Streaming multigrid for gradient-domain operations on large images

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 inmemory 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...

• Type: Journal
• Year: 2008
• Where: TOG
• Authors: Michael M. Kazhdan, Hugues Hoppe
• Keywords: Images, Second-order Finite Elements, Single Streaming Passes, TOG 2008