By Sambhunath Biswas
This booklet offers with numerous photo processing and computing device imaginative and prescient difficulties successfully with splines and comprises: the importance of Bernstein Polynomial in splines, exact assurance of Beta-splines functions that are rather new, Splines in movement monitoring, a number of deformative versions and their makes use of. ultimately the publication covers wavelet splines that are effective and powerful in numerous picture applications.
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Extra info for Bezier & Splines in Image Processing & Machine Vision
Consider a scheme that repeatedly uses an object/background segmentation algorithm for extraction of homogeneous patches. Consider an L-level image F0 (x, y). The input gray image F0 (x, y) initially provides a threshold, s on application of the object/background thresholding algorithm. The threshold, s partitions the image F0 (x, y) into two subimages F01 (x, y) and F02 (x, y). The graylevels in F01 (x, y) lie in the interval 42 2 Image Segmentation [0, s] and in F02 (x, y), it is limited to (s, L − 1].
Assume for illustration purposes, that we are using segmentation for image compression. We can think of a compression scheme that is based on modeling compact homogeneous regions or patches using B´ezier-Bernstein polynomial function. Given an image, we therefore ﬁrst try to extract from it the homogeneous subimages. There are many approaches [173, 65, 74] to achieve this goal. For example, it can be based on pixel level decision making such as iterative pixel modiﬁcation, region growing, or adaptive region growing, or it can be based on multilevel thresholding.
17) Brp Dzq u (1 − u) r = p−r v (1 − v) z q−z Vrz , r=0 z=0 p! r! , Dzq = of the B´ezier-Bernstein surface. q! (q−z)z! p and q deﬁne the order 44 2 Image Segmentation To approximate an arbitrary image surface f (x, y) of size M × M ,f (x, y) should be deﬁned in terms of a parametric surface (here spq ) with the parameters u, v in [0, 1]. Therefore, the function f (x, y) can be thought in terms of (i−1) (j−1) g(u, v) where u = (M −1) ; i = 1, 2 · · · , M and v = (M −1) ; j = 1, 2 · · · , M . Now choose the weighted least square technique for estimation of parameters Vrz for reconstruction of the decoded surface.