Modeling Symmetries for Stochastic Structural Recognition
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1 Modeling Symmetries for Stochastic Structural Recognition Second International Workshop on Stochastic Image Grammars Barcelona, November 2011 Radim Tyleček and Radim Šára Center for Machine Perception, Czech Technical University, Prague 1 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
2 Introduction Objects of Interest: images with highly structured objects (translational and reflection symmetry) Purpose of the Research: modeling and interpretation of structures Playground: simple but rich world of facades Tuscany Palace, Prague 2 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
3 Intro Model Image Recognition Related Work results 3/9 Split Grammars (Teboul 2010) Array Scopes (this work) Orthogonal structure level R. Tylec ek, R. S a ra, Czech Technical Univ. Prague Weak Neighborhood (Tylecek 2010) Free-form Modeling Symmetries for Stochastic Structural Recognition
4 Array Model of Structure Scope (facade bounding box) region of interest in the image Array (facade structure) backbone model (rows and columns define positions) structure = holes (binary labels h ij allow to exclude terminals from the array) Terminal elements (windows) allow local deviations δ ij of terminals positions from regularity of the array 4 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
5 Image Likelihood L = log p(i θ) = I log p b + w I f N k=1 ω k f k (I w ) (1) Interpretation = Image Compression Background set of independent pixels uniform p b w w L < 0 accept, L > 0 reject w Foreground conditionally grouped pixels of terminals rectangular regions w evaluated by mixture of N features f k (I w ) = g k (I w ) t k 5 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
6 Image Features Haar-like form: g k (I w ) = 1 σ k ( I w H k h k ) 2 integral image Differential: foreground differential bg. symmetric bg. p b t k - + p Symmetric: Similarity: g k Learning the Mixture selection with RealBoost from randomly generated set implicitly discovers reflection symmetry 6 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
7 Recognition Markov Chain Monte Carlo random walk in the continuous parameter space and discrete configuration (language) space find the most probable interpretation general method but easy to implement Proposals local: modify the current value of attribute a = a + resample value of an attribute from the prior a p(a) change complexity of the structure (add/remove rows/columns/scopes) RjMCMC attributes for the new symbols are sampled conditionally, exploiting the current structure 7 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
8 Results Intro Model Image Recognition Is there a facade in the image? L(I ) = 24.4 accept L(I ) = not sure L(I ) = 13.2 reject Decision Careful design allows us to decide what the result means. 8 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
9 Conclusion Intro Model Image Recognition Array Scopes structural exceptions, local irregularity flexible and suitable representation of translation symmetry Mixture of Features likelihood derived in a principled way, complete learning implicit learning of reflection symmetry Interpretation grammar-driven classifier allows to decide about the result in terms of compression Current Assumptions rectified input images, one facade scope per image 9 / 9 R. Tyleček, R. Šára, Czech Technical Univ. Prague Modeling Symmetries for Stochastic Structural Recognition
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