A Novel Interactive Image Segmentation Algorithm Based on Maximization of Submodular Function

Abstract

In this paper, an efficient interactive image segmentation method based on maximization of submodular function under user’s scribble constraint is presented. The problem of interactive image segmentation is formulated as the maximum entropy rate under user’s constraints. The objective function is submodular, and we solve the constrained submodular function maximization by incorporating a new data structure and some aggregating rules into the greedy algorithm. The main steps of our algorithm are as follows. First, the pixels scribbled by the user are clustered separately as target foreground and background clusters. Second, in the process of greedy algorithm, unscribbled pixels are aggregated to the corresponding target cluster according to the proposed aggregating rules. Finally, the segmentation result is presented by the two target clusters. The experiments and comparisons on three standard benchmarks show that our method has good performance. Our method is straightforward and efficient, and the time complexity of our method is between linear and polynomial. Furthermore, we analyze the influence of different scribbles, and propose some optimal scribble strategies.