A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection

  • Authors:

  • John Oliensis

  • Affiliations:

  • NEC Research Institute, 4 Independence Way, Princeton, NJ 08540. oliensis@research.nj.nec.com

  • Venue:
  • International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
  • Year:
  • 1999

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Abstract

We present a fast, robust algorithm for multi-framestructure from motion from point features which works for general motion andlarge perspective effects. The algorithm is for point features but easily extends to a direct method based on image intensities. Experiments on synthetic and real sequences showthat the algorithm gives results nearly as accurate as the maximum likelihoodestimate in a couple of seconds on an IRIS 10000. The results aresignificantly better than those of an optimal two-image estimate. When the camera projection is close to scaled orthographic, the accuracy is comparable to that of the Tomasi/Kanade algorithm, and the algorithms are comparablyfast. The algorithm incorporates a quantitative theoretical analysis of thebas-relief ambiguity and exemplifies how such an analysis can be exploited toimprove reconstruction. Also, we demonstrate a structure-from-motionalgorithm for partially calibrated cameras, with unknown focal length varyingfrom image to image. Unlike the projective approach, this algorithm fullyexploits the partial knowledge of the calibration. It is given by a simplemodification of our algorithm for calibrated sequences and is insensitive toerrors in calibrating the camera center. Theoretically, we show that unknownfocal-length variations strengthen the effects of the bas-reliefambiguity. This paper includes extensive experimental studies of two-framereconstruction and the Tomasi/Kanade approach in comparison to our algorithm. We find that two-frame algorithms are surprisingly robust and accurate,despite some problems with local minima. We demonstrate experimentally that anearly optimal two-frame reconstruction can be computed quickly, by aminimization in the motion parameters alone. Lastly, we show that a wellknown problem with the Tomasi/Kanade algorithm is often not a significantone.