Wavelet transform coarse-filtered

The coarse- or detail-filtered wavelet transform or a combination of the coefficients for an RDF descriptor at a certain resolution level is done right before any postprocessing, like normalization. 

Low-pass, or coarse-filtered, wavelet transforms are valuable as compressed representations of RDF descriptors for fast similarity searches in binary databases. Decreasing the resolution generally reduces the size of an RDF descriptor. However, coarse-filtered wavelet transforms, which are already half the size of a nontransformed descriptor, conserve more information than the corresponding RDF descriptors. Figure 5.24 shows a comparison of a filtered transform and an RDF descriptor. Even though both functions have the same size (i.e., same number of components), the RDF used for transform originally had a higher resolution and size. This is the reason why additional peaks appear in the transform that do not occur in the RDF descriptor. 

The additional information primarily affects analysis methods that rely on the appearance of individual peaks rather than the shape of the entire descriptor. Thus, statistical parameters like correlation coefficients and skewness are affected to a minor extent. However, coarse-filtered wavelet transformations lead to an increase in valuable information. 

FIGURE 5.21 Combination coarse- and detail-filtered transformed RDF descriptor performed at the highest resolution level (J = 6). The transform is an alternative representation of an RDF in the wavelet domain. This signal consists of the coefficients G ) + D -1- 0(S)... 

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