Contrast Enhancement

Crystal Logan

Mentored by: Dr. Lucia DettoriDr. Jacob Furst

Project Objective

Assist Radiologist in reading images

Enhance the Contrast of Images

“The Big Picture”Explore Contrast Enhancement techniques Linear binning equally divides ranges of

grey levels into binsHistogram Equalization enhances images by

plotting frequency Automatically enhance multiple regions of the

image.

Previous work on Multiple Windows

User selects the number of windows (1-3) on which to apply contrast enhancement

User specifies the grey level ranges for each window to be used

User selects the Contrast Enhancement algorithm to be used

The selected algorithm is applied to the regions

Original image, and the enhance image are displayed

Example of Windows

Example of Windows

Example of Windows

Research Objective

Enhance the Contrast of ImagesExplore Contrast Enhancement techniques Automatically enhance multiple regions of the

image

Expectation Maximization

EM algorithm identifies four Gaussian to be used to partition the histogram of the image in four regions

Parameters: means and standard deviations of the Gaussian curves

The parameters are estimated by likelihood functions

Iterative Process

Expectation Maximization

First Iteration Second Iteration

Copyright © 2001, Andrew W. Moore

Expectation Maximization

Third Iteration fourth Iteration

Copyright © 2001, Andrew W. Moore

Expectation Maximization

fifth Iteration Sixth Iteration

Copyright © 2001, Andrew W. Moore

Expectation Maximization

Copyright © 2001, Andrew W. Moore

Twentieth Iteration

Expectation Maximization Expectation Step:

Sets initial value for the parameter by using kmeans cluster.

Maximization Step:Uses the data from the expectation step to

estimate the parameter, by taking the derivative. Repeat iteration until there is Convergence.

K-means Cluster statistical algorithm k the number of clusters (4 in our case) Find the centroids for the clusters Calculates distance of all elements from

the centroids Group elements from the centroids.

EM Results

Regions Air Water Tissue Bone

0.12 0.39 0.46 0.018

location 799 1019.5 104.7 1234.1

Expectation Maximization

EM Image Histogram & Gaussian:

EM image Histogram & Gaussian

Analysis Graphs

The Gaussian graph are accurately estimating the centroids.

Identification Algorithm gives us a estimate of how much materials are in each region

based on the maximization step.

Iterations Manipulating the iterations in both the K mean and EM algorithm,

resulted in k-mean iterations isn’t crucial, and EM iterations did change one of the Gaussian curves’ amplitude

Future Works Explore CE techniques and put them into

windows by the using the EM Measure the Contrast in the image using

Greedy Algorithms