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Applications of Geometric Algebra in Computer Vision by Christian B.U. Perwass

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Applications of Geometric Algebra in Computer Vision written by Christian B.U. Perwass This is an other great mathematics book cover the following topics.

Introduction
Structure of the thesis, Geometric Algebra

A Construction of Geometric Algebra
Introduction, The Foundations, The Fundamental Axioms, The Commutator and Anti-Commutator Products, Vectors, Basis Blades, Inner and Outer Products, The Outer Product, The Inner Product, Further Development, The Grade-Projection Operator, The Reversion Operator, More on Vectors in Gn, Conclusions

Projective Geometry
Why Projective Geometry?, Fundamentals, Points, Lines and Planes, Points, Lines, Planes, Intersections, Intersection of Lines in P2, Intersection of Parallel Lines in P2, Intersections with Planes in P3, Intersection of Lines in P3, Reciprocal Vector Frames, Line Frames, Plane Frames, Determinants, Meet and Join, Cameras and Projections, Dual Representations of Lines and Points, Epipoles, Camera Matrices, Conclusions

The geometry of multiple view tensors
Introduction, The Fundamental Matrix, Derivation, Rank of F, Degrees of Freedom of F, Transferring Points with F, Epipoles of F, The Trifocal Tensor, Derivation, Transferring Lines, Transferring Points, Rank of T, Degrees of Freedom of T, Constraints on T, Relation between T and F, Second Order Constraints, Epipoles, The Quadfocal Tensor, Derivation, Transferring Lines, Rank of Q, Degrees of Freedom of Q, Constraints on Q, Relation between Q and T, Reconstruction and the Trifocal Tensor, Conclusions

3D-Reconstruction
Introduction, Image Plane Bases, Plane Collineation, Calculating the Collineation Tensor M, Rank of M, The Plane at Infinity, Vanishing Points and P8, Calculating Vanishing Points, ? 8 or M 8 from Vanishing Points, The Reconstruction Algorithm, The Geometry, The Minimisation Function, The Minimisation Routine, Experimental Results, Synthetic, Real Data, Conclusions

Conclusions
Summary of Important, Geometric Algebra, Projective Geometry, Multiple View Tensors, 3D-Reconstruction

The MVT Program

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