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Curvature Prior for MRF-based Segmentation and Shape Inpainting

Czech Technical University in Prague. Curvature Prior for MRF-based Segmentation and Shape Inpainting. This work was supported bu EU projects FP7-ICT-247870 NIFTi and FP7-ICT-247525 HUMAVIPS and the Czech project 1M0567 CAK. DAGM-OAGM 2012.

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Curvature Prior for MRF-based Segmentation and Shape Inpainting

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  1. Czech Technical University in Prague Curvature Prior for MRF-based Segmentation and Shape Inpainting This work was supported bu EU projects FP7-ICT-247870 NIFTi and FP7-ICT-247525 HUMAVIPS and the Czech project 1M0567 CAK DAGM-OAGM 2012 Alexander Shekhovtsov, Pushmeet Kohli and Carsten Rother TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAA

  2. Motivation • Would like to have a model tailored for the specific shape class Looked at higher-order MRFs and Field of Experts Experts Pixels • Focus on the curvature cost as a simple example of a shape model A.Shekhovtsov, P. Kohli, C. Rother

  3. Motivation • How can we model shapes with higher-order models? - nonlinear function of linear filters - continuous variables Black and Roth. (2009) Field of Experts hard pattern Komodakis and Paragios (2009) Pattern-based Higher Order Potentials Rother et al. (2009) Sparse Higher Order Potentials expert state soft pattern A.Shekhovtsov, P. Kohli, C. Rother

  4. Curvature in Discrete Setting • Most of the works go for explicit edge representation (discrete setting) Brukstain (2001) approximation Cell-complex Schoenemann et al. (2009) Schoenemann, Kahl ,et al. (2011) Schoenemann, Kuang, et al. (2011) Strandmark and Kahl (2011) straight on a large scale, but highly penalized • Convex relaxations in the continuous setting: Bredies et al. (2012), Goldluecke and Cremers (2011) A.Shekhovtsov, P. Kohli, C. Rother

  5. The Model • Keep the segmentation pixel-wise but assess curvature from a local window window of the higher-order model think of the curve with the lowest possible curvature consistent with discretization lager windows have a better chance of a more accurate estimate You would never thought of this curve, unless you know something A.Shekhovtsov, P. Kohli, C. Rother

  6. The Model Rother et al. (2009) • – pixel-wise segmentation densely, at every pixel location, there is a higher-order term restriction to the window Energy window locations Higher-order term: for fixed y a modular (linear) functions of x lower envelope of the modular functions of x A.Shekhovtsov, P. Kohli, C. Rother

  7. The Model • What this model can do? in the minimum or A.Shekhovtsov, P. Kohli, C. Rother

  8. Minimization • Good news: minimization reduces to pairwise model: expands as -join optimization in segmentation and latent variables y can combine with standard MRF models • Bad news: still hard to optimize  - BP-S/TRW-S (Kolmogorov, 2006) implementation saving a factor of NP(number of patterns)memory (lazy asymmetric message handling) A.Shekhovtsov, P. Kohli, C. Rother

  9. BP Schedule dependence Solution by BP-S (max-product) (swep from left to right, from top to bottom) Input (inpaint the gray area) A.Shekhovtsov, P. Kohli, C. Rother

  10. Learning • For the case of curvature model, we have a simpler learning problem – we can learn the model locally. Generate smooth curves: Discretize: true curvature cost (analytic) Fit the lower envelope model K-means like algorithm, needs good initialization A.Shekhovtsov, P. Kohli, C. Rother

  11. Learning example (circle radius = model cost) cost function to learn learned patterns size 8x8 96 in total predefined patterns: assign 0 cost to off-boundary locations A.Shekhovtsov, P. Kohli, C. Rother

  12. Learning • Approximation Error discrete approximation vs. exact contour integral Testing shape samples (analytic) (overestimating) A.Shekhovtsov, P. Kohli, C. Rother

  13. Shape Inpainting area for inpainting known segmentation inpainted segmentation A.Shekhovtsov, P. Kohli, C. Rother

  14. Shape Inpainting A.Shekhovtsov, P. Kohli, C. Rother

  15. Shape Inpainting A.Shekhovtsov, P. Kohli, C. Rother

  16. Segmentation Input with user seeds (saturation) curvature strength A.Shekhovtsov, P. Kohli, C. Rother

  17. Segmentation (skip) Input with user seeds Standard length regularization regularization strength A.Shekhovtsov, P. Kohli, C. Rother

  18. Segmentation (more) • Extending the model: we added artificially an ear pattern. • its cost was tuned manually after before A.Shekhovtsov, P. Kohli, C. Rother

  19. Curvature and Length Regularization only curvature curvature + length curvature + more length A.Shekhovtsov, P. Kohli, C. Rother

  20. Towards Object Inpainting area for completion our shape inpainting interactive segmentation Texture added automatically thanks to Barnes et al. (2009) A.Shekhovtsov, P. Kohli, C. Rother

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