Data and knowledge-driven dual surrogate-assisted multi-objective rough fuzzy clustering algorithm for image segmentation

Most multi-objective clustering algorithms (MOCAs) do not fully utilize the spatial and edge information of an image in image segmentation areas. Moreover, the objective evaluations are generally expensive for MOCAs, because the computation cost is related to the number of image pixels. Introducing approximate predictions of surrogate model to replace extensive objective evaluations can improve segmentation efficiency of MOCAs. However, accurately fitting objective functions using only a single surrogate is challenging. To resolve the above-mentioned issues, a data and knowledge-driven dual surrogate-assisted multi-objective rough fuzzy clustering algorithm (DK-DSMRFC) is proposed. First, an edge information-guided local neighborhood weighted filtering strategy is designed to obtain the spatial information with rich image details. Second, three complementary clustering objective functions are constructed to recognize complex clustering structures, which focus on rough fuzzy intra-class compactness with multi-level image information, dual centroids-based inter-class separation, and neighborhood consistency, respectively. To efficiently optimize these objective functions, we construct a data and knowledge-driven dual-surrogate assisted evolutionary framework, in which the radial basis function is used as a principal surrogate model to predict objective functions, and the Kriging model is adopted as an assistant surrogate to provide uncertainty information of predictions. Furthermore, a knowledge-induced multi-perspective infill sampling criterion is designed to promote exploration and exploitation. Finally, a rough fuzzy clustering validity index with spatial constraints and neighborhood consistency is constructed to select the optimal individual. The performance of evolutionary framework is verified on benchmark functions. Experiments on images from four datasets confirm the effectiveness and robustness of the DK-DSMRFC. Keywords: Image segmentation, Rough fuzzy clustering, Surrogate assisted multi-objective optimization, Data and knowledge-driven optimization.