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Distributed Multigrid for Processing Huge Spherical Images

Explore the use of distributed and streaming solvers for processing planar and spherical imagery, solving the Poisson equation over 2D domains for terapixel, gigapixel, and megapixel imagery on various computational platforms.

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Distributed Multigrid for Processing Huge Spherical Images

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

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

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

  4. Distributed, StreamingMultigrid for Processing Huge Spherical Images D A Spherical Image Processing Parameterize the sphere over a regular 2D domain andsolve the Poisson equation over the 2D domain Hierarchical structureenables the use of multigrid solvers B C G F Challenges: 1] Extrinsic Approach: does not accountfor distortion due to the parameterization. 2] Intrinsic Approach: defines a systemthat is inhomogenous and difficult to solve. Solutions: 1] Extrinsic Approach: choose a mapping to a2D domain that is less distorting. [Kunszt et al.] 2] Intrinsic Approach: adapt the system toaccount for the in-homogeneity. H E N N S S S N S S

  5. Distributed, StreamingMultigrid for Processing Huge Spherical Images Conclusion We will explore the implementation of distributed and streamingsolvers capable of processing planar and spherical imagery. • Computational Scope: • Processing terapixel imageryon large networked clusters • Processing gigapixel imageryon multi-core machines • Processing megapixelimagery on the GPU. • Theoretical Scope: • Solve the homogenousPoisson equation • Incorporate non-trivialboundary conditions • Extend to inhomogenous systems via alg. multigrid • Empirical Scope: • Image processing • Video processing • Level sets • Incompressible fluids • Atmospherical dynamics

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