A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. A major portion of this paper describes the application of RANSAC to the Location Determination Problem (LDP): Given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing

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Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

The LambertW function is defined to be the multivalued inverse of the functionw →we

 w
 . It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.

On the Lambert W function

* Glossary of notation * Introduction * Preliminaries * Existence and Construction of Generalized Inverses * Linear Systems and Characterization of Generalized Inverses * Minimal Properties of Generalized Inverses * Spectral Generalized Inverses * Generalized Inverses of Partitioned Matrices * A Spectral Theory for Rectangular Matrices * Computational Aspects of Generalized Inverses * Miscellaneous Applications * Generalized Inverses of Linear Operators between Hilbert Spaces * Appendix A: The Moore of the Moore-Penrose Inverse * Bibliography * Subject Index * Author Index

Generalized inverses: theory and applications

Preface How to Get the Software Part I. Linear Equations. 1. Basic Concepts and Stationary Iterative Methods 2. Conjugate Gradient Iteration 3. GMRES Iteration Part II. Nonlinear Equations. 4. Basic Concepts and Fixed Point Iteration 5. Newton's Method 6. Inexact Newton Methods 7. Broyden's Method 8. Global Convergence Bibliography Index.

/pdf/iterative-methods-for-linear-and-nonlinear-equations-1ayr7dq087.pdf

Iterative Methods for Linear and Nonlinear Equations

MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

Preface 1. A brief discussion of integral equations 2. Degenerate kernel methods 3. Projection methods 4. The Nystrom method 5. Solving multivariable integral equations 6. Iteration methods 7. Boundary integral equations on a smooth planar boundary 8. Boundary integral equations on a piecewise smooth planar boundary 9. Boundary integral equations in three dimensions Discussion of the literature Appendix Bibliography Index.

The Numerical Solution of Integral Equations of the Second Kind

Chapter 1. Taylor Polynomials. Chapter 2. Error and Computer Arithmetic. Chapter 3. Rootfinding. Chapter 4. Interpolation and Approximation. Chapter 5. Numerical Integration and Differentiation. Chapter 6. Solution of Systems of Linear Equations. Chapter 7. Numerical Linear Algebra: Advanced Topics. Chapter 8. Ordinary Differential Equations. Chapter 9. Finite Difference Method for PDEs. Appendix A: Mean Value Theorems. Appendix B: Mathematical Formulas. Appendix C: Numerical Analysis Software Packages. Appendix D: Matlab: An Introduction. Appendix E: The Binary Number System. Answers to Selected Problems. Bibliography. Index.

Elementary Numerical Analysis

A survey of numerical methods for the solution of Fredholm integral equations of the second kind

Preface 1 Linear Spaces 2 Linear Operators on Normed Spaces 3 Approximation Theory 4 Nonlinear Equations and Their Solution by Iteration 5 Finite Difference Method 6 Sobolev Spaces 7 Variational Formulations of Elliptic Boundary Value Problems 8 The Galerkin Method and Its Variants 9 Finite Element Analysis 10 Elliptic Variational Inequalities and Their Numerical Approximations 11 Numerical Solution of Fredholm Integral Equations of the Second Kind 12 Boundary Integral Equations References Index.

Theoretical Numerical Analysis: A Functional Analysis Framework

1 Preliminaries.- 2 Spherical Harmonics.- 3 Differentiation and Integration over the Sphere.- 4 Approximation Theory.- 5 Numerical Quadrature.- 6 Applications: Spectral Methods.

Kendall Atkinson

Papers

The Numerical Solution of Integral Equations of the Second Kind

Elementary Numerical Analysis

A survey of numerical methods for the solution of Fredholm integral equations of the second kind

Theoretical Numerical Analysis: A Functional Analysis Framework

Spherical Harmonics and Approximations on the Unit Sphere: An Introduction