Visual reconstruction
Extrapolation methods for vector sequences
SIAM Review
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to algorithms
Efficient implementation of minimal polynomial and reduced rank extrapolation methods
Journal of Computational and Applied Mathematics
A linear iteration time layout algorithm for visualising high-dimensional data
Proceedings of the 7th conference on Visualization '96
Inference of Surfaces, 3D Curves, and Junctions from Sparse, Noisy, 3D Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Efficient Simplicial Reconstructions of Manifolds from Their Samples
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Spaces and Video Trajectories: Using Isomap to Explore Video Sequences
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
First Order Augmentation to Tensor Voting for Boundary Inference and Multiscale Analysis in 3D
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-Dimensional Face Recognition
International Journal of Computer Vision
Representation Analysis and Synthesis of Lip Images Using Dimensionality Reduction
International Journal of Computer Vision
Pattern Recognition
Three-dimensional boundary detection for particle methods
Journal of Computational Physics
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Eigensolver methods for progressive multidimensional scaling of large data
GD'06 Proceedings of the 14th international conference on Graph drawing
Unsupervised learning of image manifolds by semidefinite programming
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Nonrigid embeddings for dimensionality reduction
ECML'05 Proceedings of the 16th European conference on Machine Learning
On bending invariant signatures for surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
The farthest point strategy for progressive image sampling
IEEE Transactions on Image Processing
Geodesic Methods in Computer Vision and Graphics
Foundations and Trends® in Computer Graphics and Vision
Prediction-oriented dimensionality reduction of industrial data sets
IEA/AIE'11 Proceedings of the 24th international conference on Industrial engineering and other applications of applied intelligent systems conference on Modern approaches in applied intelligence - Volume Part I
Densifying Distance Spaces for Shape and Image Retrieval
Journal of Mathematical Imaging and Vision
Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry
ACM Transactions on Graphics (TOG)
Improvement of surface roughness models for face milling operations through dimensionality reduction
Integrated Computer-Aided Engineering
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process usually relies on distances between neighboring features, mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non-convexity. Distortions resulting from using long geodesics indiscriminately lead to a known limitation of the Isomap algorithm when used to map non-convex manifolds. Presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries. The resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold, thus avoiding an inherent limitation of the Isomap algorithm. Since the proposed algorithm matches non-local structures, it is robust to strong noise. We show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques, both global and local in nature.