## Abstract

We present a mathematical framework and algorithm for

characterizing and extracting partial intrinsic symmetries of surfaces,

which is a fundamental building block for many modern geometry processing

algorithms. Our goal is to compute all “significant” symmetry

information of the shape, which we define as r-symmetries, i.e., we report

all isometric self-maps within subsets of the shape that contain at

least an intrinsic circle or radius r. By specifying r, the user has direct

control over the scale at which symmetry should be detected. Unlike

previous techniques, we do not rely on feature points, voting or probabilistic

schemes. Rather than that, we bound computational efforts by

splitting our algorithm into two phases. The first detects infinitesimal

r-symmetries directly using a local differential analysis, and the second

performs direct matching for the remaining discrete symmetries.

We show that our algorithm can successfully characterize and extract

intrinsic symmetries from a number of example shapes.

characterizing and extracting partial intrinsic symmetries of surfaces,

which is a fundamental building block for many modern geometry processing

algorithms. Our goal is to compute all “significant” symmetry

information of the shape, which we define as r-symmetries, i.e., we report

all isometric self-maps within subsets of the shape that contain at

least an intrinsic circle or radius r. By specifying r, the user has direct

control over the scale at which symmetry should be detected. Unlike

previous techniques, we do not rely on feature points, voting or probabilistic

schemes. Rather than that, we bound computational efforts by

splitting our algorithm into two phases. The first detects infinitesimal

r-symmetries directly using a local differential analysis, and the second

performs direct matching for the remaining discrete symmetries.

We show that our algorithm can successfully characterize and extract

intrinsic symmetries from a number of example shapes.

Original language | English |
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Pages | 1-15 |

Publication status | Published - 2014 |

Event | ECCV Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment - Zürich, Switzerland Duration: 12 Sept 2014 → 12 Sept 2014 |

### Workshop

Workshop | ECCV Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment |
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Country/Territory | Switzerland |

City | Zürich |

Period | 12/09/14 → 12/09/14 |