| Title: | Global Optimization for One-Dimensional Structure and Motion Problems |
| Fulltext: |  |
| Authors: | Enqvist, Olof and Kahl, Fredrik and Olsson, Carl and Åström, Kalle |
| Year: | 2010 |
| Publication: | SIAM Journal of Imaging Science |
| Volume: | 3 |
| Issue: | 4 |
| Document Type: | Journal Paper |
| Status: | Published |
| Refereed: | Yes |
| Keywords: | globalvision, ffl |
| BibTeX item: |  |
| Abstract: | We study geometric reconstruction problems in one-dimensional retina vision. In such problems, the scene is modeled as a 2D plane, and the camera sensor produces 1D images of the scene. Our main contribution is an efficient method for computing the global optimum to the structure and motion problem with respect to the L-infinity norm of the reprojection errors. One-dimensional cameras have proven useful in several applications, most prominently for autonomous vehicles where they are used to provide inexpensive and reliable navigational systems. Previous results on one-dimensional vision are limited to the classi cation and solving of minimal cases, bundle adjustment for fi nding local optima and linear algorithms for algebraic cost functions. In contrast, we present an approach for nding globally optimal solutions with respect to the L-infinity norm of the angular reprojection errors. We show how to solve intersection and resection problems as well as the problem of simultaneous localization and mapping (SLAM). The algorithm is robust to use when there are missing data which means that all points are not necessarily seen in all images. Our approach has been tested on a variety of different scenarios, both real and synthetic. The algorithm shows good performance for intersection, resection and for SLAM with up to fi ve views. For more views the high dimension of the search space tends to give long running times. The experimental section also gives interesting examples showing that for one-dimensional cameras with limited fi eld of view, the SLAM problem is often inherently ill-conditioned. |
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