The Hough Transform is a well known robust technique to infer shapes from a set of spatial points (Hough (1962); Duda and Hart (1972); Ballard (1981); Goldenshluger and Zeevi (2004); Dattner (2009)). Having a parametric form of the pattern of interest w.r.t. a latent variable Θ, the Hough transform computes an estimate of the density function of Θ using a histogram. Maxima of the histogram are ...

This paper proposes a new variational bound optimization framework for incorporating spatial prior information to the mean shift-based data-driven mode analysis, offering flexible control of the mean shift convergence. Two forms of Gaussian spatial priors are considered. Attractive prior pulls the convergence toward a desired location. Repulsive prior pushes away from such a location. Using a g...

The mean-shift clustering is an efficient technique for color image segmentation by dividing an image into homogeneous regions. The main drawback of mean-shift clustering is to use a fixed scale, which directly determines to use a fixed homogeneity. Since each region could have different homogeneity, using a fixed scale has a problem to segment well. To resolve this problem, we incorporate mult...

The research of its convergence of Mean Shift algorithm is the foundation of its application. Comaniciu and Li Xiang-ru have respectively provided the proof for the convergence of Mean Shift but they both made a mistake in their proofs. In this paper, the imprecise proofs existing in some literatures are firstly pointed out. Then, the local convergence is proved in a new way and the condition o...

The problem of robust mean estimation in high dimensions is studied, which a certain fraction (less than half) the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, formulated as minimization ℓ 0 -‘norm’ an outlier indic...

The conventional mean shift algorithm has been known to be sensitive to selecting a bandwidth. We present a robust mean shift algorithm with heterogeneous node weights that come from a geometric structure of a given data set. Before running MS procedure, we reconstruct un-normalized weights (a rough surface of data points) from the Delaunay Triangulation. The un-normalized weights help MS to av...

Epanechnikov Mean Shift is a simple yet empirically very effective algorithm for clustering. It localizes the centroids of data clusters via estimating modes of the probability distribution that generates the data points, using the ‘optimal’ Epanechnikov kernel density estimator. However, since the procedure involves non-smooth kernel density functions, the convergence behavior of Epanechnikov ...

Given sets of observations of training and test data, we consider the problem of re-weighting the training data such that its distribution more closely matches that of the test data. We achieve this goal by matching covariate distributions between training and test sets in a high dimensional feature space (specifically, a reproducing kernel Hilbert space). This approach does not require distrib...

Mean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on a surface constructed with a “shadow” kernel. For Gaussian kernels, mean shift is a gradient...

The mean shift algorithm is a well-known statistical method for finding local maxima in probability distributions. Besides filtering and segmentation it is applied in the field of object tracking. There are several approaches that use the mean shift method for locating target objects in video sequences. This paper compares three similar approaches and investigates their performance on different...