The talk will discuss recent work that has been done within the "Statistical Geometry Processing" group at MPI Informatics and Saarland University. We are working on "shape understanding" algorithms, i.e., algorithms that aim at discovering structure in geometric data sets and utilize it for analysis and modeling. Humans understand shapes already at an intuitive level. However, finding a formal model that explains "structure" in shapes to a certain extend is a major scientific challenge. In addition to being able to capture meaningful aspects, the models also need to be simple enough to permit efficient and robust algorithms for discovering such structure in data. The talk will focus on correspondence analysis as one approach to this problem: First, we establish correspondences between shapes, i.e., detect pieces of geometry that are essentially similar and relate these to each other. I will discuss various techniques to efficiently and robustly compute correspondences between shapes, allowing for different types of invariance. Second, we can go up one level of abstraction and look at the structure of the obtained correspondences: Assuming we have discovered multiple, potentially overlapping pairs of regions of equivalence within a piece of geometry, what does this tell us about the shape? This question is addressed by "inverse procedural modeling" techniques that characterize families of shapes that are similar to an example piece. We use correspondence information to derive shape docking rules and, alternatively, algebraic invariants to describe such shape spaces in a constructive manner.

École Polytechnique Fédérale de Lausanne, School of Computer and Communication Sciences

Geometric Computing Laboratory, BC 347, Station 14, CH-1015 Lausanne – 2010-2015 LGG, EPFL

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