Authors:
Darko Dimitrov
and
Klaus Kriegel
Affiliation:
Freie Universität Berlin, Institute of Computer Science, Germany
Keyword(s):
Reflective Symmetry, Geometric Hashing, Principal Component Analysis.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Biomedical Engineering
;
Biomedical Signal Processing
;
Computational Geometry
;
Computer Vision, Visualization and Computer Graphics
;
Data Manipulation
;
Feature Extraction
;
Features Extraction
;
Health Engineering and Technology Applications
;
Human-Computer Interaction
;
Image and Video Analysis
;
Image Formation and Preprocessing
;
Informatics in Control, Automation and Robotics
;
Methodologies and Methods
;
Neurocomputing
;
Neurotechnology, Electronics and Informatics
;
Pattern Recognition
;
Physiological Computing Systems
;
Sensor Networks
;
Signal Processing, Sensors, Systems Modeling and Control
;
Soft Computing
Abstract:
Symmetry detection is an important problem with many applications in pattern recognition, computer vision and computational geometry. In this paper, we propose a novel algorithm for computing a hyperplane of reflexive symmetry of a point set in arbitrary dimension with approximate symmetry. The algorithm is based on the geometric hashing technique. In addition, we consider a relation between the perfect reflective symmetry and the principal components of shapes, a relation that was already a base of few heuristic approaches that tackle the symmetry problem in 2D and 3D. From mechanics, it is known that, if H is a plane of reflective symmetry of the 3D rigid body, then a principal component of the body is orthogonal to H . Here we extend that result to any point set (continuous or discrete) in arbitrary dimension.