Toward designing intelligent PDEs for computer vision: An optimal   control approach

doi:10.1016/j.imavis.2012.09.004

CORC > 北京大学 > 信息科学技术学院

	Toward designing intelligent PDEs for computer vision: An optimal control approach
	Liu, Risheng ; Lin, Zhouchen ; Zhang, Wei ; Tang, Kewei ; Su, Zhixun
刊名	图像与视觉计算
	2013
关键词	Optimal control PDEs Computer vision Image processing IMAGE REMOVAL
DOI	10.1016/j.imavis.2012.09.004
英文摘要	Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing a PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we consider designing PDEs for various problems arising in computer vision and image processing in a lazy manner: learning PDEs from training data via an optimal control approach. We first propose a general intelligent PDE system which holds the basic translational and rotational invariance rule for most vision problems. By introducing a PDE-constrained optimal control framework, it is possible to use the training data resulting from multiple ways (ground truth, results from other methods, and manual results from humans) to learn PDEs for different computer vision tasks. The proposed optimal control based training framework aims at learning a PDE-based regressor to approximate the unknown (and usually nonlinear) mapping of different vision tasks. The experimental results show that the learnt PDEs can solve different vision problems reasonably well. In particular, we can obtain PDEs not only for problems that traditional PDEs work well but also for problems that PDE-based methods have never been tried before, due to the difficulty in describing those problems in a mathematical way. (C) 2012 Elsevier B.V. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000314557100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Computer Science, Artificial Intelligence; Computer Science, Software Engineering; Computer Science, Theory & Methods; Engineering, Electrical & Electronic; Optics; SCI(E); 7; ARTICLE; 1; 43-56; 31
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/291011]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Liu, Risheng,Lin, Zhouchen,Zhang, Wei,et al. Toward designing intelligent PDEs for computer vision: An optimal control approach[J]. 图像与视觉计算,2013.
APA	Liu, Risheng,Lin, Zhouchen,Zhang, Wei,Tang, Kewei,&Su, Zhixun.(2013).Toward designing intelligent PDEs for computer vision: An optimal control approach.图像与视觉计算.
MLA	Liu, Risheng,et al."Toward designing intelligent PDEs for computer vision: An optimal control approach".图像与视觉计算 (2013).