Submodular Function Optimization for Motion Clustering and Image Segmentation

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, maximi...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2019-09, Vol.30 (9), p.2637-2649
Main Authors: Shen, Jianbing, Dong, Xingping, Peng, Jianteng, Jin, Xiaogang, Shao, Ling, Porikli, Fatih
Format: Article
Language:English
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
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Summary: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.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2018.2885591