Topology-Driven Trajectory Synthesis with an Example on Retinal Cell Motions
Venue
14th Workshop on Algorithms in Bioinformatics, Springer, Wroclaw, Poland (2014), pp. 326-339
Publication Year
2014
Authors
Chen Gu, Leonidas Guibas, Michael Kerber
BibTeX
Abstract
We design a probabilistic trajectory synthesis algorithm for generating
time-varying sequences of geometric configuration data. The algorithm takes a set
of observed samples (each may come from a different trajectory) and simulates the
dynamic evolution of the patterns in O(n^2 log n) time. To synthesize geometric
configurations with indistinct identities, we use the pair correlation function to
summarize point distribution, and alpha-shapes to maintain topological shape
features based on a fast persistence matching approach. We apply our method to
build a computational model for the geometric transformation of the cone mosaic in
retinitis pigmentosa --- an inherited and currently untreatable retinal
degeneration.
