Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
CONDENSATION—Conditional Density Propagation forVisual Tracking
International Journal of Computer Vision
Improved constructions of Delaunay based contour surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
Curve reconstruction: connecting dots with good reason
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Reconstruction curves with sharp corners
Proceedings of the sixteenth annual symposium on Computational geometry
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
ICONDENSATION: Unifying Low-Level and High-Level Tracking in a Stochastic Framework
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Nonlinear manifold learning for visual speech recognition
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
One-Pass Delaunay Filtering for Homeomorphic 3D Surface Reconstruction
One-Pass Delaunay Filtering for Homeomorphic 3D Surface Reconstruction
An incremental algorithm for reconstruction of surfaces of arbitrary codimension
Computational Geometry: Theory and Applications
Cross-media manifold learning for image retrieval & annotation
MIR '08 Proceedings of the 1st ACM international conference on Multimedia information retrieval
Medial set, boundary, and topology of random point sets
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Modelling of shapes without landmarks
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Nonlinear Dimensionality Reduction by Topologically Constrained Isometric Embedding
International Journal of Computer Vision
Manifold reconstruction using tangential Delaunay complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Riemannian manifold learning for nonlinear dimensionality reduction
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Bidirectional-isomorphic manifold learning at image semantic understanding & representation
Multimedia Tools and Applications
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A new algorithm for manifold learning is presented. Given only samples of a finite-dimensional differentiable manifold and no a priori knowledge of the manifold's geometry or topology except for its dimension, the goal is to find a description of the manifold. The learned manifold must approximate the true manifold well, both geometrically and topologically, when the sampling density is sufficiently high. The proposed algorithm constructs a simplicial complex based on approximations to the tangent bundle of the manifold. An important property of the algorithm is that its complexity depends on the dimension of the manifold, rather than that of the embedding space. Successful examples are presented in the cases of learning curves in the plane, curves in space, and surfaces in space; in addition, a case when the algorithm fails is analyzed.