A unified Bayesian mixture model framework via spatial information for grayscale image segmentation

•The representation of the contextual mixing proportion is very characteristic.•The component function of the proposed method is the Student’s t-distribution.•To obtain the parameters of the method, the inherent relationships between two distributions are utilized.•The gradient method is adopted in the inference process.

Because of the Student-t distribution owning heavier tailed than the Gaussian distribution, under a Bayesian framework, a spatially variant finite mixture model with Student’s t-distribution component function is proposed for grayscale image segmentation. To avoid additional computational step and improve the efficiency of the proposed model, a representation of contextual mixing proportion is adopted. Secondly, the spatial information of the pixels is closely related to the Gaussian distribution of their neighborhood system. Thirdly, the inherent relationship between the Gaussian distribution and the Student’s t-distribution is adopted to optimize the unknown parameters of the proposed model, which simplifies the inference process and makes the proposed model to be easily implemented. Comprehensive experiments on synthetic noise images, simulated medical images and real-world grayscale images are presented to illustrate the superior performance of the proposed model in terms of the visual and quantitative comparison.