Closed Form Solutions for Reconstruction Via Complex Analysis
 R.A. Hicks,
 D. Pettey,
 K. Daniilidis,
 R. Bajcsy
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We address the problem of controlbased recovery of robot pose and environmental layout. Panoramic sensors provide a 1D projection of characteristic features of a 2D operation map. Trajectories of these projections contain information about the position of a priori unknown landmarks in the environment. We introduce the notion of spatiotemporal signatures of projection trajectories. These signatures are global measures, characterized by considerably higher robustness with respect to noise and outliers than the commonly applied point correspondence. By modeling the 2D motion plane as the complex plane we show that by means of complex analysis the reconstruction problem can be reduced to a quadraticâ€”or even linear in some casesâ€”equation. The algorithm is tested in simulations and in a real experiment.
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 Title
 Closed Form Solutions for Reconstruction Via Complex Analysis
 Journal

Journal of Mathematical Imaging and Vision
Volume 13, Issue 1 , pp 5770
 Cover Date
 20000801
 DOI
 10.1023/A:1008381724192
 Print ISSN
 09249907
 Online ISSN
 15737683
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 reconstruction
 structure from motion
 complex analysis
 Industry Sectors
 Authors

 R.A. Hicks ^{(1)}
 D. Pettey ^{(2)}
 K. Daniilidis ^{(2)}
 R. Bajcsy ^{(3)}
 Author Affiliations

 1. Department of Mathematics and Computer Science, Drexel University, USA
 2. GRASP Laboratory, Department of Computer and Information Science, University of Pennsylvania, USA
 3. CISE Directorate, National Science Foundation, USA