A Region-Based Segmentation Method for Multichannel Image Data

Segmentation has become a widely used tool in modern image analysis. Typical methods are highly nonlinear and often ad hoc, and none so far have proved accessible to detailed statistical analysis even by asymptotic approximations. Can such methods be any good? This article describes a segmentation procedure for multichannel image data and attempts to develop an understanding of its statistical performance characteristics in terms of nonparametric regression. The procedure is based on a recursive merging algorithm defined via a nested sequence of discretizations of the image domain. A cross-validation rule with a near-neighbor block replacement strategy is proposed for selecting the final segmentation model. Idealized numerical simulation experiments are used to evaluate the rate of convergence of the mean square error of estimation and also to study the efficiency of the cross-validation technique. Interestingly, the results show that the rate of convergence tends to decrease as the degree of smoothness of the underlying image increases. This complements the more familiar estimation characteristic associated with conventional nonparametric regression algorithms. The cross-validation is found to be effective at choosing a segmentation that minimizes the mean squared deviation between the segmented image and the underlying truth. Furthermore, by manipulating the block size in the replacement scheme, it is possible to maintain some robustness to artifacts caused by blurring. Physical phantom datasets taken from positron emission tomography (PET) are used to evaluate the segmentation procedure in a setting of practical interest. Some data from a human brain imaging study with PET are used for further illustration.