7,178 research outputs found
Cross-calibration of Time-of-flight and Colour Cameras
Time-of-flight cameras provide depth information, which is complementary to
the photometric appearance of the scene in ordinary images. It is desirable to
merge the depth and colour information, in order to obtain a coherent scene
representation. However, the individual cameras will have different viewpoints,
resolutions and fields of view, which means that they must be mutually
calibrated. This paper presents a geometric framework for this multi-view and
multi-modal calibration problem. It is shown that three-dimensional projective
transformations can be used to align depth and parallax-based representations
of the scene, with or without Euclidean reconstruction. A new evaluation
procedure is also developed; this allows the reprojection error to be
decomposed into calibration and sensor-dependent components. The complete
approach is demonstrated on a network of three time-of-flight and six colour
cameras. The applications of such a system, to a range of automatic
scene-interpretation problems, are discussed.Comment: 18 pages, 12 figures, 3 table
Robust dual reconstruction systems and fusion frames
We study the duality of reconstruction systems, which are g-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are particularly interested in the projective reconstruction systems that are the analogue of fusion frames in this context. Thus, we focus on dual systems of a fixed projective system that are optimal with respect to erasures of the reconstruction system coefficients involved in the decoding process. We consider two different measures of the reconstruction error in a blind reconstruction algorithm. We also study the projective reconstruction system that best approximate an arbitrary reconstruction system, based on some well known results in matrix theory. Finally, we present a family of examples in which the problem of existence of a dual projective system of a reconstruction system of this type is considered.Fil: Massey, Pedro Gustavo. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
Self-Repairing Codes for Distributed Storage - A Projective Geometric Construction
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for
distributed networked storage: they not only allow stored data to be recovered
even in the presence of node failures, they also provide a repair mechanism
where as little as two live nodes can be contacted to regenerate the data of a
failed node. In this paper, we propose a new instance of self-repairing codes,
based on constructions of spreads coming from projective geometry. We study
some of their properties to demonstrate the suitability of these codes for
distributed networked storage.Comment: 5 pages, 2 figure
- …