This paper presents a novel active surface segmentation algorithm using a multiscale shape representation and prior. We define a parametric model of a surface using spherical wavelet functions and learn a prior probability distribution over the wavelet coefficients to model shape variations at different scales and spatial locations in a training set. Based on this representation, we derive a pa...

An adaptive multilevel wavelet solver for elliptic equations on an optimal spherical geodesic grid is developed. The method is based on second-generation spherical wavelets on almost uniform optimal spherical geodesic grids. It is an extension of the adaptive multilevel wavelet solver [O. V. Vasilyev and N. K.-R. Kevlahan, J. Comput. Phys., 206 (2005), pp. 412–431] to curved manifolds. Wavelet ...

Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm ...

We test the consistency of estimates of the non-linear coupling constant fNL using nonGaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on estimation of fNL. Nevertheless, using spherical wavelets, we find results in very good agreement with (Muk...

This paper proposes and investigates a method for reducing potential numerical instability in the fast spherical harmonic transform algorithms proposed previously in [5,11]. The key objective of this study is a numerically reliable fast algorithm for computing the discrete Legendre transform (DLT); that is, the projection of sampled data onto the associated Legendre functions within a specified...

Abstract We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, thus, the whole series, converge to zero much more rapidly compared to the Taylor expansion of the same order. Furthermore, using numerical analysis with sixth-order polynomial expansion, we demonstrate ...

Huygens’ principle states that the solution of the wave equation radiated by a bounded source can be represented outside the source region as a superposition of spherical ‘Huygens wavelets’ radiated by secondary point-sources on a surface enclosing the primary source. This was originally proposed as a geometrical explanation of wave propagation, but as such it is conceptually problematic becaus...

Satellite gradiometry and its instrumentation is an ultra-sensitive detection technique of the space gravitational gradient (i.e. the Hesse tensor of the gravitational potential). Gradiometry will be of great signiicance in inertial navigation, gravity survey, geodynamics and earthquake prediction research. In this paper, satellite gradiometry formulated as an inverse problem of satellite geode...

This work is concerned with developing the hierarchical basis for meshless methods. A reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart. To form such hierarchical partition, a class of basic wavelet functions are introduced. Based upon the built-in consistency conditions, the di erential consistenc...

Optimality Theory (henceforth OT) (Prince and Smolensky 1993/2004) is based upon lexicographic optimization. It differs in this respect from Harmonic Grammar (henceforth HG) (Legendre et al. 1990a, Legendre et al. 1990b), which is based upon linear numeric optimization. Differences between the two have been discussed in several places, including (Legendre et al. 2006, Pater et al. 2007a, Prince...