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 |
|---|---|
| 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 |
|---|---|
| Country/Territory | Switzerland |
| City | Zürich |
| Period | 12/09/14 → 12/09/14 |