90 research outputs found
The ideal of the trifocal variety
Techniques from representation theory, symbolic computational algebra, and
numerical algebraic geometry are used to find the minimal generators of the
ideal of the trifocal variety. An effective test for determining whether a
given tensor is a trifocal tensor is also given
Collaborative Perception From Data Association To Localization
During the last decade, visual sensors have become ubiquitous. One or more cameras
can be found in devices ranging from smartphones to unmanned aerial vehicles and
autonomous cars. During the same time, we have witnessed the emergence of large
scale networks ranging from sensor networks to robotic swarms.
Assume multiple visual sensors perceive the same scene from different viewpoints. In
order to achieve consistent perception, the problem of correspondences between ob-
served features must be first solved. Then, it is often necessary to perform distributed
localization, i.e. to estimate the pose of each agent with respect to a global reference
frame. Having everything set in the same coordinate system and everything having
the same meaning for all agents, operation of the agents and interpretation of the
jointly observed scene become possible.
The questions we address in this thesis are the following: first, can a group of visual
sensors agree on what they see, in a decentralized fashion? This is the problem of
collaborative data association. Then, based on what they see, can the visual sensors
agree on where they are, in a decentralized fashion as well? This is the problem of
cooperative localization.
The contributions of this work are five-fold. We are the first to address the problem
of consistent multiway matching in a decentralized setting. Secondly, we propose
an efficient decentralized dynamical systems approach for computing any number of
smallest eigenvalues and the associated eigenvectors of a weighted graph with global
convergence guarantees with direct applications in group synchronization problems,
e.g. permutations or rotations synchronization. Thirdly, we propose a state-of-the
art framework for decentralized collaborative localization for mobile agents under
the presence of unknown cross-correlations by solving a minimax optimization prob-
lem to account for the missing information. Fourthly, we are the first to present an
approach to the 3-D rotation localization of a camera sensor network from relative
bearing measurements. Lastly, we focus on the case of a group of three visual sensors.
We propose a novel Riemannian geometric representation of the trifocal tensor which
relates projections of points and lines in three overlapping views. The aforemen-
tioned representation enables the use of the state-of-the-art optimization methods on
Riemannian manifolds and the use of robust averaging techniques for estimating the
trifocal tensor
The joint image handbook
International audienceGiven multiple perspective photographs, point correspondences form the " joint image " , effectively a replica of three-dimensional space distributed across its two-dimensional projections. This set can be characterized by multilinear equations over image coordinates, such as epipolar and trifocal constraints. We revisit in this paper the geometric and algebraic properties of the joint image, and address fundamental questions such as how many and which multilinearities are necessary and/or sufficient to determine camera geometry and/or image correspondences. The new theoretical results in this paper answer these questions in a very general setting and, in turn, are intended to serve as a " handbook " reference about multilinearities for practitioners
Trinocular Geometry Revisited
International audienceWhen do the visual rays associated with triplets of point correspondences converge, that is, intersect in a commπon point? Classical models of trinocular geometry based on the fundamental matrices and trifocal tensor associated with the corresponding cameras only provide partial answers to this fundamental question, in large part because of underlying, but seldom explicit, general configuration assumptions. This paper uses elementary tools from projective line geometry to provide necessary and sufficient geo- metric and analytical conditions for convergence in terms of transversals to triplets of visual rays, without any such assumptions. In turn, this yields a novel and simple minimal parameterization of trinocular geometry for cameras with non-collinear or collinear pinholes
Trinocular Geometry Revisited
International audienceWhen do the visual rays associated with triplets of point correspondences converge, that is, intersect in a common point? Classical models of trinocular geometry based on the fundamental matrices and trifocal tensor associated with the corresponding cameras only provide partial answers to this fundamental question, in large part because of underlying, but seldom explicit, general configuration assumptions. This paper uses elementary tools from projective line geometry to provide necessary and sufficient geometric and analytical conditions for convergence in terms of transversals to triplets of visual rays, without any such assumptions. In turn, this yields a novel and simple minimal parameterization of trinocular geometry for cameras with non-collinear or collinear pinholes, which can be used to construct a practical and efficient method for trinocular geometry parameter estimation. We present numerical experiments using synthetic and real data
Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar
The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference.
We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference
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