Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
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Computer Vision and Image Understanding
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SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
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International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
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International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Statistical shape characterization using the medial representation
Statistical shape characterization using the medial representation
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Deformable solid modeling via medial sampling and displacement subdivision
Deformable solid modeling via medial sampling and displacement subdivision
Second order smoothness over extraordinary vertices
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
Continuous medial models in two-sample statistics of shape
Continuous medial models in two-sample statistics of shape
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
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IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
Statistics of pose and shape in multi-object complexes using principal geodesic analysis
Miar'06 Proceedings of the Third international conference on Medical Imaging and Augmented Reality
Retrieving articulated 3-d models using medial surfaces and their graph spectra
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Swept regions and surfaces: Modeling and volumetric properties
Theoretical Computer Science
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A crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3-D medial model that allows continuous interpolation of the medial manifold and provides a map back and forth between it and the boundary. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial co-ordinates, enabling the expression of important object properties in an object-relative coordinate system. We use these integrals to optimize correspondence during model construction, reducing variability due to the model parameterization that could potentially mask true shape change effects. Discrimination and hypothesis testing of populations of shapes are expected to benefit, potentially resulting in improved significance of shape differences between populations even with a smaller sample size.