Metric-aware processing of spherical imagery
ACM Trans. Graphics (SIGGRAPH Asia), 29(6), 2010.
Adaptively discretized equirectangular map for accurate spherical processing.
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.
No hindsights yet.
ACM Copyright Notice
Copyright by the Association for Computing Machinery, Inc. Permission to make digital or
hard copies of part or all of this work for personal or classroom use is granted without fee provided that
copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the
full citation on the first page. Copyrights for components of this work owned by others than ACM must be
honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to
redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications
Dept, ACM Inc., fax +1 (212) 869-0481, or email@example.com. The definitive version of this paper can be
found at ACM's Digital Library http://www.acm.org/dl/.