Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Size functions for comparing 3D models
Pattern Recognition
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
A survey of content based 3D shape retrieval methods
Multimedia Tools and Applications
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Möbius voting for surface correspondence
ACM SIGGRAPH 2009 papers
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Ricci Flow for 3D Shape Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Interior distance using barycentric coordinates
SGP '09 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Symmetry factored embedding and distance
ACM SIGGRAPH 2010 papers
ACM Transactions on Graphics (TOG)
International Journal of Computer Vision
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Shape Recognition with Spectral Distances
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM SIGGRAPH 2011 papers
Efficient many-to-many feature matching under the l1 norm
Computer Vision and Image Understanding
Object categorization using bone graphs
Computer Vision and Image Understanding
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
A new algorithm for computing the 2-dimensional matching distance between size functions
Pattern Recognition Letters
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Comparison of Perceptually-Based Metrics for Objective Evaluation of Geometry Processing
IEEE Transactions on Multimedia
Characterizing shape using conformal factors
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
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A practical guide for researchers who are exploring the new frontiers of 3D shape analysis and managing the complex mathematical tools that most methods rely on. Many research solutions come from advances in pure and applied mathematics, as well as from re-reading classical mathematical theories. Managing these math tools is critical to understanding and solving current problems in 3D shape analysis. This course is designed to help mathematicians and scientists communicate in a world where boundaries between disciplines are (fortunately) blurred, so they can quickly find the right mathematical tools for a bright intuitive idea and strike a balance between theoretical rigor and computationally feasible solutions. The course presents basic concepts in differential geometry and proceeds to advanced topics in algebraic topology, always keeping an eye on their computational counterparts. It includes examples of applications to shape correspondence, symmetry detection, and shape retrieval that show how these mathematical concepts can be translated into practical solutions.