Minimal Representations for Uncertainty and Estimation in Projective Spaces

Abstract. Estimation using homogeneous entities has to cope with obstacles such as singularities of covariance matrices and redundant parametrizations which do not allow an immediate definition of maximum likelihood estimation and lead to estimation problems with more parameters than necessary. The paper proposes a representation of the uncertainty of all types of geometric entities and estimation procedures for geometric entities and transformations which (1) only require the minimum number of parameters, (2) are free of singularities, (3) allow for a consistent update within an iterative procedure, (4) enable to exploit the simplicity of homogeneous coordinates to represent geometric constraints and (5) allow to handle geometric entities which are at infinity or at least very far, avoiding the usage of concepts like the inverse depth. Such representations are already available for transformations such as rotations, motions (Rosenhahn 2002), homographies (Begelfor 2005), or the projec...

• Type: Journal
• Year: 2010
• Where: ACCV
• Authors: Wolfgang Förstner
• Keywords: ACCV 2010, Computer Vision, Entities, Estimation, Geometric Entities