Provably Optimal Solutions to Geometric Vision Problems


July 12, 2007


Richard Hartley


Australian National University


In the past, the main methods for solving problems in Multiview Vision Geometry have been iterative techniques, which may suffer from falling into local minima, and trouble with convergence. Recent research has turned to finding guaranteed globally optimal solutions to such problems. Techniques include quasi-convex optimization, Second Order Cone Programming, Branch-and-bound techniques and fractional programming, solving many of the common vision geometry problems. In this talk, we address problems such as essential-matrix estimation, many-view triangulation and motion of a vehicle with rigidly placed cameras. We provide optimal solutions, (in L2 or L-infinity norm) where no such solution existed previously (as of 2007). A further applications of such methods in tracking a deforming sheet of material is discussed.


Richard Hartley

Professor Richard Hartley is a member of the Vision Science, Technology and Applications Program in National ICT Australia; from 2003 until 2006 he was the leader of this research group. This program seeks to apply method of Computer Vision and Sensor Technology in a range of real-world problems, ranging from motor-vehicle safety to improved methods of health care.In 2001, Professor Hartley returned from the USA to a position in the Department of Information Engineering at the Australian National University. Before that, he worked at the General Electric Research and Development Center in Schenectady New York from 1985 to 2001. During the period 1985-1988, he was involved in the design and implementation of Computer-Aided Design tools for electronic design and created a very successful design system called the Parsifal Silicon Compiler. In 1991 he was awarded GE’s Dushman Award for this work.In 1991, he began an extended research effort in the area of applying geometric techniques to the analysis of video. This far-reaching research led to fundamental advances in machine-understanding of video, and opened up one of the most popular areas of Computer Vision research in the 1990s. The most visible outcome of this research was in automating the creation of special effects in the film entertainment industry. In 2000, he co-authored a book “Multiple View Geometry in Computer Vision” for Cambridge University Press, summarizing the previous decade’s research in this area. This has become one of the most popular research reference texts in Computer Vision.He has authored over 100 papers in Photogrammetry, Computer Vision, Geometric Topology, Geometric Voting Theory, Computational Geometry and Computer-Aided Design, and holds 34 US patents.