Submodular Function Optimization for Motion Clustering and Image Segmentation

• Published in: IEEE transaction on neural networks and learning systems Vol. 30; no. 9; pp. 2637 - 2649
• Main Authors: Shen, Jianbing, Dong, Xingping, Peng, Jianteng, Jin, Xiaogang, Shao, Ling, Porikli, Fatih
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.09.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Clustering; Clustering algorithms; Computational modeling; Computer vision; Constraints; Cybernetics; Energy; Greedy algorithms; Image processing; Image segmentation; Knapsack constraint; Knapsack problem; Linear programming; Maximization; Optimization; Random walk; segmentation; submodular maximization; Trajectories; Trajectory; trajectory clustering
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2018.2885591

In this paper, we propose a framework of maximizing quadratic submodular energy with a knapsack constraint approximately, to solve certain computer vision problems. The proposed submodular maximization problem can be viewed as a generalization of the classic 0/1 knapsack problem. Importantly, maximization of our knapsack constrained submodular energy function can be solved via dynamic programing. We further introduce a range-reduction step prior to dynamic programing as a two-stage procedure for more efficient maximization. In order to demonstrate the effectiveness of the proposed energy function and its maximization algorithm, we apply it to two representative computer vision tasks: image segmentation and motion trajectory clustering. Experimental results of image segmentation demonstrate that our method outperforms the classic segmentation algorithms of graph cuts and random walks. Moreover, our framework achieves better performance than state-of-the-art methods on the motion trajectory clustering task.