CS6640 - Project 1
Assigned Jan. 24, 2008
Due Feb. 7 (Just before midnight)

Goals

The purpose of this assignment is to familiarize you with matlab and allow you to experiment with methods for improving the constrast of an image.

Histogram Equalization

1. Implement a matlab function

   histogram(I, n, min, max)
   

   that takes a 2D array (or image) I as input (8-bit unsigned integers) and returns a 1D array of floats (length n) that give the relative frequency of the occurance of greyscale values in each of the n bins that equally (to within integer round off) divide the range of (integer) values between min and max.

2. Implement a matlab function

   histoeq(I, n)
   

   that takes a 2D array (or image) I as input (8-bit unsigned integers) and returns a 2D array of the same type that has undergone histogram equalization using n bins and has a range of outputs that spans the entire range of the data type.
3. Use this routine to transform and enhance the following images:
   1. Xinwei1
   2. Xinwei2
   3. Seeds
   4. Family
   5. Capitol
   6. Portal
4. In addition, include in your discussion 2-3 of your own greyscale images that you think would be interesting from the point of view of this exercise.
5. Discuss (briefly) why histogram equalization is or is not effective for each image.
6. Derive an algorithm that processes an image to return an image with a histogram (pdf) that has at every grey level a value that is a linear blend of the input histogram and a flat histogram. Implement a matlab function

   histoeq(I, n, alpha)
   

   where alpha is a float between 0 and 1 and every bin is (in principle) equal to . Thus, for a value of alpha = 0, the output equals the input and for a value of 1 the output is the same as histoeq(I, n,). Show, mathematically (using continuous greyscales) that your algorithm is correct. Experiment and report results on some of the images listed above.

Adaptive Histogram Equalization

1. Implement a matlab function that returns the input image which has been transformed by adaptive equalized histogram equalization using square neighborhoods (allowing for boundaries). The function should be

   AHE(I, n, windowsize)
   

   You may use whichever algorithm you choose. The windowsize is an optional parameter. If windowsize is left empty (set to -1) your routine should make a reasonable choice of tile or window size based on the size of the image, etc. Your routine may round off the given window size to some number that fits into your algorithm (if necessary). Make sure that your function is a sensibly efficient implementation of whatever algorithm you choose.
2. For the images given in 1 above (the samples given you and the ones you bring in yourself) try adaptive histogram equalization, with different values of window size.
3. Discuss the time it takes to run and its effectiveness for each image.
4. Comment on and explain any artifacts.

Clipped Local Adaptive Histogram Equalization

Implement a version of Clipped LAHE (CLAHE). Explain your algorithm in the report, and if you used ideas from any outside resources. The clip value should be specified as an input parameter. The function should be

CLAHE(I, n, cliplevel, windowsize)

Try your algorithm on a variety of images and compare against the unclipped version. What values of clipping are effective and why?

Instructions, Requirements, and Restrictions

1. Write your project code in a single directory, called project1.
2. Each individual function (including functions you define) should be a ``.m'' file, and your functions should call one another as necessary.
3. Your project report will be in the form of an html file called index.html, contained in that directory. All links from that file must be relative and all other files necessary to read your report must be in that directory (or subdirectories).
4. You should use examples of images in your report. They should be viewable in the browser when we open your html file.
5. You will submit a single tar file created from from your project directory with the unix command tar -czf project1.tgz./project1.

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