Chapter

Algorithms in Bioinformatics

Volume 8701 of the series Lecture Notes in Computer Science pp 326-339

Topology-Driven Trajectory Synthesis with an Example on Retinal Cell Motions

  • Chen GuAffiliated withGoogle Inc.
  • , Leonidas GuibasAffiliated withStanford University
  • , Michael KerberAffiliated withMax-Planck-Institute for Informatics

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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 logn) time. To synthesize geometric configurations with indistinct identities, we use the pair correlation function to summarize point distribution, and α-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.

Keywords

trajectory pair correlation function alpha shapes persistent homology retinitis pigmentosa