Bézier and Splines in Image Processing and Machine Vision by Sambhunath Biswas

By Sambhunath Biswas

This e-book bargains with a variety of snapshot processing and computing device imaginative and prescient difficulties successfully with splines and comprises: the importance of Bernstein Polynomial in splines, special assurance of Beta-splines purposes that are rather new, Splines in movement monitoring, a number of deformative types and their makes use of. eventually the ebook covers wavelet splines that are effective and powerful in numerous picture applications.

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Extra resources for Bézier and Splines in Image Processing and Machine Vision

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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. This leads to the recurrence formula y2 = 2y1 − y0 + 2aq 2 which involves just three additions to get the next value from two preceding values at hand.

The assignment of a pixel into a cluster may depend on the image properties. One should keep in mind, while forming a cluster, that the distance between any two points of a cluster is smaller compared to the distance between any two points of different clusters. A cluster can be thought of as an image region. 1 Contour-based Segmentation Contours or edges are the line segments (curved or straight) that separate one region from the other. Therefore, an edge detection technique can be used for segmentation.

To partition the image into several subimages, one should keep in mind the following points: • Each subimage consisting of different regions should be approximated well by some low order function. • Number of subimages should be as low as possible. • Homogeneity within a region and contrast between regions should be reasonably good. In order to achieve this goal, one can use either a multilevel thresholding algorithm [174, 58, 35] or an object/background thresholding algorithm. The multilevel thresholding algorithm depends on the number of local minima in the histogram of the image.

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