The Problem of Degeneracy in Structure and Motion Recovery from Uncalibrated Image Sequences

  • Authors:

  • Philip H. S. Torr;Andrew W. Fitzgibbon;Andrew Zisserman

  • Affiliations:

  • Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA. philtorr@microsoft.com;Robotics Research Group, Department of Engineering Science, Oxford University, OX1 3PJ., UK. awf@robots.ox.ac.uk;Robotics Research Group, Department of Engineering Science, Oxford University, OX1 3PJ., UK. az@robots.ox.ac.uk

  • Venue:
  • International Journal of Computer Vision - 1998 Marr Prize
  • Year:
  • 1999

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Abstract

The aim of this work is the recovery of 3D structure and cameraprojection matrices for each frame of an uncalibrated image sequence.In order to achieve this, correspondences are required throughout thesequence. A significant and successful mechanism for automaticallyestablishing these correspondences is by the use of geometricconstraints arising from scene rigidity. However, problems arise withsuch geometry guided matching if general viewpoint and general structureare assumed whilst frames in the sequence and/or scene structure donot conform to these assumptions. Such cases are termed degenerate.In this paper we describe two important cases of degeneracy and theireffects on geometry guided matching. The cases are a motion degeneracywhere the camera does not translate between frames, and a structuredegeneracy where the viewed scene structure is planar. The effectsinclude the loss of correspondences due to under or over fitting ofgeometric models estimated from image data, leading to the failure ofthe tracking method. These degeneracies are not a theoreticalcuriosity, but commonly occur in real sequences where models arestatistically estimated from image points with measurement error.We investigate two strategies for tackling such degeneracies: thefirst uses a statistical model selection test to identify whendegeneracies occur: the second uses multiple motion models to overcomethe degeneracies. The strategies are evaluated on real sequencesvarying in motion, scene type, and length from 13 to 120 frames.