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Probabilistic Image Segmentation using a Markov Random Walk

Nick Larusso (CS) ‏ Brian Ruttenberg (CS) ‏ Mike Crowell (MRS) ‏. Probabilistic Image Segmentation using a Markov Random Walk. Horizontal Cell Segmentation. Horizontal cells are found in the Retina Studied to understand how the brain works Accessible Few classes of cells.

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Probabilistic Image Segmentation using a Markov Random Walk

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  1. Nick Larusso (CS)‏ Brian Ruttenberg (CS)‏ Mike Crowell (MRS)‏ Probabilistic Image Segmentation using a Markov Random Walk

  2. Horizontal Cell Segmentation Horizontal cells are found in the Retina Studied to understand how the brain works Accessible Few classes of cells www.pigeon.psy.tufts.edu/avc/husband/avc4eye.htm

  3. Horizontal Cell Segmentation Cells dyed with florescent proteins Biologists want to study neurons in vivo Study response to injury Measure cell features (ie. size, # of neurites, branching, etc.)‏ First step is finding the cell!

  4. Markov Random Walk Segmentation of the image done by a random walk with restart on pixels in the image, using a discrete time Markov chain Finding the steady state distribution of the Markov chain is the long term behavior of the random walk Steady state is the eigenvector of our random walk transition matrix

  5. Transition Matrix The transition matrix is ~3.5 million by ~3.5 million. Each value (roughly) corresponds to the probability of moving to one pixel from another Extremely sparse, but very ugly Not positive definite Not symmetric Horizontal band of non-zeros

  6. Spy Plot

  7. Parallelization Matrix divided up onto processors by rows Each processor constructs its portion of the matrix and runs BiCGSTAB Large load balancing problem due to horizontal stripe through the matrix Added ghost rows/columns that distribute the restart row throughout the matrix (each processor has its own “local” restart)‏ Experiment on Star-P with 4 machines took 30 minutes to compute

  8. Posing the Computational Problem • (A-I) is: • Large (≈ 3.5e6 x 3.5e6)‏ • Sparse (nnz ≈ 30e6) • Non-symmetric • Real valued [-1,1]

  9. Solution Methods Iterative Krylov Subspace methods: GMRES “Generalized Minimal Residual Method” Based on the Arnoldi Iteration Arnoldi is a generalization of Lanczos to non-symmetric matrices Lanczos is based on the power method BiCGSTAB “Stabilized Biconjugate Gradient” Biconjugate gradient is a generalization of CG to non-symmetric matrices CG can also be thought of as a variation of Lanczos “stabilization” is provided by using GMRES locally between BiCG steps

  10. Parallelization Run on the Center for Bioimage Informatics cluster 16 Dual Core machines connected by fast ethernet Running 64 instances actually provides a better balance of communication and processing Complete segmentation algorithm completed in less than 3 minutes.

  11. Questions?

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