Paper Info
Title
To Find the Symmetry Plane in Any Dimension, Reflect, Register, and Compute a -1 Eigenvector.
Abstract
In this paper, we demonstrate that the problem of fitting a plane of reflection symmetry to data in any dimension can be reduced to the problem of registering two datasets, and that the exactness of the solution depends on the accuracy of the registration. The pipeline for symmetry plane detection consists of (1) reflecting the data with respect to an arbitrary plane, (2) registering the original and reflected datasets, and (3) finding the eigenvector of eigenvalue -1 of a matrix given by the reflection and registration mappings. Results are shown for 2D and 3D datasets. We discuss in detail a particular biological application in which we study the 3D symmetry of manual myelinated neuron reconstructions throughout the body of a larval zebrafish that were extracted from serial-section electron micrographs. The data consists of curves that are represented as sequences of points in 3D, and there are two goals: first, find the plane of mirror symmetry given that the neuron reconstructions are nearly symmetric; second, find pairings of symmetric curves.
Year
Venue
Field
2016
arXiv: Computer Vision and Pattern Recognition
Plane symmetry,Pure mathematics,Plane curve,Geometry,Eigenvalues and eigenvectors,Mathematics
DocType
Volume
Citations 
Journal
abs/1611.05971
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Marcelo Cicconet1287.08
David G. C. Hildebrand2192.56
Hunter Elliott301.01