We study some properties of A-homotopy groups: geometric interpretations of connectivity, excision results, and a re-interpretation of geometric quotients by solvable groups in terms of covering spaces in the sense of A-homotopy theory. These concepts and results are well-suited to the study of certain quotients via geometric invariant theory. As a case study in geometry of solvable group quoti...

We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalisation group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that...

In this paper we show (a) how the shape of a 2D-landmark configuration can be encoded based on qualitative 1Dordering information, (b) how relevant geometric shape properties of a landmark configuration (strictly based on ordering information) can be detected by a sequence of view-based snapshots. Furthermore we show how shape of landmark configurations supports view-based localization tasks sp...

This paper presents a novel approach to construct an eigen space representation from limited number of views, which is equivalent to the one obtained from large number of images captured from multiple view points. This procedure implicitly incorporates a novel view synthesis algorithm in the eigen space construction process. Inherent information in an appearance representation is enhanced using...

This paper presents a novel depth driven approach for a highly accurate joint photometric and geometric image alignment. Thereby, the registration problem is expressed in terms of a consistent, elegant and efficient energy formulation. Moreover, we propose a real-time capable alternating iterative optimization scheme to solve for a state of minimal energy. Since our energy formulation is based ...

This contribution gives an overview of automatic 3D scene reconstruction and visualisation from uncalibrated and handheld camera image sequences. We address specifically the problems that are associated with calibration and visual-geometric reconstruction of complex scenes with occlusions and view-dependent surfaces. The scene is then represented by large sets of calibrated real viewpoints with...

Transparent refractive objects are one of the main problems in geometric vision that have been largely unexplored. The imaging and multi-view geometry of scenes with transparent or translucent objects with refractive properties is relatively less well understood than for opaque objects. The main objective of our work is to analyze the underlying multi-view relationships between cameras, when th...