Tighter Relaxations for Higher-Order Models based on Generalized Roof Duality

Summary, in English

Many problems in computer vision can be turned into a large-scale boolean optimization problem, which is in general NP-hard. In this paper, we further develop one of the most successful approaches, namely roof duality, for approximately solving such problems for higher-order models. Two new methods that can be applied independently or in combination are investigated. The first one is based on constructing relaxations using generators of the submodular function cone. In the second method, it is shown that the roof dual bound can be applied in an iterated way in order to obtain a tighter relaxation. We also provide experimental results that demonstrate better performance with respect to the state-of-the-art, both in terms of improved bounds and the number of optimally assigned variables.

• Author: Johan Fredriksson; Carl Olsson; Petter Strandmark; Fredrik Kahl
• Department/s: Mathematics (Faculty of Engineering); Mathematical Imaging Group; ELLIIT: the Linköping-Lund initiative on IT and mobile communication
• Publishing year: 2012
• Language: English
• Pages: 273-282
• Publication/Series: Lecture Notes in Computer Science (Computer Vision - ECCV 2012. Workshops and Demonstrations, Florence, Italy, October 7-13, 2012, Proceedings, Part III)
• Volume: 7585
• Links: http://dx.doi.org/10.1007/978-3-642-33885-4_28
• Document type: Conference paper
• Publisher: Springer
• Topic: Computer Vision and Robotics (Autonomous Systems); Mathematics
• Keywords: computer vision; roof duality; pseudoboolean optimization
• Conference name: ECCV 2012 Workshop on Higher-Order Models and Global Constraints in Computer Vision
• Conference date: 2012-10-13
• Conference place: Florence, Italy
• Status: Published
• Research group: Mathematical Imaging Group
• ISBN/ISSN/Other: ISSN: 0302-9743; ISSN: 1611-3349; ISBN: 978-3-642-33885-4; ISBN: 978-3-642-33884-7 (print)