Distributed Multigrid for Processing Huge Spherical Images

Michael KazhdanJohns 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 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

N

S

N

A D

B CG F

H E

N

S S

S S

Distributed, Streaming Multigrid for Processing Huge Spherical Images

2

2

2sin

1sin

sin

12

ff

fS

2

2

2

2

y

f

x

ff

dd sin

dydx

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