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Streaming multigrid for gradient-domain operations on large images

Streaming multigrid for gradient-domain operations on large images
Michael Kazhdan, Hugues Hoppe.
ACM Trans. Graphics (SIGGRAPH), 27(3), 2008.
Perform k multigrid V-cycles in just k-1 streaming passes over the data.
Abstract: We introduce a new tool to solve the large linear systems arising from gradient-domain image processing. Specifically, we develop a streaming multigrid solver, which needs just two sequential passes over out-of-core data. This fast solution is enabled by a combination of three techniques: (1) use of second-order finite elements (rather than traditional finite differences) to reach sufficient accuracy in a single V-cycle, (2) temporally blocked relaxation, and (3) multi-level streaming to pipeline the restriction and prolongation phases into single streaming passes. A key contribution is the extension of the B-spline finite-element method to be compatible with the forward-difference gradient representation commonly used with images. Our streaming solver is also efficient for in-memory images, due to its fast convergence and excellent cache behavior. Remarkably, it can outperform spatially adaptive solvers that exploit application-specific knowledge. We demonstrate seamless stitching and tone-mapping of gigapixel images in about an hour on a notebook PC.
Hindsights: In later work, we distributed the solver computation over a cluster to handle terapixel images, and generalized the approach to operate over spherical imagery.
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