midterm782-2003_Anwer

midterm782-2003_Anwer - Name: SIMG-782 Introduction to...

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Name: SIMG-782 Introduction to Digital Image Processing Midterm Examination Fall Quarter 2003 Closed book and notes. Calculators are approved. Answer all questions. 1. The diagram at the right contains several curves that could be used to transform the brightness values of a monochrome image by the operation B = T [ A ] where A and B are image arrays. Shown below are four pairs of histograms. Identify the transformation curve best associated with each pair and write the letter in the space in the center column. Curve C is the identity transform. Curves A and B stretch the dark regions while curves D and E compress the dark regions. Curve B stretches the light region while curve D compresses the light region. Compare these eﬀects with the changes in the histograms to select the transforms. Answers indicated below. Input image histogram Transform Output image histogram E D A B

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2. The Sobel operator computes the following quantity at each location ( x,y ) in an image array, A : G x [ j,k ] = ( A [ j + 1 ,k + 1] + 2 A [ j + 1 ,k ] + A [ j + 1 ,k - 1]) - ( A [ j - 1 ,k + 1] + 2 A [ j - 1 ,k ] + A [ j - 1 ,k - 1]) G y [ j,k ] = ( A [ j - 1 ,k - 1] + 2 A [ j,k - 1] + A [ j + 1 ,k - 1]) - ( A [ j - 1 ,k + 1] + 2 A [ j,k + 1] + A [ j + 1 ,k + 1]) G [ j,k ] = | G x [ j,k ] | + | G y [ j,k ] | The position of A [ j,k ] is column j and row k of the array. The operation is implemented as the convolution of the image array A with two masks, M x and M y followed by the magnitude operation. (a)
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midterm782-2003_Anwer - Name: SIMG-782 Introduction to...

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