1. Contrast Enhancement Crystal Logan Mentored by: Dr. Lucia Dettori Dr. Jacob Furst

2. Project Objective  Assist Radiologist in reading images  Enhance the Contrast of Images

3. “The Big Picture”  Explore Contrast Enhancement techniques  Linear binning equally divides ranges of grey levels into bins  Histogram Equalization enhances images by plotting frequency  Automatically enhance multiple regions of the image.

4. 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

5. Example of Windows

8. Research Objective  Enhance the Contrast of Images  Explore Contrast Enhancement techniques  Automatically enhance multiple regions of the image

9. 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

10. Expectation Maximization First Iteration Second Iteration Copyright © 2001, Andrew W. Moore

11. Expectation Maximization Third Iteration fourth Iteration Copyright © 2001, Andrew W. Moore

12. Expectation Maximization fifth Iteration Sixth Iteration Copyright © 2001, Andrew W. Moore

13. Expectation Maximization Copyright © 2001, Andrew W. Moore Twentieth Iteration

14. 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.

15. 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.

16. EM Results RegionsAirWaterTissueBone 0.120.390.460.018 location7991019.5104.71234.1 Expectation Maximization

17. EM Image Histogram & Gaussian:

18. EM image Histogram & Gaussian

19. 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

20. Future Works Explore CE techniques and put them into windows by the using the EM Measure the Contrast in the image using Greedy Algorithms