Distributed Multigrid for Processing Huge Spherical Images Michael Kazhdan Johns Hopkins University

Solution Streaming Pass 1 Streaming Pass 2 Constraints Poisson Solvers for Large Image Processing 3.3 Gigapixels composited from 643 photographsFitting a scalar field to gradients by solving the Poisson equation Challenge : At 3.3 billion pixels, the system size is 90 GB Solution ‡ : With a streaming solver, we get a solution in 88 minutes with a peak memory of 408MB ‡ Kazhdan and Hoppe, 2008 Streaming Multigrid for Processing Large Images

Digitized Sky Survey 1790 individual 529-megapixel plates  One terapixel image Challenge : At one trilllion pixels, we would need: 27 TB of disk space 26,000 minutes 120 GB of memory Streaming Poisson Solvers for Large Image Processing Solution : With a distributed solver we can split the storage, memory, and computation. Distributed, Streaming Multigrid for Processing Huge Image CPU 1CPU 2... CPU P

Spherical Image Processing Parameterize the sphere over a regular 2D domain and solve the Poisson equation over the 2D domain Challenges : 1] Extrinsic Approach: does not account for distortion due to the parameterization. 2] Intrinsic Approach: defines a system that is inhomogenous and difficult to solve. Solutions : 1] Extrinsic Approach: choose a mapping to a 2D domain that is less distorting. [Kunszt et al.] 2] Intrinsic Approach: adapt the system to account for the in-homogeneity. Hierarchical structure enables the use of multigrid solvers N S N A D BC GF H E N SS SS Distributed, Streaming Multigrid for Processing Huge Spherical Images

Conclusion We will explore the implementation of distributed and streaming solvers capable of processing planar and spherical imagery. Distributed, Streaming Multigrid for Processing Huge Spherical Images Computational Scope : Processing terapixel imagery on large networked clusters Processing gigapixel imagery on multi-core machines Processing megapixel imagery on the GPU. Theoretical Scope : Solve the homogenous Poisson equation Incorporate non-trivial boundary conditions Extend to inhomogenous systems via alg. multigrid Empirical Scope : Image processing Video processing Level sets Incompressible fluids Atmospherical dynamics