Detecting Similarity of Rational Plane Curves

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page

Symmetry Detection of Rational Space Curves from their Curvature and Torsion

We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar problem. To support this claim, we present an analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage.Comment: 25 page

Involutions of polynomially parametrized surfaces

We provide an algorithm for detecting the involutions leaving a surface defined by a polynomial parametrization invariant. As a consequence, the symmetry axes, symmetry planes and symmetry center of the surface, if any, can be determined directly from the parametrization, without computing or making use of the implicit representation. The algorithm is based on the fact, proven in the paper, that any involution of the surface comes from an involution of the parameter space (the real plane, in our case); therefore, by determining the latter, the former can be found. The algorithm has been implemented in the computer algebra system Maple 17. Evidence of its efficiency for moderate degrees, examples and a complexity analysis are also given

A Framework for SAR-Optical Stereogrammetry over Urban Areas

Currently, numerous remote sensing satellites provide a huge volume of diverse earth observation data. As these data show different features regarding resolution, accuracy, coverage, and spectral imaging ability, fusion techniques are required to integrate the different properties of each sensor and produce useful information. For example, synthetic aperture radar (SAR) data can be fused with optical imagery to produce 3D information using stereogrammetric methods. The main focus of this study is to investigate the possibility of applying a stereogrammetry pipeline to very-high-resolution (VHR) SAR-optical image pairs. For this purpose, the applicability of semi-global matching is investigated in this unconventional multi-sensor setting. To support the image matching by reducing the search space and accelerating the identification of correct, reliable matches, the possibility of establishing an epipolarity constraint for VHR SAR-optical image pairs is investigated as well. In addition, it is shown that the absolute geolocation accuracy of VHR optical imagery with respect to VHR SAR imagery such as provided by TerraSAR-X can be improved by a multi-sensor block adjustment formulation based on rational polynomial coefficients. Finally, the feasibility of generating point clouds with a median accuracy of about 2m is demonstrated and confirms the potential of 3D reconstruction from SAR-optical image pairs over urban areas.Comment: This is the pre-acceptance version, to read the final version, please go to ISPRS Journal of Photogrammetry and Remote Sensing on ScienceDirec

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks