distributed multigrid for processing huge spherical images michael kazhdan johns hopkins university
TRANSCRIPT
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 equationChallenge:At 3.3 billion pixels, thesystem size is 90 GB
Solution‡:With a streaming solver, weget a solution in 88 minuteswith 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 space26,000 minutes120 GB of memory
Streaming Poisson Solvers for Large Image Processing
Solution:With a distributed solver we can split thestorage, memory, and computation.
Distributed, Streaming Multigrid for Processing Huge Image
CPU 1 CPU 2 ... CPU P
Spherical Image Processing
Parameterize the sphere over a regular 2D domain andsolve the Poisson equation over the 2D domain
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.
Hierarchical structure enables the use of multigrid solvers
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B CG F
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Distributed, Streaming Multigrid for Processing Huge Spherical Images
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Conclusion
We will explore the implementation of distributed and streamingsolvers 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