Researchers: Sami Brandt and Jukka Heikkonen
Viewing geometry imposes constraints in images taken from an arbitrary object or scene. The underlying geometrical constraints can be represented by multiple view tensors called fundamental matrix, trifocal and quadrifocal tensor. In short, these tensors consists of all the projective information in the presence of two, three and four images, that is, the camera projection matrices can be reconstructed up to an projective transformation. Moreover, they can be directly used in computing projective reconstruction of given correspondences in images.
We have studied the robust estimation of the fundamental matrix. In fact our research has resulted in some sense, theoretically optimal method for the fundamental matrix estimation as far as the camera model can be considered affine. In practice, the fundamental matrix contains the minimal information in order to construct the epipolar geometry between two images. In other words, as far as the fundamental matrix or the epipolar geometry is known between two images and one shows one point in the one image, one can immediately show the corresponding line where the corresponding point lies in the other image (Figure 11).
In future, we are going to extend the present work to other image geometry estimation problems such as plane homography estimation and develop methods for problems where data are fatally contaminated by outliers. We are also researching image matching and tracking using point matches where the geometrical aspects are fully utilized.
Figure 11: (a) Five points are selected and marked with '+' on the one image of a stereo image pair. (b) The epipolar lines (solid line) and the corresponding 95% confidence intervals (dash-dot line) computed with the proposed Bayesian method. The ground truth epipolar line computed from the calibrated F-matrix are shown by the dashed line. Image copyrights belong to INRIA-Syntim. |