Linear Differential Algorithm for Motion Recovery: AGeometric Approach

  • Authors:

  • Yi Ma;Jana Košecká;Shankar Sastry

  • Affiliations:

  • Electronics Research Laboratory, University of California at Berkeley, Berkeley, CA 94720-1774, USA. mayi@robotics.eecs.berkeley.edu;Electronics Research Laboratory, University of California at Berkeley, Berkeley, CA 94720-1774, USA. janka@robotics.eecs.berkeley.edu;Electronics Research Laboratory, University of California at Berkeley, Berkeley, CA 94720-1774, USA. sastry@robotics.eecs.berkeley.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2000

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Abstract

The aim of this paper is to explore a linear geometricalgorithm for recovering the three dimensional motion of a movingcamera from image velocities. Generic similarities and differencesbetween the discrete approach and the differential approach areclearly revealed through a parallel development of an analogousmotion estimation theory previously explored in Vieville, T. andFaugeras, O.D. 1995. In Proceedings of Fifth InternationalConference on Computer Vision, pp. 750–756; Zhuang, X. andHaralick, R.M. 1984. In Proceedings of the First InternationalConference on Artificial Intelligence Applications, pp. 366–375.We present a precise characterization of the space of differentialessential matrices, which gives rise to a noveleigenvalue-decomposition-based 3D velocity estimation algorithm fromthe optical flow measurements. This algorithm gives a unique solutionto the motion estimation problem and serves as a differentialcounterpart of the well-known SVD-based 3D displacement estimationalgorithm for the discrete case. Since the proposed algorithm onlyinvolves linear algebra techniques, it may be used to provide a fastinitial guess for more sophisticated nonlinear algorithms (Ma et al.,1998c. Electronic Research Laboratory Memorandum, UC Berkeley,UCB/ERL(M98/37)). Extensive simulation results are presented forevaluating the performance of our algorithm in terms of bias andsensitivity of the estimates with respect to different noise levelsin image velocity measurements.