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Vision with Direction: A Systematic Introduction to Image Processing and Computer Vision

Josef Bigun;

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2006 SpringerLink

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Neuronal Pathways of Vision

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part I - Human and Computer Vision | Pp. 3-20

Color

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part I - Human and Computer Vision | Pp. 21-32

Discrete Images and Hilbert Spaces

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 35-56

Continuous Functions and Hilbert Spaces

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 57-60

Finite Extension or Periodic Functions—Fourier Coefficients

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 61-68

Fourier Transform—Infinite Extension Functions

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 69-83

Properties of the Fourier Transform

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 85-101

Reconstruction and Approximation

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 103-117

Scales and Frequency Channels

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part II - Linear Tools of Vision | Pp. 119-149

Direction in 2D

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part III - Vision of Single Direction | Pp. 153-207

Direction in Curvilinear Coordinates

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part III - Vision of Single Direction | Pp. 209-244

Direction in D, Motion as Direction

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part III - Vision of Single Direction | Pp. 245-276

World Geometry by Direction in Dimensions

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part III - Vision of Single Direction | Pp. 277-308

Group Direction and -Folded Symmetry

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part IV - Vision in Multiple Directions | Pp. 311-326

Reducing the Dimension of Features

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part V - Grouping, Segmentation, and Region Description | Pp. 329-340

Grouping and Unsupervised Region Segregation

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part V - Grouping, Segmentation, and Region Description | Pp. 341-357

Region and Boundary Descriptors

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part V - Grouping, Segmentation, and Region Description | Pp. 359-375

Concluding Remarks

Josef Bigun

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain.

Part V - Grouping, Segmentation, and Region Description | Pp. 377-378

Información

Tipo: libros

ISBN impreso

978-3-540-27322-6

ISBN electrónico

978-3-540-27323-3

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación