Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Shape versus Size: Improved Understanding of the Morphology of Brain Structures
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
The space of human body shapes: reconstruction and parameterization from range scans
ACM SIGGRAPH 2003 Papers
Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
SCAPE: shape completion and animation of people
ACM SIGGRAPH 2005 Papers
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
Variational harmonic maps for space deformation
ACM SIGGRAPH 2009 papers
Multilinear (tensor) ICA and dimensionality reduction
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Exploration of continuous variability in collections of 3D shapes
ACM SIGGRAPH 2011 papers
ACM SIGGRAPH 2011 papers
Functional maps: a flexible representation of maps between shapes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Exploring collections of 3D models using fuzzy correspondences
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
SMI 2012: Full Posture-invariant statistical shape analysis using Laplace operator
Computers and Graphics
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We develop a novel formulation for the notion of shape differences, aimed at providing detailed information about the location and nature of the differences or distortions between the two shapes being compared. Our difference operator, derived from a shape map, is much more informative than just a scalar global shape similarity score, rendering it useful in a variety of applications where more refined shape comparisons are necessary. The approach is intrinsic and is based on a linear algebraic framework, allowing the use of many common linear algebra tools (e.g, SVD, PCA) for studying a matrix representation of the operator. Remarkably, the formulation allows us not only to localize shape differences on the shapes involved, but also to compare shape differences across pairs of shapes, and to analyze the variability in entire shape collections based on the differences between the shapes. Moreover, while we use a map or correspondence to define each shape difference, consistent correspondences between the shapes are not necessary for comparing shape differences, although they can be exploited if available. We give a number of applications of shape differences, including parameterizing the intrinsic variability in a shape collection, exploring shape collections using local variability at different scales, performing shape analogies, and aligning shape collections.