The variable bandwidth mean shift and data-driven scale selection

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.