Detection of edges is a very important application in image processing. Taking the gradient of a two-dimensional function detects the changes the edges of an image. A filter than is commonly used in edge detection is Sobel’s filter. Consider the generation of two related impulse responses

For a given input x[m, n] the output of the Sobel is

(a) Use imread to read in the image peppers.png, and convert it into a gray image with double precision by means of the functions rgb2gray and double. Letting this image be input x[m, n] implement the Sobel filter to obtain an image y[m, n]. Determine a threshold T such that whenever y[m, n] > T we let a final image z[m, n] = 1 and zero otherwise. Display the complement of the image z[m, n].

(b) Repeat the above for the image circuit.tif, choose a threshold T so that you obtain a binarized image displaying the edges of the image.

Transcribed Image Text:

h„[m, n] = ő[m, n] – 8[m – 2, n] + 26[m, n – 1] – 26[m – 2, n – 1] + ő[m, n – 2] – 6[m – 2, n – 2] h, [m, n] = 6[m, n] + 28[m – 1, n] + ő[m – 2, n] – 8[m, n – 2] – 26[m – 1, n – 2] – ő[m – 2, n – 2] Y1[m, n] = (h, * x)[m,n], y2[m, n] = (h, * 1)[m, n] y[m, n] = V(yn [m, n])? + (y2[m, n])²