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Euclidean upgrading from segment lengths

Authors
Publisher
Springer
Publication Date
Keywords
  • Inteligencia Artificial
  • Geometría
Disciplines
  • Mathematics

Abstract

We address the problem of the recovery of Euclidean structure of a projectively distorted n-dimensional space from the knowledge of segment lengths. This problem is relevant, in particular, for Euclidean reconstruction with uncalibrated cameras, extending previously known results in the affine setting. The key concept is the Quadric of Segments (QoS), defined in a higher-dimensional space by the set of segments of a fixed length from which Euclidean structure can be obtained in closed form. We have intended to make a thorough study of the properties of the QoS, including the determination of the minimum number of segments of arbitrary length that determine it and its relationship with the standard geometric objects associated to the Euclidean structure of space. Explicit formulas are given to obtain the dual absolute quadric and the absolute quadratic complex from the QoS. Experiments with real and synthetic images evaluate the performance of the techniques.

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