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Publication# Variational Segmentation using Fuzzy Region Competition and Local Non-Parametric Probability Density Functions

Abstract

We describe a novel variational segmentation algorithm designed to split an image in two regions based on their intensity distributions. A functional is proposed to integrate the probability density functions of both regions within the optimization process. The method simultaneously performs segmentation and non-parametric density estimation. It does not make any assumption on the underlying distributions, hence it is flexible and can be applied to a wide range of applications. Although a boundary evolution scheme may be used to minimize the functional, we choose to consider an alternative formulation with membership functions. The latter has the advantage of being convex in each of the variables, so that the minimization is faster and less sensitive to initial conditions. Finally, to improve the accuracy and the robustness to low-frequency artifacts, we present an extension for the more general case of local probability densities, allowed to vary in space. The approach readily extends to multi-channel images and 3D volumes, and we show several results on synthetic and photographic images, as well as on 3D medical data.

Official source

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Related concepts (3)

Image segmentation

In and computer vision, image segmentation is the process of partitioning a into multiple image segments, also known as image regions or image objects (sets of pixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Density estimation

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population. A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization.