Matching trajectories between video sequences by exploiting a sparse projective invariant representation

Identifying correspondences between trajectory segments observed from nonsynchronized cameras is important for reconstruction of the complete trajectory of moving targets in a large scene. Such a reconstruction can be obtained from motion data by comparing the trajectory segments and estimating both the spatial and temporal alignments. Exhaustive testing of all possible correspondences of trajectories over a temporal window is only viable in the cases with a limited number of moving targets and large view overlaps. Therefore, alternative solutions are required for situations with several trajectories that are only partially visible in each view. In this paper, we propose a new method that is based on view-invariant representation of trajectories, which is used to produce a sparse set of salient points for trajectory segments observed in each view. Only the neighborhoods at these salient points in the view--invariant representation are then used to estimate the spatial and temporal alignment of trajectory pairs in different views. It is demonstrated that, for planar scenes, the method is able to recover with good precision and efficiency both spatial and temporal alignments, even given relatively small overlap between views and arbitrary (unknown) temporal shifts of the cameras. The method also provides the same capabilities in the case of trajectories that are only locally planar, but exhibit some nonplanarity at a global level.

Omnidirectional vision and conformal geometric algebra for visual landmark identification

The automatic landmark identification is very important in autonomous robot navigation tasks. In this paper, we use a monocular omnidirectional vision system to extract the image features and the conformal geometric algebra to compute the projective invariants from such features. We show how these features can be used to compute projective and permutationp2-invariantsfrom any kind of omnidirectional vision system. Thep2-invariantsrepresent scene sublandmarks, and a set of them characterize a landmark. The advantage of this representation is that the landmarks are more robust than the single cross-ratio.

Lie methods for color robot vision

We describe how Lie-theoretical methods can be used to analyze color related problems in machine vision. The basic observation is that the nonnegative nature of spectral color signals restricts these functions to be members of a limited, conical section of the larger Hilbert space of square-integrable functions. From this observation, we conclude that the space of color signals can be equipped with a coordinate system consisting of a half-axis and a unit ball with the Lorentz groups as natural transformation group. We introduce the theory of the Lorentz group SU(1, 1) as a natural tool for analyzing color image processing problems and derive some descriptions and algorithms that are useful in the investigation of dynamical color changes. We illustrate the usage of these results by describing how to compress, interpolate, extrapolate, and compensate image sequences generated by dynamical color changes.