Geometry and Kinematics with Uncertain Data

Abstract. In Computer Vision applications, one usually has to work with uncertain data. It is therefore important to be able to deal with uncertain geometry and uncertain transformations in a uniform way. The Geometric Algebra of conformal space offers a unifying framework to treat not only geometric entities like points, lines, planes, circles and spheres, but also transformations like reflection, inversion, rotation and translation. In this text we show how the uncertainty of all elements of the Geometric Algebra of conformal space can be appropriately described by covariance matrices. In particular, it will be shown that it is advantageous to represent uncertain transformations in Geometric Algebra as compared to matrices. Other important results are a novel pose estimation approach, a uniform framework for geometric entity fitting and triangulation, the testing of uncertain tangentiality relations and the treatment of catadioptric cameras with parabolic mirrors within this framewor...

• Type: Conference
• Year: 2006
• Where: ECCV
• Authors: Christian Perwass, Christian Gebken, Gerald Sommer
• Keywords: Computer Vision, ECCV 2006, Geometric Algebra, Geometric Entity Fitting, Non-linear Geometric Entities, Uncertain Tangentiality Relations, Uncertain Transformations