By David S. Touretzky (Editor)
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32(a) produces the composite mask in Fig. 27(b). Convolving this mask with f (x , y ) produces g (x , y ), the unsharp result. 28 Consider the following equation: f (x , y ) − ∇2 f (x , y ) = f (x , y ) − f (x + 1, y ) + f (x − 1, y ) + f (x , y + 1) + f (x , y − 1) − 4f (x , y ) = 6f (x , y ) − f (x + 1, y ) + f (x − 1, y ) + f (x , y + 1) + f (x , y − 1) + f (x , y ) CHAPTER 3. 2f (x , y ) − f (x , y ) where f (x , y ) denotes the average of f (x , y ) in a predefined neighborhood centered at (x , y ) and including the center pixel and its four immediate neighbors.
This condition was not given in the problem statement on purpose in order to force the student to arrive at that conclusion. If the instructor wishes to simplify the problem, this should then be mentioned when the problem is assigned. A further simplification is to tell the students that the intensity level of the background is 0. Let B represent the intensity level of background pixels, let a i denote the intensity levels of points inside the mask and o i the levels of the objects. In addition, let S a denote the set of points in the averaging mask, So the set of points in the object, and S b the set of points in the mask that are not object points.
A Laplacian mask with a -4 in the center and 1s in the vertical and horizontal directions will obviously produce an image with sharpening in both directions and in general will appear sharper than with the previous mask. Similarly, and mask with a −8 in the center and 1s in the horizontal, vertical, and diagonal directions will detect the same intensity changes as the mask with the −4 in the center but, in addition, it will also be able to detect changes along the diagonals, thus generally producing sharper-looking results.
Categories: Computer Vision Pattern Recognition