Question 1 Given the image f(x,y) with x,y (0,1,2,3,4), answer the following questions and show...

Transcribed Image Text:

Question 1 Given the image f(x,y) with x,y € (0,1,2,3,4), answer the following questions and show your work. 100 55 52 100 101 100 101 52 52 55 52 51 52 52 55 52 55 52 52 55 51 52 51 f(x,y) = 105 50 (a) [1 marks] Find (1,1), the output of a 3 x 3 averaging filter at pixel location (1.1). (b) [1 marks] Find g(2,2) where g(x, y) = median {f(i.j)} (1J)EN. and N₂, is a 5 x 5 neighbourhood around pixel (r,y). (c) [1 marks] Find (1,3) and (3,1) using Sobel operators. (d) [1 marks] Find f(3,3) using a 45° isotropic Laplacian. (e) [1 marks] Find f(4,4) while dealing with the boundary conditions. (f) [1 marks] Find f(2.5, 2.5) using interpolation. (g) [2 marks] Find P(f>55), the probability that f is greater than 55. (h) [3 marks] Compress the image using Huffman coding and calculate the average code length Larg, the redundancy R, and the compression ratio C compared to 8-bit per symbol representation. (i) [2 marks] If r(z,y) is the recovered image after passing f(z.y) through an image processing block, find the peak signal to noise ratio (PSNR). [102 100 r(x, y) = 105 103 99 55 52 101 41 53 55 43 46 53 51 40 54 51 59 62 38 39 44 52 51 (j) [2 marks] Find F(0,0) where F(u, v) is the Fourier transform of f(x,y) given by F(u,0) = f(x,y)/(+)dzdy Question 1 Given the image f(x,y) with x,y € (0,1,2,3,4), answer the following questions and show your work. 100 55 52 100 101 100 101 52 52 55 52 51 52 52 55 52 55 52 52 55 51 52 51 f(x,y) = 105 50 (a) [1 marks] Find (1,1), the output of a 3 x 3 averaging filter at pixel location (1.1). (b) [1 marks] Find g(2,2) where g(x, y) = median {f(i.j)} (1J)EN. and N₂, is a 5 x 5 neighbourhood around pixel (r,y). (c) [1 marks] Find (1,3) and (3,1) using Sobel operators. (d) [1 marks] Find f(3,3) using a 45° isotropic Laplacian. (e) [1 marks] Find f(4,4) while dealing with the boundary conditions. (f) [1 marks] Find f(2.5, 2.5) using interpolation. (g) [2 marks] Find P(f>55), the probability that f is greater than 55. (h) [3 marks] Compress the image using Huffman coding and calculate the average code length Larg, the redundancy R, and the compression ratio C compared to 8-bit per symbol representation. (i) [2 marks] If r(z,y) is the recovered image after passing f(z.y) through an image processing block, find the peak signal to noise ratio (PSNR). [102 100 r(x, y) = 105 103 99 55 52 101 41 53 55 43 46 53 51 40 54 51 59 62 38 39 44 52 51 (j) [2 marks] Find F(0,0) where F(u, v) is the Fourier transform of f(x,y) given by F(u,0) = f(x,y)/(+)dzdy

Answer rating: 100% (QA)

The image is a set of math problems based on digital image processing concepts such as filtering edge detection interpolation probability calculations ... View the full answer