Admissible Diffusion Wavelets and Their Applications in Space-Frequency Processing

Citations Over TimeTop 11% of 2012 papers

Abstract

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.

Related Papers

• → Critically Sampled Wavelets With Composite Dilations(2011)14 cited
• WAVELETS: AN ELEMENTARY INTRODUCTION AND EXAMPLES(1995)
• → On the lifting construction of a class of non-separable 2d orthonormal wavelets(2004)1 cited
• → Multicomposite wavelet estimation(2011)
• ANALYTIC WAVELETS AND MULTIRESOLUTION ANALYSIS A NOTE ON CERTAIN ORTHOGONALITY CONDITIONS(2004)