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# Mean-shift

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 Title: Mean-shift Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Mean-shift

Mean shift is a non-parametric feature-space analysis technique, a so-called mode seeking algorithm. Application domains include cluster analysis in computer vision and image processing.

## History

The mean shift procedure was originally presented in 1975 by Fukunaga and Hostetler.

## Overview

Mean shift is a procedure for locating the maxima of a density function given discrete data sampled from that function. It is useful for detecting the modes of this density. This is an iterative method, and we start with an initial estimate $x$. Let a kernel function $K\left(x_i - x\right)$ be given. This function determines the weight of nearby points for re-estimation of the mean. Typically Gaussian kernel on the distance to the current estimate is used, $K\left(x_i - x\right) = e^\left\{-c||x_i - x||^2\right\}$. The weighted mean of the density in the window determined by $K$ is

$m\left(x\right) = \frac\left\{ \sum_\left\{x_i \in N\left(x\right)\right\} K\left(x_i - x\right) x_i \right\} \left\{\sum_\left\{x_i \in N\left(x\right)\right\} K\left(x_i - x\right)\right\}$

where $N\left(x\right)$ is the neighborhood of $x$, a set of points for which $K\left(x\right) \neq 0$.

The mean-shift algorithm now sets $x \leftarrow m\left(x\right)$, and repeats the estimation until $m\left(x\right)$ converges.

## Mean shift for visual tracking

The mean shift algorithm can be used for visual tracking. The simplest such algorithm would create a confidence map in the new image based on the color histogram of the object in the previous image, and use mean shift to find the peak of a confidence map near the object's old position. The confidence map is a probability density function on the new image, assigning each pixel of the new image a probability, which is the probability of the pixel color occurring in the object in the previous image. A few algorithms, such as ensemble tracking, CAMshift, expand on this idea.

## See also

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