Active shape models—their training and application
Computer Vision and Image Understanding
Hilbert-Schmidt Lower Bounds for Estimators on Matrix Lie Groups for ATR
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Means and Averaging in the Group of Rotations
SIAM Journal on Matrix Analysis and Applications
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Medial Models Incorporating Object Variability for 3D Shape Analysis
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
Journal of Cognitive Neuroscience
Monte Carlo extrinsic estimators of manifold-valued parameters
IEEE Transactions on Signal Processing
Guest Editorial—Medial & Medical: A Good Match for Image Analysis
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
How to Put Probabilities on Homographies
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Meshless geometric subdivision
Graphical Models
Statistical Multi-Object Shape Models
International Journal of Computer Vision
Regularized Reconstruction of Shapes with Statistical a priori Knowledge
International Journal of Computer Vision
Principal Geodesic Analysis for the Study of Nonlinear Minimum Description Length
Medical Imaging and Informatics
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
Speculation on the generality of the backward stepwise view of PCA
Proceedings of the international conference on Multimedia information retrieval
A Markov random field approach to multi-scale shape analysis
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
An SL(2) Invariant Shape Median
Journal of Mathematical Imaging and Vision
Relational statistical deformation models for morphological image analysis and classification
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
2D-shape analysis using conformal mapping
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
An Elasticity-Based Covariance Analysis of Shapes
International Journal of Computer Vision
Hypothesis testing with nonlinear shape models
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Robustness in motion averaging
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
Conjugate gradient on Grassmann manifolds for robust subspace estimation
Image and Vision Computing
Lie bodies: a manifold representation of 3D human shape
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Augmentation of paramedian 3D ultrasound images of the spine
IPCAI'13 Proceedings of the 4th international conference on Information Processing in Computer-Assisted Interventions
Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds
International Journal of Computer Vision
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Principal component analysis has proven to be useful for understanding geometric variability in populations of parameterized objects. The statistical framework is well understood when the parameters of the objects are elements of a Euclidean vector space. This is certainly the case when the objects are described via landmarks or as a dense collection of boundary points. We have been developing representations of geometry based on the medial axis description or m-rep. Although this description has proven to be effective, the medial parameters are not naturally elements of a Euclidean space. In this paper we show that medial descriptions are in fact elements of a Lie group. We develop methodology based on Lie groups for the statistical analysis of medially-defined anatomical objects.