One Approach to the Analysis Influence of Change Background Statistical Parameters on the Capability of Tracking Objects using “Mean Shift” Procedure DIMITRIJE BUJAKOVIC, MILENKO ANDRIC Military Academy University of Belgrade General Pavla Jurisica Sturma 33, 11000 Belgrade SERBIA dbujakovic@verat.net , asmilenko@beotel.net Abstract: - A quantitative analysis of change background statistics on the capability of tracking objects using “mean shift” procedure is present in this paper. Change of background statistics assumed changing of mean of brightness and changing noise variance in the scene. Quantitative analysis implies detection error and number of iteration needed for position determination using “mean shift” procedure. Key-Words: - Object detection, object tracking, background statistical parameters, “mean shift” procedure, quantitative analysis, detection error, number of iterations, 1 Introduction In real scenes, probability density function of brightness could be often assumed as a Gaussian mixture probability density function. „Mean shift“ procedure is a method for determinating statistics of modes that probability density function. This procedure could be used in various applications: image filtration, image segmentation [1], detecting of countour [2] and tracking objects [3,4]. Influence of change mean gray and variance on the capability of tracking object is analysed in this paper. Analysis is done using MATLAB. 2 Detection object position in the scene using “mean shift” procedure Algorithm for detection object using “mean shift” procedure is presented in [3, 4]. A part of picture where is object model, is described by modified histogram. Modified histogram defines as: [ ] ∑ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = = n i i i u u x b x k C q 1 * 2 * ) ( ˆ δ (1) u is probability of appearance gray-level, and b(x i * ) is a bin of i-th pixel. C is normalization constant. Modified histogram ascribes bigger values to pixels nearer to the center of tracking object. This can be achieved due using of monotonic decreasing kernel. Let we assumed that a part of picture where is candidate for object in current frame, is moved for y. Modified histogram of object candidate can be defined as [ ] ∑ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = = h n i i i h u u x b h x y k C y p 1 * 2 ) ( ) ( ˆ δ (2) h is kernel height and C h is normalization constant. An idea of object detection using “mean shift” procedure is based on the position determination that candidate for object which modified histogram and modified histogram of object model has a maximum likelihood. As a measure of likelihood, it has been used a function of likelihood, defined as [ ] ∑ = = ≡ m u u u q y p q y p y 1 ˆ ) ( ˆ ˆ ), ( ˆ ) ( ˆ ρ ρ (3) The distance between modified histograms defines as [ ] q y p y d ˆ ), ( ˆ 1 ) ( ρ − = (4) Using Taylor expansion around , function of likelihood is: ) ( ˆ 0 y p [ ] ∑ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + ∑ ≈ = = h n i i i h m u u u h x y k w C q y p q y p 1 2 1 0 2 ˆ ) ˆ ( ˆ 5 . 0 ˆ ), ( ˆ ρ (5) Weighting coefficients can be calculate as [ ] ∑ − = = m u u u i i y p q u x b w 1 0 ) ˆ ( ˆ ˆ ) ( δ (6) A minimum distance between modified histograms is obtained by maximization second part in (5). If it is used an Epanechnikov kernel, object position for which this distance is minimal, can be defined as WSEAS TRANSACTIONS on SIGNAL PROCESSING Dimitrije Bujakovic, Milenko Andric ISSN: 1790-5052 1 Issue 1, Volume 4, January 2008