CSCE 5683 - Homework 4
Due Date - 11/04/2010

1. Problem Statement:

The purpose of this assignment is to learn about interactive image restoration using frequency domain filters. In particular, you are asked to implement two versions of notch filters to remove periodic noise from input images.

Circular notch: Removes frequencies in a circular region of frequency space centered on frequency (Cu, Cv) and with a radius of R. Since the FT is symmetric, you should also remove frequencies at (-Cu, -Cv). The "shape" of your circular region can have a Butterworth or Gaussian profile.

Rectangular notch: Removes frequencies in a rectangular region of frequency space given by four parameters (u1, v1, u2, v2). In this case, the "shape" of your region should have a sharp cutoff at the perimeter of the rectangle.

You should test your program using the distorted images provided in the class website hw4 directory. Try a variety of circular notch and rectangular notch filters to get the best looking output image. There is no MSE calculation needed this time.

2. Design:

The lecture notes for the class have the formulas for Butterworth and Gaussian high pass filters centered at frequency (0,0). You will need to adapt these to implement the circular notch. The rectangular notch should be easier to implement. You just need to check the ordering of (u1, v1, u2, v2) values and handle frequency wrap around properly.

3. Implementation:

You should use the im_short and im_complex classes to implement your restoration filters. Use im_short for image input/output, and im_complex for the FastFT and FastIFT methods. You can also use the GetReal, GetImaginary, GetAmplitude and GetPhase methods to "extract" the Fourier transform values. For example:

// Read image
im_short Input;
Input.ReadJpg("input.jpg");
im_complex Freq(Input);

// Do frequency domain filtering
Freq.FastFT();
...
Freq.FastIFT();

// Write image
im_short Output;
Freq.GetReal(Output);
Output.WriteJpg("output.jpg");

4. Testing:

Test your program to check that it operates correctly for all of the requirements listed above. Also check for the error handling capabilities of the code. Save your testing output in text files for submission on the program due date.

5. Documentation:

When you have completed your C++ program, write a short report (less than one page long) describing what the objectives were, what you did, and the status of the program. Does it work properly for all test cases? Are there any known problems? Save this report in a separate text file to be submitted electronically.

6. Project Submission:

In this class, we will be using electronic project submission to make sure that all students hand their programming projects and labs on time, and to perform automatic analysis of all programs that are submitted. When you have completed the tasks above go to the class web site to "submit" your documentation, C++ program, and testing files.

The dates on your electronic submission will be used to verify that you met the due date above. All late projects will receive reduced credit (50% off if less than 24 hours late, no credit if more than 24 hours late), so hand in your best effort on the due date.

You should also PRINT a copy of these files and hand them into your teaching assistant in your next lab. Include a title page which has your name and uaid, and attach your hand written design notes from above.