Population Shape Regression From Random Design Data

Davis, Bradley Moore; Fletcher, P. Thomas; Bullitt, Elizabeth; Joshi, Sarang

doi:10.1109/iccv.2007.4408977

Cited by 154 publications

(123 citation statements)

References 36 publications

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“…A major feature of the di↵eomorphic approach to shape modeling is that di↵eomorphic flows are invertible and, thus, a metric may be defined in the space of the deformations. This property has been used by Joshi and Davis to define a mean anatomical image with variation, and they apply these estimators to the problems of unbiased anatomical atlas construction and regression analysis [62,32].…”

Section: Computationally-derived Shape Modelsmentioning

confidence: 99%

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

139

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%

Shape Modeling and Analysis with Entropy-Based Particle Systems

Cates

Fletcher

Styner

et al. 2007

Lecture Notes in Computer Science

139

224

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“…This is the case for instance for features sampled on a surface or points sampled along a trajectory (time sequences). While the one dimensional case can be tackled by regression [21], the problem for higher dimensional sub-manifolds remains quite open. Some solutions may come from manifold embedding techniques as exemplified for instance in [17].…”

Section: Covariance Matrix and Principal Geodesic Analysismentioning

confidence: 99%

Statistical Computing on Non-Linear Spaces for Computational Anatomy

Pennec

Fillard

2015

Handbook of Biomedical Imaging

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Computational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings.

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“…For instance, they have been used to model shape changes in the brain [1] and human motion [3]. In this work we tackle the problem of approximating the Probability Density Function (PDF) of a potentially large dataset that lies on a known Riemannian manifold.…”

Section: Institut De Robòtica I Informàtica Industrial (Csic-upc) 080mentioning

confidence: 99%

Geodesic Finite Mixture Models

Simo-Serra¹,

Torras²,

Moreno-Noguer³

2014

Proceedings of the British Machine Vision Conference 2014

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The use of Riemannian manifolds and their statistics has recently gained popularity in a wide range of applications involving non-linear data modeling. For instance, they have been used to model shape changes in the brain [1] and human motion [3]. In this work we tackle the problem of approximating the Probability Density Function (PDF) of a potentially large dataset that lies on a known Riemannian manifold. We address this by creating a completely data-driven algorithm consistent with the manifold, i.e., an algorithm that yields a PDF defined exclusively on the manifold.In the proposed finite mixture model, we simultaneously consider multiple tangent spaces, distributed along the whole manifold as seen in Fig. 1. We draw inspiration on the unsupervised Expectation Maximization (EM) algorithm from [2], which given data lying in an Euclidean space, automatically computes the number of model components that Minimize a Message Length (MML) cost. By representing each component as a distribution on the tangent space at its corresponding mean on the manifold, we are then able to generalize the algorithm to Riemannian manifolds and at the same time mitigate the accuracy loss produced when using a single tangent space.Given an input dataset, [2] starts by randomly initializing a large number of components. During the Maximization (M) step, the MML criterion is used to annihilate those components not well supported by the data. In addition, upon EM convergence, the least probable mixture component is also forcibly annihilated and the algorithm continues until a minimum number of components is reached.In order to extend [2] to Riemannian manifolds, we define each mixture component as a normal distribution on its own tangent space T µ k M, with a mean µ k and a concentration matrix Γ k = Σ −1 k :

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Population Shape Regression From Random Design Data

Cited by 154 publications

References 36 publications

Shape Modeling and Analysis with Entropy-Based Particle Systems

Shape Modeling and Analysis with Entropy-Based Particle Systems

Statistical Computing on Non-Linear Spaces for Computational Anatomy

Geodesic Finite Mixture Models

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