A Fast 3D Correspondence Method for Statistical Shape Modeling

Dalai, P.; Munsell, Brent C.; Wang, Song; Tang, Jijun; Oliver, Kenton; Ninomiya, Hiroki; Zhou, Xiangrong; Fujita, Hiroshi

doi:10.1109/cvpr.2007.383143

Cited by 30 publications

(31 citation statements)

References 34 publications

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“…Medial-axis parameterizations of shape have also been used to construct nonlinear shape models and applied in a number of neurobiology studies [46,97]. Dalal, et al proposed a sliding landmark method which has been shown to compare favorably to the spherical harmonics methods [24,80]. Their method establishes correspondence by minimizing the bending energy of the thin-plate spline mapping between sample landmarks and a template.…”

Section: Computationally-derived Shape Modelsmentioning

confidence: 99%

“…Correspondence-based computational models of shape in the literature rely on spherical parameterizations of shape and can therefore represent only manifold surfaces with spherical topologies. This limitation also precludes the analysis of many important open-boundary anatomical structures such as the diaphragm [24] or of localized regions of a structure, such as head of a bone. Another important consideration is that medical or biological shapes are typically derived from the interfaces between organs or tissue types and usually defined implicitly in the form of segmented volumes, rather than explicit parameterizations, triangulations, or surface point samples.…”

Section: Shape Representationmentioning

confidence: 99%

“…Typical processing times for around 1000 correspondences in small populations (N ⇡ 20) are on the order of hours to days for MDL models [24]. Computation times may be similarly high even for unoptimized correspondence models, such as spherical harmonic models [24].…”

Section: Ease-of-use and Computational Complexitymentioning

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

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%

Section: Shape Representationmentioning

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

139

224

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“…Related to this paper is the 3D landmark-sliding method SLIDE [10] that can be used to correspond both opensurface and closed-surface shape instances. In this method, each target shape instance is first aligned with a given template shape.…”

Section: Introductionmentioning

confidence: 99%

“…Based on this alignment, an initial estimate of the corresponding landmarks is established and a landmarksliding framework is developed to refine the initial estimates of corresponding landmarks. Compared to MDL and SPHARM, this method requires less CPU time and usually leads to a PDM with better compactness, generality and specificity characteristics [10]. However, this method does not guarantee that the landmarks identified across shape instances have consistent topology.…”

Section: Introductionmentioning

confidence: 99%

3D open-surface shape correspondence for statistical shape modeling: Identifying topologically consistent landmarks

Dalal

McLaughlin

et al. 2009

2009 IEEE 12th International Conference on Computer Vision

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Anatomically Standardized Maps Reveal Distinct Patterns of Cartilage Thickness With Increasing Severity of Medial Compartment Knee Osteoarthritis

Favre

Erhart‐Hledik

Blazek

et al. 2017

Journal Orthopaedic Research

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While cartilage thickness alterations are a central element of knee osteoarthritis (OA), differences among disease stages are still incompletely understood. This study aimed to quantify the spatial-variations in cartilage thickness using anatomically standardized thickness maps and test if there are characteristic patterns in patients with different stages of medial compartment knee OA. Magnetic resonance images were acquired for 75 non-OA and 100 OA knees of varying severities (Kellgren and Lawrence (KL) scores 1-4). Three-dimensional cartilage models were reconstructed and a shape matching technique was applied to convert the models into two-dimensional anatomically standardized thickness maps. Difference thickness maps and statistical parametric mapping were used to compare the four OA and the non-OA subgroups. This analysis showed distinct thickness patterns for each clinical stage that formed a coherent succession from the non-OA to the KL 4 subgroups. Interestingly, the only significant difference for early stage (KL 1) was thicker femoral cartilage. With increase in disease severity, typical patterns developed, including thinner cartilage in the anterior area of the medial condyle (significant for KL 3 and 4) and thicker cartilage in the posterior area of the medial and lateral condyles (significant for all OA subgroups). The tibial patterns mainly consisted of thinner cartilage for both medial and lateral compartments (significant for KL 2-4). Comparing anatomically standardized maps allowed identifying patterns of thickening and thinning over the entire cartilage surface, consequently improving the characterization of thickness differences associated with OA. The results also highlighted the value of anatomically standardized maps to analyze spatial variations in cartilage thickness. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2442-2451, 2017.

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A Fast 3D Correspondence Method for Statistical Shape Modeling

Abstract: Accurately identifying corresponded landmarks from a population of shape instances is the major challenge in con-

Cited by 30 publications

References 34 publications

Shape Modeling and Analysis with Entropy-Based Particle Systems

Shape Modeling and Analysis with Entropy-Based Particle Systems

3D open-surface shape correspondence for statistical shape modeling: Identifying topologically consistent landmarks

Anatomically Standardized Maps Reveal Distinct Patterns of Cartilage Thickness With Increasing Severity of Medial Compartment Knee Osteoarthritis

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