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# Math Methods of Image Proc MA 439

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This 6 page Class Notes was uploaded by Eldon Trantow on Monday October 19, 2015. The Class Notes belongs to MA 439 at Rose-Hulman Institute of Technology taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/225076/ma-439-rose-hulman-institute-of-technology in Mathematics (M) at Rose-Hulman Institute of Technology.

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Date Created: 10/19/15

Mathematics of Image Processing Matlab Session 2 Due Monday September 30 1 Images 1 N 9 Type in all the commands below and gure out what is going on l7ll go over some of this in class if necessary load Clown who size X size map map imshowXmap if you have not installed the Image Processing Toolbox replace the command imshowXmapby the two commands imagesc X colormap map or image X colormap map Find the maximum and minimum colors ie What Matlab commands did you use color index in the clown Type in the command imshowX55 map or image X55 colormap map What happens and why 4 Work with sub images sub matrices to show exactly the clowns7s nose Write down the matlab commands 5 What commands do you need to show the clown upside down 6 Fiddle with the color map gray to get the monochrome negative of the clown Write down the Matlab commands 2 Edge Detection 7 Type in the commands and explain what is happening load Clown YX 213201J imshowabs Y X D or load Clown YX 213201J imagesc abs Y X colormap gray 8 Type in the commands and explain what is going on when you vary cps load Clown YX 223201J Z absX Y M maXZI eps 05 ZfindZ lt epsM 0 imshowZ El 3 Energy Noise and Distortion 9 Write out a script to compute the energy of an m gtlt 71 image X where energy 2 Suggestion rst atten X Via Y X 10 Now add some noise Y X 6N7 where X is some image The noise image N N2rand mn 1 has its entries uniformly distributed between 71 and 17 and the parameter 6measures the strength of the noise Compute the maximum distortion see notes you can allow and still have reasonable delity Use a grayscale for showing the image HY XHZ ilele EZHNHZ HXHZ W W Mathematics of Image Processing Matlab Session 1 Due Tuesday September 17 Make sure you make liberal use of help Keep a diary of your work and attach a cleaned up version of it 1 Matrices and vectors 1 Set up the following system of equations in matrix form using mathematical notation Find the solution Via Matlab 25t1 s2tu1 t2uv1 u2 w1 02w1 w2y1 x2yz1 y221 2 Scalar Products 2 Are any of the columns of the matrix in question 1 orthogonal Use Mat lab matrix multiplication to get your answer Write out the mathematical notation for the matrix computation you did in Matlab to answer problem 3 Do the same for the rows 4 Repeat questions 2 and 3 for the matrices Ncossinmat10 Download the script into your working directory httpwwwrosehulmaneduclassmabroughtoncoursesma439scriptsNcossinmatm 3 Plotting and Aliasing U 03 5 Plot the function sin5 27ft at N 128 points in 0 S t S 1 as done in handouts skip t 1 What is the apparent frequency of the sampled signal cycles per second Now ll in the following table for sinn 27ft sampled at N points n 5 24 69 102 300 5 8 24 60 1000 N 128 128 128 128 128 32 32 32 apparent frequency What conclusions can you draw from Question 5 4 Noise and distortion 8 3 Create a simple sum of sines an cosines of varying frequencies for 0 S t S 1 Sample at 8192 points and call the vector X Play the signal with the sound command Now add some noise Y X6N The noise vector N N2rand8192 1 1 has its entries uniformly distributed between 71 and 17 and the parameter 6measures the strength of the noise Compute the maximum distortion see notes you can allow and still have reasonable delity HY J12 116N1126211N112 W W HXHZ39

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