Elements of information theory
Elements of information theory
Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
3D Statistical Shape Models Using Direct Optimisation of Description Length
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Curvature-Based Transfer Functions for Direct Volume Rendering: Methods and Applications
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Robust Particle Systems for Curvature Dependent Sampling of Implicit Surfaces
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
A unified information-theoretic approach to groupwise non-rigid registration and model building
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Particle Systems for Efficient and Accurate High-Order Finite Element Visualization
IEEE Transactions on Visualization and Computer Graphics
Particle-Based Shape Analysis of Multi-object Complexes
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Entropy-Optimized Texture Models
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Discovering Sparse Functional Brain Networks Using Group Replicator Dynamics (GRD)
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Cortical Correspondence with Probabilistic Fiber Connectivity
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Particle Based Shape Regression of Open Surfaces with Applications to Developmental Neuroimaging
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Computer Methods and Programs in Biomedicine
Prediction of dementia by hippocampal shape analysis
MLMI'10 Proceedings of the First international conference on Machine learning in medical imaging
Geometric correspondence for ensembles of nonregular shapes
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Automatic construction of statistical shape models for vertebrae
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
A comparison study of inferences on graphical model for registering surface model to 3D image
MLMI'11 Proceedings of the Second international conference on Machine learning in medical imaging
Polynomial regression on riemannian manifolds
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Mixed-Effects shape models for estimating longitudinal changes in anatomy
STIA'12 Proceedings of the Second international conference on Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data
Group-wise cortical correspondence via sulcal curve-constrained entropy minimization
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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This paper presents a new method for constructing compact statistical point-based models of ensembles of similar shapes that does not rely on any specific surface parameterization. The method requires very little preprocessing or parameter tuning, and is applicable to a wider range of problems than existing methods, including nonmanifold surfaces and objects of arbitrary topology. The proposed method is to construct a point-based sampling of the shape ensemble that simultaneously maximizes both the geometric accuracy and the statistical simplicity of the model. Surface point samples, which also define the shape-to-shape correspondences, are modeled as sets of dynamic particles that are constrained to lie on a set of implicit surfaces. Sample positions are optimized by gradient descent on an energy function that balances the negative entropy of the distribution on each shape with the positive entropy of the ensemble of shapes. We also extend the method with a curvature-adaptive sampling strategy in order to better approximate the geometry of the objects. This paper presents the formulation; several synthetic examples in two and three dimensions; and an application to the statistical shape analysis of the caudate and hippocampus brain structures from two clinical studies.