By Professor Dr. Heinrich Niemann (auth.)
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Extra info for Pattern Analysis
1. The prefilter is to assure band limitation of the pattern. Sampling is assumed here to be done equally spaced and in orthogonal directions in the case of images or three-dimensional scenes. 17]. Storage and transmission may involve modulation, error correcting and error detecting coding, and their inverse operations. This is not considered because it is of little interest to pattern analysis. 2] that pre- and postfilters may be chosen as ideal low-pass filters with cutoff frequencies chosen to avoid aliasing effects.
57). The impulse response is very useful because it allows one to compute the output h(x) of a linear, shift-invariant system to any input f(x). 59) In the discrete case this amounts to hJ. = I v=- = \'/.. v=- g. 60) 41 = v~u may be approximated arbitrarily closely by an impulse of height f(v~u) and width ~u, the whole function may be represented by a sum of impulses. 57). 6-15] for the discrete case. 6 is one reason for the importance of linear, shift-invariant systems. It gives a fairly simple closed-form solution.
8]. 13). 6]). Having transformed a number of subpatterns which cover the whole pattern the next step is to quantize the coefficients cv of the subpatterns. It is useful to normalize cv by its variance and to quantize the normalized coefficients. 2. 6]. The best transformation in the sense of minimum mean-square error and also of subjective quality is discrete Karhunen-Loeve transformation, but the Fourier and Hadamard transformations perform nearly as well. 5 Ms coefficients should be stored for a subpattern with Ms sample values.