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Initial Parameter Estimation

Since both the EM model fitting algorithm and the ICM labelling algorithm converge locally, the choice of initial conditions, including the initial parameter set and the classification, is important. Without prior information, histogram analysis is widely used to estimate statistics such as means and variances of a distribution. Histogram fitting is the most commonly adopted method, especially for the Gaussian mixture model [29]. But in the case when the image has high noise level, the Gaussian mixture assumption may not hold and fitting may fail. From the standpoint of classification, we want the classes to be widely separated from each other while at the same time having relatively low intra-class variances. Whether the intensity PDF follows a Gaussian mixture or not is relatively unimportant. According to this, we adopt an initial estimation in this paper a discriminant measure-based thresholding method proposed by Otsu [25]. The basic idea is to find thresholds maximizing the inter-class variances thus also minimizing the intra-class variances. According to theories of discriminant analysis, such thresholds are optimal solutions. Once the optimal thresholds have been determined, the mean $\mu$ and the standard deviation $\sigma$ for each class type can then be used as the initial parameters for further estimation. The initial classification can also be obtained either directly through the thresholding, or through an ML estimation with those known parameters.
next up previous
Next: Experiments Up: Segmentation Using the HMRF-EM Previous: Segmentation Using the HMRF-EM
Yongyue Zhang
2000-05-11