On minimal energy trajectories
Computer Vision, Graphics, and Image Processing
Surface reconstruction from unorganized points
Surface reconstruction from unorganized points
Matching 3-D Models to 2-D Images
International Journal of Computer Vision
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
An Efficient Algorithm for Graph Isomorphism
Journal of the ACM (JACM)
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
A Fast Backtracking Algorithm to Test Directed Graphs for Isomorphism Using Distance Matrices
Journal of the ACM (JACM)
Proceedings of the sixth ACM symposium on Solid modeling and applications
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Reflective Symmetry Descriptor
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Interpolation and Approximation of Surfaces from Three-dimensional Scattered Data Points
Dagstuhl '97, Scientific Visualization
3D zernike descriptors for content based shape retrieval
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Augmented Reeb Graphs for Content-Based Retrieval of 3D Mesh Models
SMI '04 Proceedings of the Shape Modeling International 2004
A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Computation of Isometry-Invariant Distances Between Surfaces
SIAM Journal on Scientific Computing
ACM SIGGRAPH 2002 conference abstracts and applications
Reeb graph based partial shape retrieval for non-rigid 3D object
Proceedings of the 10th International Conference on Virtual Reality Continuum and Its Applications in Industry
Image and Vision Computing
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We propose a method for 3-D shape recognition based on inexact subgraph isomorphisms, by extracting topological and geometric properties of a shape in the form of a shape model, referred to as topo-geometric shape model (TGSM). In a nutshell, TGSM captures topological information through a rigid transformation invariant skeletal graph that is constructed in a Morse theoretic framework with distance function as the Morse function. Geometric information is then retained by analyzing the geometric profile as viewed through the distance function. Modeling the geometric profile through elasticre yields a weighted skeletal representation, which leads to a complete shape signature. Shape recognition is carried out through inexact subgraph isomorphisms by determining a sequence of graph edit operations on model graphs to establish subgraph isomorphisms with a test graph. Test graph is recognized as a shape that yields the largest subgraph isomorphism with minimal cost of edit operations. In this paper, we propose various cost assignments for graph edit operations for error correction that takes into account any shape variations arising from noise and measurement errors.