عنوان

Group-Theoretical Methods in Image Understanding

(Number (ISBN

3540512535

(Number (ISBN

364261275X

(Number (ISBN

9783540512530

(Number (ISBN

9783642612756

Number

b571744

Title Proper

Group-Theoretical Methods in Image Understanding

General Material Designation

[Book]

First Statement of Responsibility

by Kenichi Kanatani.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1990

Specific Material Designation and Extent of Item

(xii, 459 pages 138 illustrations)

Series Title

Springer Series in Information Science, 20.

Text of Note

1. Introduction --; 1.1 What is Image Understanding? --; 1.2 Imaging Geometry of Perspective Projection --; 1.3 Geometry of Camera Rotation --; 1.4 The 3D Euclidean Approach --; 1.5 The 2D Non-Euclidean Approach --; 1.6 Organization of This Book --; 2. Coordinate Rotation Invariance of Image Characteristics --; 2.1 Image Characteristics and 3D Recovery Equations --; 2.2 Parameter Changes and Representations --; 2.3 Invariants and Weights --; 2.4 Representation of a Scalar and a Vector --; 2.5 Representation of a Tensor --; 2.6 Analysis of Optical Flow for a Planar Surface --; 2.7 Shape from Texture for Curved Surfaces --; Exercises --; 3. 3D Rotation and Its Irreducible Representations --; 3.1 Invariance for the Camera Rotation Transformation --; 3.2 Infinitesimal Generators and Lie Algebra --; 3.3 Lie Algebra and Casimir Operator of the 3D Rotation Group --; 3.4 Representation of a Scalar and a Vector --; 3.5 Irreducible Reduction of a Tensor --; 3.6 Restriction of SO(3) to SO(2) --; 3.7 Transformation of Optical Flow --; Exercises --; 4. Algebraic Invariance of Image Characteristics --; 4.1 Algebraic Invariants and Irreducibility --; 4.2 Scalars, Points, and Lines --; 4.3 Irreducible Decomposition of a Vector --; 4.4 Irreducible Decomposition of a Tensor --; 4.5 Invariants of Vectors --; 4.6 Invariants of Points and Lines --; 4.7 Invariants of Tensors --; 4.8 Reconstruction of Camera Rotation --; Exercises --; 5. Characterization of Scenes and Images --; 5.1 Parametrization of Scenes and Images --; 5.2 Scenes, Images, and the Projection Operator --; 5.3 Invariant Subspaces of the Scene Space --; 5.4 Spherical Harmonics --; 5.5 Tensor Expressions of Spherical Harmonics --; 5.6 Irreducibility of Spherical Harmonics --; 5.7 Camera Rotation Transformation of the Image Space --; 5.8 Invariant Measure --; 5.9 Transformation of Features --; 5.10 Invariant Characterization of a Shape --; Exercises --; 6. Representation of 3D Rotations --; 6.1 Representation of Object Orientations --; 6.2 Rotation Matrix --; 6.3 Rotation Axis and Rotation Angle --; 6.4 Euler Angles --; 6.5 Cayley-Klein Parameters --; 6.6 Representation of SO(3) by SU(2) --; 6.7 Adjoint Representation of SU(2) --; 6.8 Quaternions --; 6.9 Topology of SO(3) --; 6.10 Invariant Measure of 3D Rotations --; Exercises --; 7. Shape from Motion --; 7.1 3D Recovery from Optical Flow for a Planar Surface --; 7.2 Flow Parameters and 3D Recovery Equations --; 7.3 Invariants of Optical Flow --; 7.4 Analytical Solution of the 3D Recovery Equations --; 7.5 Pseudo-orthographic Approximation --; 7.6 Adjacency Condition of Optical Flow --; 7.7 3D Recovery of a Polyhedron --; 7.8 Motion Detection Without Correspondence --; Exercises --; 8. Shape from Angle --; 8.1 Rectangularity Hypothesis --; 8.2 Spatial Orientation of a Rectangular Corner --; 8.3 Interpretation of a Rectangular Polyhedron --; 8.4 Standard Transformation of Corner Images --; 8.5 Vanishing Points and Vanishing Lines --; Exercises --; 9. Shape from Texture --; 9.1 Shape from Texture from Homogeneity --; 9.2 Texture Density and Homogeneity --; 9.3 Perspective Projection and the First Fundamental Form --; 9.4 Surface Shape Recovery from Texture --; 9.5 Recovery of Planar Surfaces --; 9.6 Numerical Scheme of Planar Surface Recovery --; Exercises --; 10. Shape from Surface --; 10.1 What Does 3D Shape Recovery Mean? --; 10.2 Constraints on a

Text of Note

This book presents the mathematics relevant to image understanding by computer vision and gives examples of actual applications. Group representation theory, Lie groups and Lie algebras, the theory of invariance, tensor calculus, differential geometry and projective geometry are used for three-dimensional shape and motion analysis from images, making use of techniques such as shape from motion, shape from texture, shape from angle and shape from surface. Although the mathematics itself may be well known to mathematicians, people working in areas related to computer science, image understanding, computer vision and image processing have usually never studied such mathematics, and so may be surprised to learn that abstract mathematical concepts can be of enormous help in building intelligent computer vision systems.

Computer vision.

Mathematical physics.

Physics.

by Kenichi Kanatani.

Kenichi Kanatani

Electronic name

[Book]

Y