Bezier & Splines in Image Processing & Machine Vision by Sambhunath Biswas

By Sambhunath Biswas

This booklet offers with quite a few photo processing and desktop imaginative and prescient difficulties successfully with splines and comprises: the importance of Bernstein Polynomial in splines, certain insurance of Beta-splines purposes that are rather new, Splines in movement monitoring, a variety of deformative versions and their makes use of. ultimately the booklet covers wavelet splines that are effective and potent in several picture applications.

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Here only the horizontally right and vertically lower transitions are considered. The following definition of tik gives a symmetrical co-occurence matrix. M N tik = δ, i=1 j=1 where δ = 1 if f (i, j) = i and f (i, j + 1) = k, or f (i, j) = i and f (i, j − 1) = k, or f (i, j) = i and f (i + 1, j) = k, 38 2 Image Segmentation or f (i, j) = i and f (i − 1, j) = k, δ = 0, otherwise. b. 5) i=1 n pi = 1 and 0 ≤ pi ≤ 1, pi is the probability of the i-th state of where i=1 the system. Such a measure is claimed to give information about the actual probability structure of the system.

Let the incremental value be q. Then the corresponding y values will be c, aq 2 + bq + c, 4aq 2 + 2bq + c, 9aq 2 +3bq +c, · · ·. 1 for recursive computation of points for B´ezier curve then takes the following form. 1. Difference table for recursive computation of points. t y 0 c q aq 2 + bq + c 2q 4aq 2 + 2bq + c 3q 9aq 2 + 3bq + c 4q 16aq 2 + 4bq + c y (1st difference) aq 2 + bq 3aq 2 + bq 5aq 2 + bq 7aq 2 + bq 2 y (2nd difference) 2aq 2 2aq 2 2aq 2 26 1 Bernstein Polynomial and B´ezier-Bernstein Spline 2 yj = 2aq 2 and yj+2 + 2yj+1 + yj = 2aq 2 , f or all j ≥ 0.

Define tik = δ, a∈F , b∈a8 where δ = 1 if the graylevel of “a” is “i” and that of ‘b’ is ‘k’, δ = 0 otherwise. Obviously, tik gives the number of times the gray level ‘k’ follows graylevel ‘i’ in any one of the eight directions. The matrix T = [tik ]L×L is, therefore, the co-occurrence matrix of the image F . , considering b ∈ a8 , where a8 ⊆ a8 . The co-occurrence matrix may again be either asymmetric or symmetric. One of the asymmetrical forms can be defined considering M N tik = δ i=1 j=1 with δ = 1 if f (i, j) = i and f (i, j + 1) = k, f (i, j) = i and f (i + 1, j) = k, δ = 0 otherwise.

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