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

By Sambhunath Biswas

This ebook offers with numerous photo processing and laptop imaginative and prescient difficulties successfully with splines and comprises: the importance of Bernstein Polynomial in splines, exact insurance of Beta-splines functions that are fairly new, Splines in movement monitoring, quite a few deformative types and their makes use of. ultimately the booklet covers wavelet splines that are effective and powerful in several snapshot applications.

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8. Arc with its associated right triangle. Both of these conditions lead to the existence of another key pixel outside the line AC or BC. This is a contradiction. Algorithm for Key Pixel Extraction The following algorithm can be used for extraction of key pixels. Algorithm for extraction of key pixels. We assume: {Pi }ni=1 are the contour points in the binary image and {(xi , yi )}ni=1 are their position coordinates. 5 Key Pixels and Contour Approximation 21 Since for a closed contour there is a possibility of missing the first key pixel, we need to examine a few more points after the starting point is reached to enable us to get the same back.

1. Partitioning of the co-occurrence matrix for thresholding. The uniformity of quadrant one will be maintained, but that of quadrants three and four will be affected causing a lowering of entropy of quadrants three and four. 4 Extraction of Compact Homogeneous Regions 41 be reduced. Hence, its maximization with respect to s is expected to provide a good object/background segmentation. Next, we provide a schematic description of the algorithm. c. Algorithm Cond threshold (X , th) begin Compute Co-occurrence matrix, t = [tij ]L×L .

18 1 Bernstein Polynomial and B´ezier-Bernstein Spline Fig. 4. Possible behavior of fa (x) when f (x) is constant. (a) Considering local maxima/minima of fa (x); (b) considering global maximum/minimum of fa (x), • denotes the position of key pixel. Proof : When the key pixels are on the horizontal line at x = c, it follows from the definition of key pixel that either f (c) > f (x) or f (c) < f (x) in both the intervals [(k1 −δ1 ), K1 ] and [K2 , (k2 +δ2 )], where f (x) is constant in [K1 , K2 ] and δ1 , δ2 ∈ {0, 1}.

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