Computer Aided Geometric Design
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd 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
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Anisotropic geometric diffusion in surface processing
Proceedings of the conference on Visualization '00
Theoretical Foundations of Anisotropic Diffusion in Image Processing
Proceedings of the 7th TFCV on Theoretical Foundations of Computer Vision
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
High-pass quantization for mesh encoding
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric surface processing via normal maps
ACM Transactions on Graphics (TOG)
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Image Compression with Anisotropic Diffusion
Journal of Mathematical Imaging and Vision
Beating the Quality of JPEG 2000 with Anisotropic Diffusion
Proceedings of the 31st DAGM Symposium on Pattern Recognition
Outer surface reconstruction for 3D fractured objects
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part II
Optimising spatial and tonal data for homogeneous diffusion inpainting
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Curvature minimization for surface reconstruction with features
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
| Hi-index | 0.00 |
Partial differential equations (PDEs) have recently shown to be very promising for image interpolation and compression. Inspired from this work, we present a PDE based approach to interpolation of surfaces from scattered point sets using the geometric diffusion equation. Triangulated surfaces are considered in the discrete setting, and the geometric diffusion equation is discretized by the finite element method directly on the triangular mesh. Furthermore, a PDE based method for lossy compression of triangulated surfaces is presented. The idea is to store only a few relevant vertex coordinates in the encoding step. In the decoding step, the remaining vertices are reconstructed by solving the geometric diffusion equation. Finally, two modified reconstruction methods are proposed that are shown to improve the compression quality for both images and surfaces. These reconstruction methods approximate instead of interpolating, and have links to Hopscotch methods for the numerical solution of PDEs. Experiments are presented illustrating that results of high quality can be obtained using simple geometric diffusion without any information on surface normals.