IEEE Trans Vis Comput Graph - Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing.

Tópicos

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{ signal(2180) analysi(812) frequenc(800) }
{ method(984) reconstruct(947) comput(926) }
{ data(3963) clinic(1234) research(1004) }
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Resumo

As signal processing tools, diffusion wavelets and biorthogonal diffusion wavelets have been propelled by recent research in mathematics. They employ diffusion as a smoothing and scaling process to empower multiscale analysis. However, their applications in graphics and visualization are overshadowed by nonadmissible wavelets and their expensive computation. In this paper, our motivation is to broaden the application scope to space-frequency processing of shape geometry and scalar fields. We propose the admissible diffusion wavelets (ADW) on meshed surfaces and point clouds. The ADW are constructed in a bottom-up manner that starts from a local operator in a high frequency, and dilates by its dyadic powers to low frequencies. By relieving the orthogonality and enforcing normalization, the wavelets are locally supported and admissible, hence facilitating data analysis and geometry processing. We define the novel rapid reconstruction, which recovers the signal from multiple bands of high frequencies and a low-frequency base in full resolution. It enables operations localized in both space and frequency by manipulating wavelet coefficients through space-frequency filters. This paper aims to build a common theoretic foundation for a host of applications, including saliency visualization, multiscale feature extraction, spectral geometry processing, etc.

Resumo Limpo

signal process tool diffus wavelet biorthogon diffus wavelet propel recent research mathemat employ diffus smooth scale process empow multiscal analysi howev applic graphic visual overshadow nonadmiss wavelet expens comput paper motiv broaden applic scope spacefrequ process shape geometri scalar field propos admiss diffus wavelet adw mesh surfac point cloud adw construct bottomup manner start local oper high frequenc dilat dyadic power low frequenc reliev orthogon enforc normal wavelet local support admiss henc facilit data analysi geometri process defin novel rapid reconstruct recov signal multipl band high frequenc lowfrequ base full resolut enabl oper local space frequenc manipul wavelet coeffici spacefrequ filter paper aim build common theoret foundat host applic includ salienc visual multiscal featur extract spectral geometri process etc

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