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
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Texture and Shape Synthesis on Surfaces
Proceedings of the 12th Eurographics Workshop on Rendering Techniques
ACM SIGGRAPH 2003 Papers
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
Rendering and managing spherical data with sphere quadtrees
VIS '90 Proceedings of the 1st conference on Visualization '90
Interactive digital photomontage
ACM SIGGRAPH 2004 Papers
Appearance-space texture synthesis
ACM SIGGRAPH 2006 Papers
Isocube: Exploiting the Cubemap Hardware
IEEE Transactions on Visualization and Computer Graphics
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Streaming multigrid for gradient-domain operations on large images
ACM SIGGRAPH 2008 papers
Fourier Analysis of the 2D Screened Poisson Equation for Gradient Domain Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
The rhombic dodecahedron map: an efficient scheme for encoding panoramic video
IEEE Transactions on Multimedia
Distributed gradient-domain processing of planar and spherical images
ACM Transactions on Graphics (TOG)
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Processing spherical images is challenging. Because no spherical parameterization is globally uniform, an accurate solver must account for the spatially varying metric. We present the first efficient metric-aware solver for Laplacian processing of spherical data. Our approach builds on the commonly used equirectangular parameterization, which provides differentiability, axial symmetry, and grid sampling. Crucially, axial symmetry lets us discretize the Laplacian operator just once per grid row. One difficulty is that anisotropy near the poles leads to a poorly conditioned system. Our solution is to construct an adapted hierarchy of finite elements, adjusted at the poles to maintain derivative continuity, and selectively coarsened to bound element anisotropy. The resulting elements are nested both within and across resolution levels. A streaming multigrid solver over this hierarchy achieves excellent convergence rate and scales to huge images. We demonstrate applications in reaction-diffusion texture synthesis and panorama stitching and sharpening.