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Spherical Wavelet ITK Filter

Gao, Yi, Nain, Delphine, LeFaucheur, Xavier, Tannenbaum, Allen
Georgia Institute of Technology
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Submitted by Yi Gao on 2007-06-13.

This paper describes the Insight Toolkit (ITK) Spherical Wavelet object: itkSWaveletSource. This ITK object is an implementation of a paper by Schr¨oder and W. Sweldens, “Spherical Wavelets: Effi- ciently Representing Functions on the Sphere” [8], with pseudo-code given in their paper entitled “Spherical wavelets: Texture processing” [7]. In these papers, Swelden et. al. show how to do decompose a scalar signal defined on a spherical mesh into spherical wavelet coefficients (analysis step, also called forward transform), and vice-versa (synthesis step, also called inverse transform). We have implemented the spherical wavelet transform in ITK entitled itkSWaveletSource object, which will take the scalar function defined on a spherical mesh as input and apply spherical wavelet analysis and synthesis on it. In this paper, we describe our code and provide the user with enough details to reproduce the results which we present in this paper. This filter has a variety of applications including shape representation and shape analysis of brain surfaces, which was the initial motivation for this work. This paper is accompanied with the source code, input data, parameters and output data that the authors used for validating the spherical wavelet transform described in this paper.