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## NON-PARAMETRIC IMAGE REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0008
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces non-parametric registrations. The idea behind this type of registration is to come up with an appropriate measure both for the similarity as well as for the likelihood of a ... More

## ELASTIC REGISTRATION

*Jan Modersitzki*

### in Numerical Methods for Image Registration

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198528418
- eISBN:
- 9780191713583
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528418.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces elastic registration using the general framework introduced in Chapter 8. A physical motivation for this particular regularizer is given. The two images are viewed as two ... More

## The Stationary Action Principle

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse ... More

## Lagrangian Mechanics

*David D. Nolte*

### in Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198844624
- eISBN:
- 9780191880216
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198844624.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and ... More

## From classical to modern

*Dusa McDuff and Dietmar Salamon*

### in Introduction to Symplectic Topology

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198794899
- eISBN:
- 9780191836411
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198794899.003.0002
- Subject:
- Mathematics, Analysis, Geometry / Topology

The first chapter develops the basic concepts of symplectic topology from the vantage point of classical mechanics. It starts with an introduction to the Euler–Lagrange equation and shows how the ... More

## Differential Equations

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0035
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used ... More

## Hamiltonian mechanics

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0009
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th ... More

## Point Transformations in Lagrangian Mechanics

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses point transformations in Lagrangian mechanics. Sometimes, when solving problems, it is useful to change coordinates in velocity phase space to better suit and simplify the ... More

## Principles of minimum potential energy and complementary energy

*Lallit Anand and Sanjay Govindjee*

### in Continuum Mechanics of Solids

- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198864721
- eISBN:
- 9780191896767
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198864721.003.0012
- Subject:
- Physics, Condensed Matter Physics / Materials

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential ... More

## Introduction

*Laurent Baulieu, John Iliopoulos, and Roland Sénéor*

### in From Classical to Quantum Fields

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is ... More

## Absolute time

*George Jaroszkiewicz*

### in Images of Time: Mind, Science, Reality

- Published in print:
- 2016
- Published Online:
- January 2016
- ISBN:
- 9780198718062
- eISBN:
- 9780191787553
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198718062.003.0014
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses Newton’s concept of absolute time and its use in classical mechanics. It defines clocks and our freedom to change them, that is, reparametrization of time. The chapter goes on ... More

## Mathematics and physics preliminaries: of hills and plains and other things

*Jennifer Coopersmith*

### in The Lazy Universe: An Introduction to the Principle of Least Action

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198743040
- eISBN:
- 9780191802966
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198743040.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

The link between mathematics and physics is explained, and how the concepts “coordinates,” “generalized coordinates,” “time,” and “space” have evolved, starting with Galileo. It is also shown that ... More

## Density Functional Approaches to Relativistic Quantum Mechanics

*Kenneth G. Dyall and Knut Faegri*

### in Introduction to Relativistic Quantum Chemistry

- Published in print:
- 2007
- Published Online:
- November 2020
- ISBN:
- 9780195140866
- eISBN:
- 9780197561744
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195140866.003.0020
- Subject:
- Chemistry, Quantum and Theoretical Chemistry

The wave function is an elusive and somewhat mysterious object. Nobody has ever observed the wave function directly: rather, its existence is inferred from ... More

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