114_1_image_proc_exam_solns_2011

# 114_1_image_proc_exam_solns_2011 - EE114 Winter Quarter...

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EE114 Introduction to Speech and Image Processing Winter Quarter, 2011 Page 1 of 8 EE114 Image Processing Exam Solutions Notes: - For all problems please circle or otherwise clearly indicate your answers! The use of calculators or other electronic devices with calculator-like functionality is not permitted on this test. You may find one or both of the following formulas useful: p k = 1 1 - p k = 0 , where p < 1 kp k = p 1 - p ( 29 2 k = 1 , where p < 1 1. Filter Identification (25 points) There are two images below, with the input image on the left (32 by 32) and the output image (34 by 34) on the right. The output image was generated by convolving the input image with a 3 by 3, 2D filter of the form a b c d e f g h i where some of the elements a through i may be zero. All of the elements a through i are non- negative. (Given the information in the input and output images below, the specific location of the origin in the above representation of the 3 by 3 filter is not needed to solve this problem). Pixel values in the images shown below are represented from 0 (black) to 255 (white). In the input image, all pixels have a value of either 0 or 255. The white vertical and horizontal “stripes” in the input image on the left are one pixel thick. In displaying the output image, no “clipping” was needed – in other words, the range of output pixel values after convolving with the 3 by 3 filter was within [0,255]. Give all of the elements of the 2D function that was convolved with the original to produce the filtered image. Express your answer in the form of a 3 x 3 matrix with elements a through i as shown above. There should be no variables in your answer; each of the positions a through i should be associated with a number. You do not need to specify the location of the origin in your answer.

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EE114 Introduction to Speech and Image Processing Winter Quarter, 2011 Page 2 of 8 Input Output Answer 1 0 1 1 0 1 0 3 1 0 0
EE114 Introduction to Speech and Image Processing Winter Quarter, 2011 Page 3 of 8 2. 2D DCT (25 points) a) (7 points) Consider the following 2x2 image: 4 3 5 4 Take the 2D 2x2 unitary DCT of this image

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114_1_image_proc_exam_solns_2011 - EE114 Winter Quarter...

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