Applications of Invariance in Computer Vision

and chapter summary.- Cartan's moving frame method and its application to the geometry and evolution of curves in the euclidean, affine and projective planes.- Representation of three-dimensional object structure as cross-ratios of determinants of stereo image points.- A case against epipolar geometry.- Repeated structures: Image correspondence constraints and 3D structure recovery.- How to use the cross ratio to compute projective invariants from two images.- On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views.- The double algebra: An effective tool for computing invariants in computer vision.- Matching perspective views of parallel plane structures.- Invariants for recovering shape from shading.- Fundamental difficulties with projective normalization of planar curves.- Invariant size functions.- Euclidean reconstruction from uncalibrated views.- Accurate projective reconstruction.- Applications of motion field of curves.- Affine reconstruction from perspective image pairs obtained by a translating camera.- Using invariance and quasi-invariance for the segmentation and recovery of curved objects.- Representations of 3D objects that incorporate surface markings.- Model-based invariant functions and their use for recognition.- Integration of multiple feature groups and multiple views into a 3D object recognition system.- Hierarchical object description using invariants.- Generalizing invariants for 3-D to 2-D matching.- Recognition by combinations of model views: Alignment and invariance.- Classification based on the cross ratio.- Correspondence of coplanar features through P2-invariant representations.- Integrating algebraic curves and surfaces, algebraic invariants and Bayesian methods for 2D and 3D object recognition.