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

  • Chen Gu
  • Leonidas Guibas
  • Michael Kerber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8701)

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(n2 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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Chen Gu
    • 1
  • Leonidas Guibas
    • 2
  • Michael Kerber
    • 3
  1. 1.Google Inc.USA
  2. 2.Stanford UniversityUSA
  3. 3.Max-Planck-Institute for InformaticsGermany

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