Geometric Reasoning For Perception And Action

Geometric Reasoning for Perception and Action

Geometric Reasoning for Perception and Action

Geometry is a powerful tool to solve a great number of problems in robotics and computer vision. Impressive results have been obtained in these fields in the last decade. It is a new challenge to solve problems of the actual world which require the ability to reason about uncertainty and complex motion constraints by combining geometric, kinematic, and dynamic characteristics. A necessary step is to develop appropriate geometric reasoning techniques with reasonable computational complexity. This volume is based on a workshop held in Grenoble, France,in September 1991. It contains selected contributions on several important areas in the field of robotics and computer vision. The four chapters cover the following areas: - motion planning with kinematic and dynamic constraints, - motion planning and control in the presence of uncertainty, - geometric problems related to visual perception, -numerical problems linked to the implementation of practical algorithms for visual perception.

Invariant Algebras And Geometric Reasoning

The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics — among them, Grassmann-Cayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries.This book contains the author and his collaborators' most recent, original development of Grassmann-Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras — Cayley bracket algebra, conformal geometric algebra, and null bracket algebra — for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide.