Using partial differential equations to generate free-form surfaces: 91787
Computer-Aided Design
Rapid, stable fluid dynamics for computer graphics
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Simulating the Grassfire Transform Using an Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ridge points in Euclidean distance maps
Pattern Recognition Letters
Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
Skeletonization via distance maps and level sets
Computer Vision and Image Understanding
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Depicting fire and other gaseous phenomena using diffusion processes
SIGGRAPH '95 Proceedings of the 22nd 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
Modeling the motion of a hot, turbulent gas
Proceedings of the 24th 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
Computational fluid dynamics in a traditional animation environment
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Anisotropic nonlinear diffusion in flow visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the sixth ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
Strategies for Direct Volume Rendering of Diffusion Tensor Fields
IEEE Transactions on Visualization and Computer Graphics
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
Penalized-Distance Volumetric Skeleton Algorithm
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the Workshop on Geometry and Robotics
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Interactive shape design using volumetric implicit PDEs
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Skeletal Methods of Shape Manipulation
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Skeleton Extraction of 3D Objects with Radial Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
ACM SIGGRAPH 2003 Papers
Characterization and Recognition of 3D Organ Shape in Medical Image Analysis Using Skeletonization
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Computer-Aided Design
On the decomposition of cell clusters
Journal of Mathematical Imaging and Vision
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
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Shape skeletonization (i.e., medial axis extraction) is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. This is because medial axis (or skeleton) provides more compact representations for solid models while preserving their topological properties and other features. Meanwhile, PDE techniques are widely utilized in computer graphics fields to model solid objects and natural phenomena, formulate physical laws to govern the behavior of objects in real world, and provide means to measure the feature of movements, such as velocity, acceleration, change of energy, etc. Certain PDEs such as diffusion equations and Hamilton-Jacobi equation have been used to detect medial axes of 2D images and volumetric data with ease. However, using such equations to extract medial axes or skeletons for solid objects bounded by arbitrary polygonal meshes directly is yet to be fully explored. In this paper, we expand the use of diffusion equations to approximate medial axes of arbitrary 3D solids represented by polygonal meshes based on their differential properties. It offers an alternative but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, our system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, our model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated solid objects.