The Minimal Structure and Motion Problems with Missing Data for 1D Retina Vision

Authors:
Magnus Oskarsson;Kalle Åström;Niels Chr. Overgaard
Affiliations:
Centre for Mathematical Sciences, Lund University, Lund, Sweden SE-221 00;Centre for Mathematical Sciences, Lund University, Lund, Sweden SE-221 00;School of Technology and Society, Malmö University, Malmö, Sweden SE-205 06
Venue:
Journal of Mathematical Imaging and Vision
Year:
2006

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Abstract

In this paper we investigate the structure and motion problem for calibrated one-dimensional projections of a two-dimensional environment. The theory of one-dimensional cameras are useful in several areas, e.g. within robotics, autonomous guided vehicles, projection of lines in ordinary vision and vision of vehicles undergoing so called planar motion. In a previous paper the structure and motion problem for all cases with non-missing data was classified and solved. Our aim is here to classify all structure and motion problems, even those with missing data, and to solve them. In the classification we introduce the notion of a prime problem. A prime problem is a minimal problem that does not contain a minimal problem as a sub-problem. We further show that there are infinitely many such prime problems. We give solutions to four prime problems, and using the duality of Carlsson these can be extended to solutions of seven prime problems. Finally we give some experimental results based on synthetic data.