Statistical model for simulation of deformable elastic endometrial tissue shapes

Kurtek, Sebastian; Xie, Qian; Samir, Chafik; Canis, Michel

doi:10.1016/j.neucom.2015.03.098

Cited by 11 publications

(4 citation statements)

References 15 publications

(16 reference statements)

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“…A Riemannian metric on such a space provides means to define distances between shapes, to interpolate between shapes by computing shortest geodesic paths, and to explore the space by constructing the geodesic curve starting from a point into a given direction. Shape spaces have proven useful for applications in areas such as computer graphics (Kilian et al, 2007;Heeren et al, 2012;Wang et al, 2018) and vision (Heeren et al, 2018;Xie et al, 2014), medical imaging (Kurtek et al, 2011b;Samir et al, 2014;Kurtek et al, 2016;Bharath et al, 2018), computational biology (Laga et al, 2014), and computational anatomy (Miller et al, 2006;Pennec, 2009;Kurtek et al, 2011a). For an introduction to the topic, we refer to the textbook of Younes (2010).…”

Section: Related Workmentioning

confidence: 99%

Parametrizing Product Shape Manifolds by Composite Networks

Sassen¹,

Hildebrandt²,

Rumpf³

et al. 2023

Preprint

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Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural network approximation. We show that this is indeed possible for shape spaces with a special product structure, namely those smoothly approximable by a direct sum of low-dimensional manifolds. Our proposed architecture leverages this structure by separately learning approximations for the low-dimensional factors and a subsequent combination. After developing the approach as a general framework, we apply it to a shape space of triangular surfaces. Here, typical examples of data manifolds are given through datasets of articulated models and can be factorized, for example, by a Sparse Principal Geodesic Analysis (SPGA). We demonstrate the effectiveness of our proposed approach with experiments on synthetic data as well as manifolds extracted from data via SPGA.

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Section: Related Workmentioning

confidence: 99%

Parametrizing Product Shape Manifolds by Composite Networks

Sassen¹,

Hildebrandt²,

Rumpf³

et al. 2023

Preprint

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“…The simplicity of the computation of this pseudo-distance has led to several implementations [5,38], which have been shown to be effective in applications, see e.g. [30,36,37,41].…”

Section: Related Work In Riemannian Shape Analysismentioning

confidence: 99%

Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework

Hartman¹,

Sukurdeep²,

Klassen³

et al. 2022

Preprint

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This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic distances between parametrized or unparametrized immersed surfaces represented as 3D meshes. Building on this, we develop tools for the statistical shape analysis of sets of surfaces, including methods for estimating Karcher means and performing tangent PCA on shape populations, and for computing parallel transport along paths of surfaces. Our proposed approach fundamentally relies on a relaxed variational formulation for the geodesic M. Bauer and E.

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“…Later, Jermyn et al [13] used a different representation of surfaces termed square-root normal fields (SRNFs) for the same purpose, which was based on an elastic Riemannian metric. This method was successfully applied to study shapes of endometrial tissues and cropped faces [16,17]. The last two approaches overcome the issue of re-parameterization and result in natural shape models.…”

Section: Introductionmentioning

confidence: 99%

A Novel Riemannian Framework for Shape Analysis of Annotated Surfaces

Kurtek¹

2015

Procedings of the Proceedings of the 1st International Workshop on DIFFerential Geometry in Computer Vision for Analysis of Sha

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We present a novel, parameterization-invariant method for shape analysis of annotated surfaces. While the method can handle various types of annotation including color and texture, in this paper we focus on soft landmark annotations. Landmark annotations are commonly provided in various applications including medical imaging where an expert marks points of interest on the objects. Most methods in current literature either study shapes using landmarks only or surfaces only. In either case, the analyst is forced to ignore a lot of useful information. We propose a novel representation of surfaces that can jointly incorporate shape and landmark annotation. Our framework properly removes all shape preserving transformations from the representation space including translation, scale, rotation and re-parameterization. We present results of comparing, averaging and classifying annotated shapes on toy and real data.

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Statistical model for simulation of deformable elastic endometrial tissue shapes

Cited by 11 publications

References 15 publications

Parametrizing Product Shape Manifolds by Composite Networks

Parametrizing Product Shape Manifolds by Composite Networks

Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework

A Novel Riemannian Framework for Shape Analysis of Annotated Surfaces

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