Article

Journal of Scientific Computing

, Volume 54, Issue 2, pp 513-530

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Statistical Density Estimation Using Threshold Dynamics for Geometric Motion

  • Tijana KostićAffiliated withMathematics Department, UCLA
  • , Andrea BertozziAffiliated withMathematics Department, UCLA Email author 

Abstract

Our goal is to estimate a probability density based on discrete point data via segmentation techniques. Since point data may represent certain activities, such as crime, our method can be successfully used for detecting regions of high activity. In this work we design a binary segmentation version of the well-known Maximum Penalized Likelihood Estimation (MPLE) model, as well as a minimization algorithm based on thresholding dynamics originally proposed by Merriman et al. (The Computational Crystal Growers, pp. 73–83, 1992). We also present some computational examples, including one with actual residential burglary data from the San Fernando Valley.

Keywords

Statistical density estimation Image segmentation Thresholding Ginzburg-Landau functional