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hw2 - CSE166 Image Processing Homework#2 Instructor Prof...

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CSE166 – Image Processing – Homework #2 Instructor: Prof. Serge Belongie http://www-cse.ucsd.edu/classes/fa06/cse166 Due (in class) 11:00am Thursday Oct. 12, 2006. Reading GW 10.0-10.1. GW 4.0-4.2, 4.6 (except for 4.6.6). General Homework Guidelines Use the Cover Sheet provided. Please attach all code that you use. Attach code at end of submission. In general try to keep your answers concise. Use as many words as you need and no more. Also work on your presentation skills. This means organize your plots and displays. Always use titles and add captions when appropriate. Points will be awarded for clarity and presentation. Written exercises 1. GW, Problem 10.5. 2. GW, Problem 10.8. 3. Compute 2 f for the function f ( x, y ) = e - ( x 2 + y 2 ) / 2 σ 2 . Show your work. 4. GW, Problem 10.11. 5. GW, Problem 4.1. 6. GW, Problem 4.4. 7. GW, Problem 4.6. Explain how this relates to the Matlab function fftshift . Matlab exercises 1. The Binomial Approximation The binomial coefficients are commonly used as a discrete approximation to the Gaussian function. Recall that the expression for a Gaussian in 1D is given by G σ ( x ) = 1 2 πσ 2 e - x 2 / 2 σ 2 To produce a discrete approximation to a Gaussian with effective width σ 2 , use the N th row of Pascal’s triangle, where N = 4 σ 2 + 1. The corresponding normalization factor is 2 - ( N - 1) . (a) Make plots comparing the binomial kernel to the continuous Gaussian kernel for σ 2 = 1 . 0 , 2 . 5 , 4 . 0 , 5 . 5. In each plot, use stem to plot the binomial kernel and fplot to plot the

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hw2 - CSE166 Image Processing Homework#2 Instructor Prof...

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