In image segmentation, superpixels composed of locally adjacent similar pixels have the effect of suppressing noise sensitivity and reducing feature calculation, and further improving the performance of segmentation in terms of both accuracy and efficiency. With a number of superpixels, an image can be segmented well with a perfect merging condition. However, existing superpixel-based segmentation methods are highly dependent on the dataset, extremely time-consuming, and lack generalization and explainability. For that, we design an interpretable mathematical programming model with submodular function to merge superpixels in this paper. After we map the superpixels and their adjacency relationships into a graph structure, the image segmentation problem is transformed into a graph partition problem. Through the application of the submodular function to the constructed graph, the partition problem the partition problem is flexibly transformed into that of finding a cut set. To figure out this problem, we design an approximate algorithm within the time complexity of O(n), where n is the total number of superpixels. We demonstrate that the approximation ratio of the algorithm is \((1-\frac{1}{e})\) , which is proven with an arbitrarily small constant \(e >0\) . An ocean remote-sensing dataset is used to verify its high performance and efficiency. It indirectly demonstrate that our merging model is generalizable and explainable.