equalization
x 10
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x 10
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50
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4
16
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Histogram Equalization
12
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Histogram Equalization
(a) A face image
from the CALTECH
face database, (b)
its histogram, (c)
the equalized face
image using HE, (d)
and its respective
histogram.
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Singular Value Equalization
Singular value decomposition : any matrix, A, can be written
as multiplication of two orthogonal square matrices, U and V, and
a matrix containing the sorted singular values on its main
diagonal, Σ.
A=UΣV T
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Singular Value Equalization
Note : as σ1 is much bigger than other σs then changing it will
affect on the reconstructed image, i.e. changing σ1 will directly
change the luminance of the image.
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Singular Value Equalization
G(0.5, 1) :
is a synthetic intensity matrix whose pixel values
have Gaussian distribution with mean of 0.5 and variance of 1
with the same size of the original image.
ξ:
is ratio of the largest singular value of the generated
normalized matrix over a normalized image.


max G  0.5, 1 
max   A 

Gholamreza Anbarjafari, PhD
Video Lecturers on Digital Image Processing
Singular Value Equalization


T
Equalized Im age  UA A VA
Video Lecturers on Digital Image Processing
Gholamreza Anbarjafari, PhD
Singular Value Equalization
Low contrast
Histogram equalization
Singular value
equalization
Video Lecturers on Digital Image Processing
Summary
•We have looked at:
– How histogram equalization works.
– What is SVD?
– How SVE works
•Next time we will continue our talk
about image enhancement in spatial
domain
Gholamreza Anbarjafari, PhD