Statistical Density Estimation Using Threshold Dynamics for Geometric Motion
Tijana Kostic,Andrea L. Bertozzi +1 more
TL;DR: 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.
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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.
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Citations
Two-species particle aggregation and stability of co-dimension one solutions
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Non-local crime density estimation incorporating housing information.
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Numerical Optimization Methods for Image Processing and Machine Learning
Joseph Woodworth
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TL;DR: It is proved that given data and a measurement matrix from a broad class of matrices, one can choose parameters for these classes of shrinkages to guarantee exact recovery of the sparsest solution and further prove convergence of the algorithm iterative $p-shrinkage (IPS) for solving one such relaxed problem.
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Part I: Steady States in Two-Species Particle Aggregation; Part II: Sparse Representations For Multiscale PDE
Alan Patrick Mackey
- 01 Jan 2015
TL;DR: In this paper, a continuous model with densities supported on co-dimension one curves for two-species particle interaction in two-dimensional Euclidean space, and linear stability analysis of concentric ring steady states to characterize the steady state patterns and instabilities which form Conditions for linear well-posedness are determined and these results are compared to simulations of the discrete particle dynamics, showing predictive power of the linear theory.
A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber
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References
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
14K
Active contours without edges
Tony F. Chan,Luminita A. Vese +1 more
TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
Optimal approximations by piecewise smooth functions and associated variational problems
David Mumford,Jayant Shah +1 more
TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.
The Split Bregman Method for L1-Regularized Problems
Tom Goldstein,Stanley Osher +1 more
TL;DR: This paper proposes a “split Bregman” method, which can solve a very broad class of L1-regularized problems, and applies this technique to the Rudin-Osher-Fatemi functional for image denoising and to a compressed sensing problem that arises in magnetic resonance imaging.
On the Mathematical Foundations of Theoretical Statistics
TL;DR: In this paper, the authors define the center of location as the abscissa of a frequency curve for which the sampling errors of optimum location are uncorrelated with those of optimum scaling.