Introduction. The problem that the author solved has its origin in Nomography: 1 how to reduce a nomogram of aligned points to a circular nomogram? In more mathematical terms: what are local diffeomorphisms that send germs of lines to germs of circles? This question was initially posed for 2-dimensional nomograms by G.S. Khovanskii and, solved by A.G. A discipline which was discovered by the Fr...

A wheel that is capable of producing thrust and maintaining vehicle internal integrity is presented. The wheel can be seen as an organic extension to the central unit (eg the vehicle) it is attached to, that is, the system and the wheel can be completely surrounded by the same tegument while enabling continuous wheel rotation without tearing the tegument. Furthermore, a skeleton linking the cen...

..................................................................................................... III PREFACE........................................................................................................VII ACKNOWLEDGMENTS...................................................................................IX LIST OF PUBLICATIONS .........................................................

We describe a complete system for image rectification in sport video sequences. Relying both on geometrical properties of the field elements and on photogrammetric data, we compute an estimate of the field-to-image homography either incrementally – by inter-image data processing – or “from scratch” when direct image-model correspondences are possible. Examples are given in a soccer context.

We present a system to determine ground-plane parameters in densely crowded scenes where use of geometric features such as parallel lines or reliable estimates of agent dimensions are not possible. Using feature points tracked over short intervals, together with some plausible scene assumptions, we can estimate the parameters of the ground-plane to a sufficient degree of accuracy to correct use...

Augmented Reality overlays computer generated images over the real world. This requires precise knowledge of the viewing projection of the headmounted display (HMD) and its position. Most of the previously published methods are complicated or use special equipment for the calibration process. We present a collection of calibration methods usable for fast and easy calibration of camera parameter...

A K-theoretic analogue of RSK insertion and Knuth equivalence relations was first introduced in 2006 [1]. The resulting K-Knuth equivalence relations on words and increasing tableaux on [n] has prompted investigation into the equivalence classes of tableaux arising from these relations. Of particular interest are the tableaux that are unique in their class, which we refer to as unique rectifica...

Catadioptric systems are realizations of omnidirectional vision through mirror-lens combinations. Designs preserving the uniqueness of an effective viewpoint have recently gained attraction. We present here a novel approach for estimating the intrinsic parameters of a well-known catadioptric system consisting of a paraboloid mirror and an orthographic lens. We introduce the geometry of catadiop...