Analysis on convergence of mean-shift and angle of continuous mean-shift vector

Mean shift is an effective iterative algorithm.It has been widely used in the image processing and computer vision,but whose properties are not been perfectly proved.The convergence of the mean-shift is proved according to cauchy convergence criterion for the wrong and deficiency at the literatures.The angle of the mean shift vectors based on the arbitrary kernel in the same window is less than 90 degree.