The finite mixture model (FMM) is an unsupervised learning method that is widely applied to data classification tasks

particularly image segmentation. The Gaussian mixture model is a successful example of FMM used in image segmentation. However

segmentation result is sensitive to noise because the spatial relationship among neighboring pixels is not considered. To solve this problem

spatially variant FMM (SVFMM) and its improvements have been proposed by incorporating spatial constraints into the prior distribution of each pixel. These improvements have been demonstrated to be capable of noise suppression. The spatial constraint of SVFMM has been widely studied and improved. To enhance the robustness of FMM against noise

a new SVFMM is proposed in this study. The proposed model based on the concept of morphological dilation considers the existence of a spatial relation in the posteriori probability distribution of the pixel neighborhood to reduce the interference of noise in image segmentation result. The proposed model is also introduced to prior probability distribution. Spatial relationships are incorporated into prior distribution for spatial smoothness by redesigning morphological dilation. The concept of morphological dilation is adopted to increase the probability of the features of a pixel in the statistic instead of the feature value itself. The neighboring pixels are smoothened iteratively by the label with the highest probability in the neighborhood. To maximize the likelihood function

gradient descent technology instead of the expectation-maximization algorithm is employed to estimate the parameters of the proposed model. The proposed model is implemented via MATLAB. Experimental data include synthetic and medical computed tomography (CT) images. Synthetic images are interrupted by different degrees of noise to test the robustness against noise of the proposed model. Medical CT images are used to analyze effectiveness in real applications. Experiments on image segmentation show that the proposed model exhibits considerable noise suppression effect and computational efficiency. Compared with the existing SVFMM improvements presented in literature

the proposed model uses less parameters in estimation

is easier to implement

and has lower computational cost. The proposed model is superior to compared models in terms of robustness against noise

segmentation accuracy

and computational efficiency. The computational efficiency of the proposed model is better than that of most SVFMMs with spatial constraints in terms of image segmentation performance. The result for the CT images shows that this research can provide valuable help in analyzing similar criminal cases. In the field of criminal investigation

accurate extraction of a segmented region is a prerequisite to analyze images related to crime.