A Probabilistic Theory of Pattern Recognition (Stochastic by Luc Devroye

By Luc Devroye

A self-contained and coherent account of probabilistic options, masking: distance measures, kernel ideas, nearest neighbour ideas, Vapnik-Chervonenkis concept, parametric category, and have extraction. each one bankruptcy concludes with difficulties and routines to additional the readers figuring out. either examine employees and graduate scholars will take advantage of this wide-ranging and up to date account of a quick- relocating box.

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If multiple images of a scene are obtained, noise is effectively reduced by ensemble averaging. Let gk(i,j) denote the kth image (k=1,2, ... n). 12) gk(i,j) This simple averaging of multiple images reduces noise by a factor of (tin) in the variance without loss of detail. A simple method of smoothing is to take an average over a local region, called a 'window'. A conventional way is to replace a pixel g (i,j) by an average of pixels in the 3 x 3 window around the pixel. 2 Geometrical Correction Geometrical distortion is caused by optical and electronic imaging systems.

15) y' = hy(x,y) These equations are usually linear (for perspective distortion) or quadratic (for camera tube distortion as shown in Fig. 21). N ow positions of image points are corrected, and thus lengths or areas can be precisely calculated. Sometimes correction of an original image is necessary so that image processing may be applied to a better image. This is called resampling and usually takes much computation. (x,y) and g(x,y) denote the ideal and distorted image respectively. 16) f(x,y) =g(x', y') where x' and y' are defined by Eq.

For each edge point, the curve is obtained in the parameter space. The rest of the processing is the same as that described in the previous subsection. If the direction of edges is known, curves in the parameter space also degenerate to points. The direction of an edge () represents dy/dx of the equation of the curve. Edge-Following Methods p .. : . •• • IT e--- Fig. 21. Hough transformation of edges with known directions For example, if a curve is represented by Eq. 41), the following equation is derived by differentiating Eq.

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