Estimating the number of components in Gaussian mixture models adaptively for medical image

An important but difficult problem of Gaussian mixture models (GMM) for medical image analysis is estimating and testing the number of components by model selection criterion. There are many available methods to estimate the k based on likelihood function. However, some of them need the maximum number of components is known as priori and data is usually over-fitted by them when log-likelihood function is far larger than penalty function. We investigate the log-characteristic function of the GMM to estimate the number of models adaptively for medical image. Our method defines the sum of weighted real parts of all log-characteristic functions of the GMM as a new convergent function and model selection criterion. Our new model criterion makes use of the stability of the sum of weighted real parts of all log-characteristic functions of the GMM when the number of components is larger than the true number of components. The univariate acidity, simulated 2D datasets and real 2D medical images are used to test and experiment results suggest that our method without any priori is more suited for large sample applications than other typical methods.