Learning Multiple Maps from Conditional Ordinal Triplets

Ordinal embedding seeks a low-dimensional representation of objects based on relative comparisons of their similarities. This low-dimensional representation lends itself to visualization on a Euclidean map. Classical assumptions admit only one valid aspect of similarity. However, there are increasing scenarios involving ordinal comparisons that inherently reflect multiple aspects of similarity, which would be better represented by multiple maps. We formulate this problem as conditional ordinal embedding, which learns a distinct low-dimensional representation conditioned on each aspect, yet allows collaboration across aspects via a shared representation. Our geometric approach is novel in its use of a shared spherical representation and multiple aspect-specific projection maps on tangent hyperplanes. Experiments on public datasets showcase the utility of collaborative learning over baselines that learn multiple maps independently.

Adapted Approach for Omnidirectional Egomotion Estimation

Egomotion estimation is based principally on the estimation of the optical flow in the image. Recent research has shown that the use of omnidirectional systems with large fields of view allow overcoming the limitation presented in planar-projection imagery in order to address the problem of motion analysis. For omnidirectional images, the 2D motion is often estimated using methods developed for perspective images. This paper adapts motion field calculated using adapted method which takes into account the distortions existing in the omnidirectional image. This 2D motion field is then used as input to the egomotion estimation process using spherical representation of the motion equation. Experimental results are shown and comparison of error measures are given to confirm that succeeded estimation of camera motion will be obtained when using an adapted method to estimate optical flow.