Modified mean shift algorithm

Abstract

The mean shift (MS) algorithm is an iterative method introduced for locating modes of a probability density function. Although the MS algorithm has been widely used in many applications, the convergence of the algorithm has not yet been proven. In this study, the authors modify the MS algorithm in order to guarantee its convergence. The authors prove that the generated sequence using the proposed modified algorithm is a convergent sequence and the density estimate values along the generated sequence are monotonically increasing and convergent. In contrast to the MS algorithm, the proposed modified version does not require setting a stopping criterion a priori; instead, it guarantees the convergence after a finite number of iterations. The proposed modified version defines an upper bound for the number of iterations which is missing in the MS algorithm. The authors also present the matrix form of the proposed algorithm and show that, in contrast to the MS algorithm, the weight matrix is required to be computed once in the first iteration. The performance of the proposed modified version is compared with the MS algorithm and it was shown through the simulations that the proposed version can be used successfully to estimate cluster centres.