Given a static or dynamic series of noise corrupted observations {Xt, t is time}, the main problem is the detection of whether some meaningful parameters associated with {Xt} have changed, and if these parameters have changed, then estimate the time of the change and the size of the change. A typical example is the regression update (or the least square estimation) where the values of regression coefficients may have been changed during the time of collecting data. In this paper we discuss several statistical methods for solving this main problem. The Bayesian approach and the maximum likelihood method are emphasized in the discussion. Experiments of edge detection and detection of singular points on smooth bent surfaces in image processing by using some of the discussed methods have been run and some good results are shown here.