The Robotics Institute
RI | Seminar | February 14

Robotics Institute Seminar, February 14
Time and Place | Seminar Abstract | Speaker Biography | Speaker Appointments

PowerFactorization: An approach to low-rank factorization problems

Richard Hartley

Department of Systems Engineering, Australian National University

Time and Place

1305 Newell-Simon Hall
Refreshments 3:15 pm
Talk 3:30 pm

Abstract

The Factorization Algorithm of Tomasi and Kanade is a well known method for computing affine Structure from Motion.  Its appeal springs from its simplicity and the fact that it provably gives an optimal solution for the affine problem.  A major drawback of this method, however is the requirement that all points must be visible in all views.  Though several methods have been suggested for working round this requirement, they are largely heuristic, and not entirely satisfactory.  In this talk, I will describe a connection of Factorization with the Power Method of computing the largest eigenvalue of a matrix.  From this is derived a new method of carrying out Factorization with the following advantages:

  1. It is far quicker than the standard SVD approach, particularly on large problems.
  2. It is extremely simple to implement.
  3. It provably converges rapidly to the optimal global solution (at least with full data).
  4. It extends immediately to handle missing data (up to 80% or 90% randomly missing data is reliably handled).
  5. It allows the incorporation of uncertainly information for each point measurement.
  6. Incremental addition of points is efficiently handled.

Speaker Biography

Professor Richard Hartley is head of the computer vision group in the Department of Systems Engineering, at the Australian National University, where he has been since January, 2001.  He is also leader of the Automated Systems and Sensor Technology Program in National ICT Australia, a new government-funded research institute located in Sydney and Canberra.

Before returning to academia, Dr. Hartley worked at the General Electric Research and Development Center 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.

Dr. Hartley began work in Image Understanding and Scene Reconstruction for GE's Simulation and Control Systems Division.  This division built large-scale flight-simulators.  Dr. Hartley's projects in this area were in the construction of terrain models and texture mosaics from aerial and satellite imagery.  This involved research in camera modelling, stereo matching and scene reconstruction.

In 1991, he began an extended research effort in the area of applying projective geometry techniques to reconstruction using calibrated and semi-calibrated cameras.  He was among the first to emphasize the importance of techniques of projective geometry in scene analysis from multiple views.  Subsequently he introduced the trifocal tensor for the analysis of image triples and gave one of the first effective algorithms for self calibration and geometrically correct (Euclidean) reconstruction from minimally calibrated cameras. In 2000, he co-authored (with Andrew Zisserman) a book for Cambridge University Press, summarizing the previous decade’s research in this area.

He has authored over 100 papers in Photogrammetry, Computer Vision, Geometric Topology, Geometric Voting Theory, Computational Geometry and Computer-Aided Design, and holds 32 US patents

EDUCATION:

University of Toronto, Canada  PhD Mathematics, 1976,  MSc 1972 

Stanford University, MSc Computer Science, 1985 

Australian National University, BSc, 1971

Speaker Appointments

For appointments, please contact Yanxi Liu (yanxi@cs.cmu.edu)

The Robotics Institute is part of the School of Computer Science, Carnegie Mellon University.