Modelling of Learning and Perception

Centre of Excellence in Computational Complex Systems Research


Statistical Methods in Vision Geometry

Researchers: Sami Brandt and Jukka Heikkonen

The field of computer vision is aimed at the development of intelligent artificial vision systems, and research on image understanding, image analysis and related areas. The geometric branch of computer vision has been focusing on geometry related problems such as autonomous motion detection, motion estimation, imaging geometry estimation, and 3D reconstruction of the scene. Since the solutions must deal with data corrupted by both measurement noise and outliers, statistical approach can seen as a most natural approach.

Our aim has thus been approaching geometric problems from a pure statistical view point. We have been contributing, for example, by developing a robust estimator that has been proved optimal in the sense of consistence with similar assumptions to the ordinary maximum likelihood estimator. The estimator has been applied, for instance, in two-view geometry and its uncertainty estimation with both affine and projective camera models. Other contributions include novel statistical reconstruction algorithms and a probabilistic formulation for the two-view, epipolar constraint (Figure 1).

Figure 1a


Figure 1b


Figure 1c


Figure 1. A point in the left corner of the mouth is selected in the left image of a stereo image pair (not shown here). (a) The maximum likelihood robust estimate for the epipolar line (dashed) and the estimated, conventional confidence intervals of the epipolar line. (b) Probability distribution characterising the probability that any point the second image is on the true epipolar line. This is, in fact, a probabilistic representation for the epipolar line where the uncertainty of the estimated epipolar geometry has been taken into account. (c) One thousand independent samples drawn from the probability distribution. (Original image copyright belongs to INRIA-Syntim.)