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.
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