Parametrization of Closed Surfaces for 3-D Shape Description

Brechbühler, Christian; Gerig, Guido; Kübler, Olaf

doi:10.1006/cviu.1995.1013

Cited by 592 publications

(450 citation statements)

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“…Brechbühler, Styner, and Gerig, for example, developed approaches based on spherical harmonic descriptions of shape segmentations. The spherical harmonic representations are first aligned and then sampled into surface meshes to establish correspondence [15,97]. This idea is an extension of earlier work using Fourier descriptors to parameterize closed contours in two dimensions [88,71].…”

Section: Computationally-derived Shape Modelsmentioning

confidence: 99%

“…A parametric representation defines shape as a function of a set of parameters. The SPHARM methodology [15,98], for example, represents shape boundaries as a linear combination of spherical harmonic basis functions. Other methods have been proposed that rely on wavelet basis functions [81] and Fourier decompositions [101].…”

Section: Shape Representationmentioning

confidence: 99%

“…Outside of the shape analysis literature, a standard approach to statistical model selection is to choose a model that explains the sample data in an optimally e cient way, while avoiding overfitting to the data [50,105]. The spherical harmonic, wavelet, and sampled medial mesh correspondence methods (Section 1.2), however, use a purely geometric solution; they seek only consistently regular parameterizations, not optimal correspondences [15,97,81]. The correspondence methods that minimize information content across the shape samples are capable of generating more powerful shape models [70,27], but a significant concern is how to regularize the models so that they e↵ectively balance the inherent trade-o↵ between model compactness and good representations of shape geometry.…”

Section: The Model Selection Problemmentioning

confidence: 99%

“…The three-dimensional MDL correspondence method, for example, relies on spherical parameterizations and subdivisions of an octahedral base shape with smoothed updates that are represented as Cauchy kernels [29]. The initial parameterization must be obtained through another process such as [15], which relaxes a spherical parameterization onto an input mesh. The overall procedure requires significant data preprocessing, including a sequence of optimizations-first to establish the parameterization and then on the correspondences-each of which entails a set of free parameters or inputs in addition to the segmented volumes.…”

Section: Ease-of-use and Computational Complexitymentioning

confidence: 99%

“…Correspondence positions are manipulated through the parameterization using smoothed updates represented as Cauchy kernels. The parameterization must be obtained through another process such as [15], which relaxes a spherical parameterization onto each input mesh from the sample set.…”

Section: Optimized Correspondencesmentioning

confidence: 99%

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Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

137

224

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Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from three-dimensional images and surface descriptions. While computationally-derived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address.In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the state-of-the-art by overcoming many of the limitations of existing methods. The framework uses a particle-system representation of shape, with a fast correspondence-point optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy metrics and no free parameters. The idea is to maximize both the geometric accuracy and the statistical simplicity of the shape model, in accordance with the principle of parsimony in model selection. The nonparametric representation allows the method to be applied to a larger class of problems than existing methods, including nonspherical surfaces, open surfaces, and sets of multiple surfaces.The relative simplicity of the surface representation and the low number of free parameters results in a framework that is easy to use and can operate directly on image segmentations. In collaboration with scientists from several important areas of biomedicine, I have demonstrated that the proposed method is indeed an e↵ective tool for scientific research.The specific research contributions of this dissertation are as follows. First, I describe a mathematical framework and a robust numerical algorithm for computing optimized correspondence-point shape models using an entropy-based optimization and particle-system technology. Second, I develop a series of extensions of the framework to more general classes of shape analysis problems, including the analysis of multiple-object complexes, the generalization to correspondence based on generic functions of position, an extension to handle surfaces with open boundaries, and shape modeling with simple regression. Third, I describe the application of statistical hypothesis testing, regression analysis, and multiple-analysis of covariance to the proposed shape models. I also introduce new techniques for visualization and interpretation of these statistics. Finally, in cooperation with biomedical researchers, I present validation of the above research contributions by their successful application to real-world research problems.

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Section: Computationally-derived Shape Modelsmentioning

confidence: 99%

Section: Shape Representationmentioning

confidence: 99%

Section: The Model Selection Problemmentioning

confidence: 99%

Section: Ease-of-use and Computational Complexitymentioning

confidence: 99%

Section: Optimized Correspondencesmentioning

confidence: 99%

See 3 more Smart Citations

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

137

224

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Association of Maternal Psychological Distress With In Utero Brain Development in Fetuses With Congenital Heart Disease

Kapse

Jacobs

et al. 2020

JAMA Pediatr

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IMPORTANCE Prenatal maternal psychological distress can result in detrimental mother and child outcomes. Maternal stress increases with receipt of a prenatal diagnosis of fetal congenital heart disease (CHD); however, the association between maternal stress and the developing brain in fetuses with CHD is unknown.OBJECTIVE To determine the association of maternal psychological distress with brain development in fetuses with CHD. DESIGN, SETTING, AND PARTICIPANTS This longitudinal, prospective, case-control study consecutively recruited 48 pregnant women carrying fetuses with CHD and 92 healthy volunteers with low-risk pregnancies from the Children'

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