Abstract

We present two solutions for the scale selection problem in computer vision. The first one is completely nonparametric and is based on the the adaptive estimation of the normalized density gradient. Employing the sample point estimator, we define the Variable Bandwidth Mean Shift, prove its convergence, and show its superiority over the fixed bandwidth procedure. The second technique has a semiparametric nature and imposes a local structure on the data to extract reliable scale information. The local scale of the underlying density is taken as the bandwidth which maximizes the magnitude of the normalized mean shift vector. Both estimators provide practical tools for autonomous image and quasi real-time video analysis and several examples are shown to illustrate their effectiveness. 1 Motivation for Variable Bandwidth The efficacy of Mean Shift analysis has been demonstrated in computer vision problems such as tracking and segmentation in [5, 6]. However, one of the limitations of the mean shift procedure as defined in these papers is that it involves the specification of a scale parameter. While results obtained appear satisfactory, when the local characteristics of the feature space differs significantly across data, it is difficult to find an optimal global bandwidth for the mean shift procedure. In this paper we address the issue of locally adapting the bandwidth. We also study an alternative approach for data-driven scale selection which imposes a local structure on the data. The proposed solutions are tested in the framework of quasi real-time video analysis. We review first the intrinsic limitations of the fixed bandwidth density estimation methods. Then, two of the most popular variable bandwidth estimators, the balloon and the sample point, are introduced and...

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