Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th 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
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Surface processing methods for point sets using finite elements
Computers and Graphics
Rectangular multi-chart geometry images
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Particle-based fluid flow visualization on meshes
Proceedings of the 6th International Conference on Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa
A Superresolution Framework for High-Accuracy Multiview Reconstruction
Proceedings of the 31st DAGM Symposium on Pattern Recognition
Optimized Conformal Surface Registration with Shape-based Landmark Matching
SIAM Journal on Imaging Sciences
Journal of Computational Physics
Particle-based drop animation on meshes in real time
Computer Animation and Virtual Worlds
Real-Time Fluid Effects on Surfaces using the Closest Point Method
Computer Graphics Forum
A Super-Resolution Framework for High-Accuracy Multiview Reconstruction
International Journal of Computer Vision
| Hi-index | 0.00 |
In this paper, we propose a method to solve PDEs on surfaces with arbitrary topologies by using the global conformal parametrization. The main idea of this method is to map the surface conformally to 2D rectangular areas and then transform the PDE on the 3D surface into a modified PDE on the 2D parameter domain. Consequently, we can solve the PDE on the parameter domain by using some well-known numerical schemes on ℝ2. To do this, we have to define a new set of differential operators on the manifold such that they are coordinates invariant. Since the Jacobian of the conformal mapping is simply a multiplication of the conformal factor, the modified PDE on the parameter domain will be very simple and easy to solve. In our experiments, we demonstrated our idea by solving the Navier-Stoke’s equation on the surface. We also applied our method to some image processing problems such as segmentation, image denoising and image inpainting on the surfaces.