|Symmetry in Shapes – Theory and Practice|
This tutorial addresses symmetry in shapes. Our goal is to introduce the audience to the notion of symmetry in shapes and familiarize them with the formal models as well as the algorithmic tools for detecting, describing, and utilizing symmetry in shapes. Our tutorial is built on the idea of switching back and forth between the abstract mathematical models, which concisely capture the structure of the problem and let us reason about its consequences, and proven practical, algorithmic tools, which permit us to implement and utilize the presented ideas. On the theory side, we will in particular discuss the group theoretical foundations of symmetries in shapes, and apply the theory to different scenarios of global and partial symmetry, as well as to different notions of transformation groups characterizing extrinsic and intrinsic notions of symmetry. On the practical side, we will explain the two most important approaches to efficient symmetry detection: voting methods and local feature-matching techniques. Further, we will explain the main ideas on how regularity can be detected from pairwise correspondence information, and discuss recent ideas for making symmetry detection scalable for large geometric data sets. Our tutorial will conclude with a summary of open problems and a discussion of possible future impact of symmetry-based models in computer graphics and vision.
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