Periodic Pattern Analysis Under Affine Distortions Using Wallpaper Groups - Robotics Institute Carnegie Mellon University

Periodic Pattern Analysis Under Affine Distortions Using Wallpaper Groups

Yanxi Liu and Robert Collins
Workshop Paper, 2nd International Workshop on Algebraic Frames for the Perception Action Cycle (AFPAC '00), pp. 241 - 250, September, 2000

Abstract

In this paper, the mathematical theory of wallpaper groups is used to construct a computational tool for symmetry analysis of periodic patterns. Starting with a novel peak detection algorithm based on “regions of dominance”, an input periodic pattern can be automatically classified into one of the 17 wallpaper groups. The orbits of stabilizer subgroups within the group lead to a small set of candidate motifs that exhibit local symmetry consistent with the global symmetry of the entire pattern. We further consider affine distorted periodic patterns and show that each such pattern can be classified into a small set of symmetry groups that describe the patterns’ potential symmetries under affine transformation.

BibTeX

@workshop{Liu-2000-16763,
author = {Yanxi Liu and Robert Collins},
title = {Periodic Pattern Analysis Under Affine Distortions Using Wallpaper Groups},
booktitle = {Proceedings of 2nd International Workshop on Algebraic Frames for the Perception Action Cycle (AFPAC '00)},
year = {2000},
month = {September},
pages = {241 - 250},
}