Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast level set method for propagating interfaces
Journal of Computational Physics
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A Level-Set Approach to 3D Reconstruction from Range Data
International Journal of Computer Vision
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
International Journal of Computer Vision
A PDE-based fast local level set method
Journal of Computational Physics
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Digital Image Processing
Geometric surface smoothing via anisotropic diffusion of normals
Proceedings of the conference on Visualization '02
Optimal Surface Smoothing as Filter Design
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Polyhedral Surface Smoothing with Simultaneous Mesh Regularization
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Geometric partial differential equations in image analysis: past, present, and future
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 3)-Volume 3 - Volume 3
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
The trilateral filter for high contrast images and meshes
EGRW '03 Proceedings of the 14th Eurographics workshop on Rendering
Fuzzy Vector Median-Based Surface Smoothing
IEEE Transactions on Visualization and Computer Graphics
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
Modeling Deformable Surfaces with Level Sets
IEEE Computer Graphics and Applications
Rough Interface Reconstruction Using the Level Set Method
VIS '04 Proceedings of the conference on Visualization '04
A sharpness dependent filter for mesh smoothing
Computer Aided Geometric Design - Special issue: Geometry processing
Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vectorfield isosurface-based reconstruction from oriented points
SIGGRAPH '05 ACM SIGGRAPH 2005 Sketches
The trilateral filter for high contrast images and meshes
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
A variational approach to Eulerian geometry processing
ACM SIGGRAPH 2007 papers
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
A Sharpness-Dependent Filter for Recovering Sharp Features in Repaired 3D Mesh Models
IEEE Transactions on Visualization and Computer Graphics
Technical Section: A direction-oriented sharpness dependent filter for 3D polygon meshes
Computers and Graphics
An Improved LOT Model for Image Restoration
Journal of Mathematical Imaging and Vision
Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
International Journal of Computer Vision
Geometric Mesh Denoising via Multivariate Kernel Diffusion
MIRAGE '09 Proceedings of the 4th International Conference on Computer Vision/Computer Graphics CollaborationTechniques
A sharpness dependent filter for mesh smoothing
Computer Aided Geometric Design - Special issue: Geometry processing
Geometric surface evolution with tangential contribution
Journal of Computational and Applied Mathematics
IEEE Transactions on Image Processing
A smart stochastic approach for manifolds smoothing
SGP '08 Proceedings of the Symposium on Geometry Processing
Feature-preserving kernel diffusion for surface denoising
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
ℓ1-Sparse reconstruction of sharp point set surfaces
ACM Transactions on Graphics (TOG)
Feature-preserving mesh denoising via attenuated bilateral normal filtering and quadrics
Proceedings of the 26th Spring Conference on Computer Graphics
Higher-Order Feature-Preserving Geometric Regularization
SIAM Journal on Imaging Sciences
A level-set method for skinning animated particle data
SCA '11 Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing - Volume Part II
3D shape from unorganized 3d point clouds
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Partial differential equations for interpolation and compression of surfaces
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Mode Decomposition Evolution Equations
Journal of Scientific Computing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
CUDA optimization strategies for compute- and memory-bound neuroimaging algorithms
Computer Methods and Programs in Biomedicine
A Gauss-Newton Method for the Integration of Spatial Normal Fields in Shape Space
Journal of Mathematical Imaging and Vision
Image Denoising Using Mean Curvature of Image Surface
SIAM Journal on Imaging Sciences
Surface embedding narrow volume reconstruction from unorganized points
Computer Vision and Image Understanding
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We propose that the generalization of signal and image processing to surfaces entails filtering the normals of the surface, rather than filtering the positions of points on a mesh. Using a variational strategy, penalty functions on the surface geometry can be formulated as penalty functions on the surface normals, which are computed using geometry-based shape metrics and minimized using fourth-order gradient descent partial differential equations (PDEs). In this paper, we introduce a two-step approach to implementing geometric processing tools for surfaces: (i) operating on the normal map of a surface, and (ii) manipulating the surface to fit the processed normals. Iterating this two-step process, we efficiently can implement geometric fourth-order flows by solving a set of coupled second-order PDEs. The computational approach uses level set surface models; therefore, the processing does not depend on any underlying parameterization. This paper will demonstrate that the proposed strategy provides for a wide range of surface processing operations, including edge-preserving smoothing and high-boost filtering. Furthermore, the generality of the implementation makes it appropriate for very complex surface models, for example, those constructed directly from measured data.