Digital halftoning
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
SMI '03 Proceedings of the Shape Modeling International 2003
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2007 papers
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
Direct sampling on surfaces for high quality remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Constructing Laplace operator from point clouds in Rd
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Sub-sampling for efficient spectral mesh processing
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Approximating a gram matrix for improved kernel-based learning
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Efficient and prioritized point subsampling for CSRBF compression
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
Blue-noise point sampling using kernel density model
ACM SIGGRAPH 2011 papers
Differential domain analysis for non-uniform sampling
ACM SIGGRAPH 2011 papers
Point sampling with general noise spectrum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Adaptive surface splatting for facial rendering
Computer Animation and Virtual Worlds
Computer Graphics Forum
Geodesic analysis on the gaussian RKHS hypersphere
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Edge-aware point set resampling
ACM Transactions on Graphics (TOG)
Line segment sampling with blue-noise properties
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG)
Least-squares hermite radial basis functions implicits with adaptive sampling
Proceedings of Graphics Interface 2013
Improving spatial coverage while preserving the blue noise of point sets
Computer-Aided Design
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A central problem in computer graphics is finding optimal sampling conditions for a given surface representation. We propose a new method to solve this problem based on spectral analysis of manifolds which results in faithful reconstructions and high quality isotropic samplings, is efficient, out-of-core, feature sensitive, intuitive to control and simple to implement. We approach the problem in a novel way by utilizing results from spectral analysis, kernel methods, and matrix perturbation theory. Change in a manifold due to a single point is quantified by a local measure that limits the change in the Laplace-Beltrami spectrum of the manifold. Hence, we do not need to explicitly compute the spectrum or any global quantity, which makes our algorithms very efficient. Although our main focus is on sampling surfaces, the analysis and algorithms are general and can be applied for simplifying and resampling point clouds lying near a manifold of arbitrary dimension.