Statistics of Anatomic Geometry: Information Theory and Automatic Model Building Carole Twining Imaging Science and Biomedical Engineering (ISBE) University of Manchester, UK Contributions from: Rhodri Davies, Stephen Marsland, Tim Cootes, Vlad Petrovic, Roy Schestowitz, & Chris Taylor
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Statistics of Anatomic Geometry:Information Theory and Automatic Model Building
Imaging Science and Biomedical Engineering (ISBE)
University of Manchester, UK
Rhodri Davies, Stephen Marsland, Tim Cootes, Vlad Petrovic,
Roy Schestowitz, & Chris Taylor
Set of Shapes
& Corresponding Points
Shape & Appearance Space
Shape & Texture Model
The Correspondence Problem
Varying correspondence varies the shape statistics
(Baumberg & Hogg)
Automatic Groupwise Correspondence
Optimisation Problem Framework:
Varying correspondence varies shape!
Vary correspondence but not shape!
Sphere & Spherical Polar coordinates
(Davies et al, IPMI 2003)
(see section on Model Evaluation Criteria)
MDL Groupwise Image Registration
groupwise dense correspondence
groupwise dense correspondence = groupwise registration
(Twining et al 2005)
Model Evaluation Criteria
Sample Set from model pdf:
General but not Specific
Specific but not General
Space of Shapes/Images
:distance on image/shape space
Size of Perturbation
Active appearance models,
IEEE Trans. Pattern Anal. Machine Intell., vol. 23, no. 6, pp. 681-685, 2001.
Active shape models – their training and application,
Computer Vision and Image Understanding, 61(1), 38-59, 1995
The use of active shape models for locating structures in medical images,
Image and Vision Computing, vol. 12, no. 6, pp. 276-285, July 1994.
Active shape model segmentation with optimal features,
IEEE Trans. Med. Imag., vol. 21, pp. 924-933, 2002.
Vertebral shape: Automatic measurement with active shape models,
Radiology, vol. 211, no. 2, pp. 571-578, 1999.
Segmentation and interpretation of MR brain images: An improved active shape model,
IEEE Trans. Med. Imag., vol. 17, pp. 1049-1067, 1998.
Further references, as well as notes on the historical meanderings in the development of these techniques
can be found on Tim Cootes’ website:
Zoom-invariant vision of figural shape: The mathematics of cores,
Computer Vision and Image Understanding, vol. 69, no. 1, pp. 055-071, 1998.
Fourier descriptors, spherical harmonics & SPHARM
Parameterisation of closed surfaces for 3D shape description,
Computer Vision, Graphics and Image Processing, vol. 61, pp. 154-170, 1995.
Elastic model-based segmentation of 3D neurological data sets,
IEEE Trans. Med. Imag., vol. 18, no. 10, pp. 828-839, Oct. 1999.
Parametrization of closed surfaces for 3D shape description,
Computer Vision and Image Understanding, vol. 61, no. 2, pp. 154-170, 1995.
Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations
of flexible fourier contour and surface models,
Medical Image Analysis, vol. 1, pp. 19-34, 1996.
Fourier descriptors, spherical harmonics & SPHARM
Parameter space warping: Shape-based correspondence between morphologically different objects,
IEEE Trans. Med. Imag., vol. 21, no. 1, pp. 31-47, Jan. 2002.
Boundary and medial shape analysis of the hippocampus in schizophrenia,
in Proc. International Conference on Medical Image Computing and Computer Aided Intervention
(MICCAI), 2003, pp. 464-471.
Feature-Based Shape correspondence
A method of automatic landmark generation for automated 3D PDM construction,
Image and Vision Computing, vol. 18, pp. 739-748, 2000.
Shape-based 3D surface correspondence using geodesics and local geometry,
in Proc. IEEE conference on Computer Vision and Pattern Recognition (CVPR), 2000, pp. 644-651.
A scheme for automatically building three-dimensional morphometric anatomical atlases: application
to a skull atlas,
Medical Image Analysis, vol. 2, no. 1, pp. 37-60, 1998.
Elastic and Distortion based methods of shape correspondence
Automated 3-D PDM construction from segmented images using deformable models,
IEEE Trans. Med. Imag., vol. 22, no. 8, pp. 1005-1013, Aug. 2003.
Morphable surface models,
International Journal of Computer Vision, vol. 38, pp. 75-91, 2000.
Modal matching for correspondence and recognition,
IEEE Trans. Pattern Anal. Machine Intell., vol. 17, no. 6, pp. 545-561, 1995.
Landmark methods for forms without landmarks: morphometrics of group differences in outline shape,
Medical Image Analysis, vol. 1, no. 3, pp. 225-244, 1997.
Minimum Description Length
This is the information theory stuff behind MDL.
Stochastic Complexity in Statistical Inquiry,
World Scientific Press, 1989.
MDL for Shape Correspondence
Note that the freely available code distributed by Thodberg is only approximate MDL, not full state-ofthe-
art MDL as used by other groups. In fact, the objective function used in these papers is equivalent
to what is used to initialise other algorithms. This fact has caused a little confusion in the literature.
MDL shape and appearance models,
in Proc. 18th Conference on Information Processing in Medical Imaging (IPMI), 2003, pp. 51-62.
Adding curvature to MDL shape models,
in Proc. 14th British Machine Vision Conference (BMVC), vol. 2, 2003, pp. 251-260.
3D Active Shape Models Using Gradient Descent Optimization of Description Length ,
MDL for 2D Shape
This uses the initial genetic algorithm search, which was later improved upon.
A minimum description length approach to statistical shape modelling,
IEEE Trans. Med. Imag., vol. 21, no. 5, pp. 525-537, May 2002.
Building optimal 2D statistical shape models,
Image and Vision Computing, vol. 21, pp. 1171-1182, 2003.
MDL for 3D Shape
3D statistical shape models using direct optimisation of description length,
in Proc. 7th European Conference on Computer Vision (ECCV), 2002, pp. 3-21.
MDL for Image Registration
A Unified Information-Theoretic Approach to Groupwise Non-Rigid Registration and Model
Building, Presented at IPMI 2005
Groupwise Non-Rigid Registration: The Minimum Description Length Approach,
In Proceedings of BMVC 2004.
A Unified Information-Theoretic Approach to the Correspondence Problem in Image Registration,
International Conference on Pattern Recognition (ICPR), Cambridge, U.K. 2004.