Statistical 2D and 3D Shape Analysis Using Non-Euclidean Metrics

Larsen, Rasmus; Hilger, Klaus Baggesen; Wrobel, Mark C.

doi:10.1007/3-540-45787-9_54

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…A good representation of the training data is particularly hard to obtain in three dimensions. Finding a basis of homologous points is thus a fundamental issue that comes before generalized Procrustes alignment [3] and decomposition [4] in the shape tangent space.…”

Section: Introductionmentioning

confidence: 99%

Shape Modelling Using Markov Random Field Restoration of Point Correspondences

Paulsen

Hilger

2003

Lecture Notes in Computer Science

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Abstract. A method for building statistical point distribution models is proposed. The novelty in this paper is the adaption of Markov random field regularization of the correspondence field over the set of shapes. The new approach leads to a generative model that produces highly homogeneous polygonized shapes and improves the capability of reconstruction of the training data. Furthermore, the method leads to an overall reduction in the total variance of the point distribution model. Thus, it finds correspondence between semi-landmarks that are highly correlated in the shape tangent space. The method is demonstrated on a set of human ear canals extracted from 3D-laser scans.

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Section: Introductionmentioning

confidence: 99%

Shape Modelling Using Markov Random Field Restoration of Point Correspondences

Paulsen

Hilger

2003

Lecture Notes in Computer Science

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Growth modeling of human mandibles using non-Euclidean metrics

Hilger

Larsen

Wrobel

2003

Medical Image Analysis

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From a set of 31 three-dimensional computed tomography (CT) scans we model the temporal shape and size of the human mandible for analysis, simulation, and prediction purposes. Each anatomical structure is represented using 14851 semi-landmarks, and mapped into Procrustes tangent space. Exploratory subspace analyses are performed leading to linear models of mandible shape evolution in Procrustes space. The traditional variance analysis results in a one-dimensional growth model. However, working in a non-Euclidean metric results in a multimodal model with uncorrelated modes of biological variation related to independent component analysis. The applied non-Euclidean metric is governed by the correlation structure of the estimated noise in the data. The generative models are compared, and evaluated on the basis of a cross validation study. The new non-Euclidean analysis is completely data driven. It not only gives comparable results w.r.t. previous studies of the mean modeling error, but seems to better correlate to growth, and in addition provides the data analyst with alternative hypothesis of plausible shape evolution; hence aiding in the understanding of cranio-facial growth.

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Sparse modeling of landmark and texture variability using the orthomax criterion

2006

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In the past decade, statistical shape modeling has been widely popularized in the medical image analysis community. Predominantly, principal component analysis (PCA) has been employed to model biological shape variability. Here, a reparameterization with orthogonal basis vectors is obtained such that the variance of the input data is maximized. This property drives models toward global shape deformations and has been highly successful in fitting shape models to new images. However, recent literature has indicated that this uncorrelated basis may be suboptimal for exploratory analyses and disease characterization. This paper explores the orthomax class of statistical methods for transforming variable loadings into a simple structure which is more easily interpreted by favoring sparsity. Further, we introduce these transformations into a particular framework traditionally based on PCA; the Active Appearance Models (AAMs). We note that the orthomax transformations are independent of domain dimensionality (2D/3D etc.) and spatial structure. Decompositions of both shape and texture models are carried out. Further, the issue of component ordering is treated by establishing a set of relevant criteria. Experimental results are given on chest radiographs, magnetic resonance images of the brain, and face images. Since pathologies are typically spatially localized, either with respect to shape or texture, we anticipate many medical applications where sparse parameterizations are preferable to the conventional global PCA approach.

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Statistical 2D and 3D Shape Analysis Using Non-Euclidean Metrics

Cited by 3 publications

References 13 publications

Shape Modelling Using Markov Random Field Restoration of Point Correspondences

Shape Modelling Using Markov Random Field Restoration of Point Correspondences

Growth modeling of human mandibles using non-Euclidean metrics

Sparse modeling of landmark and texture variability using the orthomax criterion

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