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# HW1 - MP230 Modern Diagnostic Imaging Systems Fall 2010...

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MP230 Modern Diagnostic Imaging Systems, Fall 2010. Homework #1 Due: Septemer 8 by 5:00 pm Part I: Thoroughly answer all questions. Clearly and neatly show your work. Part II & III: Fully answer all questions and print out a copy of your Matlab code, including any figures or tables. I. PROBLEMS (PP 56-61 OF PRINCE) 1.) Evaluate the following: Z -∞ Z -∞ f ( x, y ) δ ( x - 2 , y + 3) dxdy Z -∞ Z -∞ f ( x, y ) * δ ( x + 4 , y - 1) dxdy 2.) 2.12 3.) a.) Qualitatively describe how a convolution with the following kernels would affect a digital image: i.) 0 0 0 0 1 0 0 0 0 ii.) 1 0 0 0 0 0 0 0 0 iii.) 1 1 1 1 1 1 1 1 1 b.) Write an equation for the kernels in part a. Assume the distance between adjacent pixels is 1. c.) What is the center pixel value of the following image convolved with the third kernel? a b c d e f g h i 4. 2.19 5. 2.22 Extra Credit: 2.23 1

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II. MATLAB EXCERCISE: SPATIAL RESOLUTION Define a zero-filled 256x256 matrix using the command, zeros. Set 5 vertical bars of thickness 1 separated from each other by 9 pixels to the value 1. Label this matrix as Bars . 1. Display the image, Bars. Your matrix can be displayed as a 2D grayscale image by using the commands, imagesc and colormap .
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