Emphasizing the Essential — Wavelet Transforms

The transformation of an RDF, in particular the wavelet transform, can enhance or suppress features that are typical or atypical for a given task. Two decomposition methods are useful. 

FIGURE 5.19 Comparison of the coarse-filtered D20 transformed RDF (128 components) with the original Cartesian RDF (256 components). The transformed RDF represents a smoothed descriptor containing all the valuable information in a vector half the size of the original RDF descriptor. 

Coarse-Filtered One-Level Decomposition The coarse-filtered (low-pass) 

The resolution level can be chosen arbitrarily between 1 and J. Any of the valid combinations of coarse and detail coefficients at a certain resolution level that lead to a descriptor of the same size are possible. For example, an original RDF descriptor with 256 components (i.e., / = 6) can be decomposed up to the resolution level j = 3, and the Wavelet transform (WLT) can be represented as + D -1- + ) ( This 

Combining coarse- and detail-filtered complete decomposition results in a combination of the coarse coefficients of the last resolution level and all the detail coefficients D -  

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