Ebook: Mathematical Models for Registration and Applications to Medical Imaging

Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume. Moreover, the importance of registration for industry and medical imaging is discussed from a medical doctor and from a manufacturer point of view.

---

This volume provides an up-to-date survey on mathematical and computational methods in image registration. This is an emerging topic in applied and computational science, with profound applications for instance in medicine, and image and video processing.

Especially during the last year sophisticated numerical models for registration and efficient numerical methods (in particular variational methods and partial differential equations) have been proposed. Many of them are contained in this volume.

Moreover, some practical applications and novel directions with industrial relevance in data processing are indicated.

The combination of practice and novel mathematical aspects makes the book very suitable for the ECMI series "Mathematics in Industry".

The most important contributions in this volume summarize the state of the art in mathematical and computational methods in image registration, based on variational and partial differential equations. The key contributions state sophisticated mathematical modelling, as well as numerical methods.

The book contains many realistic examples with real world data.

---

This volume provides an up-to-date survey on mathematical and computational methods in image registration. This is an emerging topic in applied and computational science, with profound applications for instance in medicine, and image and video processing.

Especially during the last year sophisticated numerical models for registration and efficient numerical methods (in particular variational methods and partial differential equations) have been proposed. Many of them are contained in this volume.

Moreover, some practical applications and novel directions with industrial relevance in data processing are indicated.

The combination of practice and novel mathematical aspects makes the book very suitable for the ECMI series "Mathematics in Industry".

The most important contributions in this volume summarize the state of the art in mathematical and computational methods in image registration, based on variational and partial differential equations. The key contributions state sophisticated mathematical modelling, as well as numerical methods.

The book contains many realistic examples with real world data.

Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
A Generalized Image Registration Framework using Incomplete Image Information – with Applications to Lesion Mapping....Pages 3-25
Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity....Pages 27-61
Registration of Histological Serial Sectionings....Pages 63-80
Computational Methods for Nonlinear Image Registration....Pages 81-101
A Survey on Variational Optic Flow Methods for Small Displacements....Pages 103-136
Front Matter....Pages 137-137
Fast Image Matching for Generation of Panorama Ultrasound....Pages 139-150
Inpainting of Movies Using Optical Flow....Pages 151-162
Front Matter....Pages 163-163
Multimodality Registration in Daily Clinical Practice....Pages 165-183
Colour Images....Pages 185-191

---

This volume provides an up-to-date survey on mathematical and computational methods in image registration. This is an emerging topic in applied and computational science, with profound applications for instance in medicine, and image and video processing.

Especially during the last year sophisticated numerical models for registration and efficient numerical methods (in particular variational methods and partial differential equations) have been proposed. Many of them are contained in this volume.

Moreover, some practical applications and novel directions with industrial relevance in data processing are indicated.

The combination of practice and novel mathematical aspects makes the book very suitable for the ECMI series "Mathematics in Industry".

The most important contributions in this volume summarize the state of the art in mathematical and computational methods in image registration, based on variational and partial differential equations. The key contributions state sophisticated mathematical modelling, as well as numerical methods.

The book contains many realistic examples with real world data.

Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
A Generalized Image Registration Framework using Incomplete Image Information – with Applications to Lesion Mapping....Pages 3-25
Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity....Pages 27-61
Registration of Histological Serial Sectionings....Pages 63-80
Computational Methods for Nonlinear Image Registration....Pages 81-101
A Survey on Variational Optic Flow Methods for Small Displacements....Pages 103-136
Front Matter....Pages 137-137
Fast Image Matching for Generation of Panorama Ultrasound....Pages 139-150
Inpainting of Movies Using Optical Flow....Pages 151-162
Front Matter....Pages 163-163
Multimodality Registration in Daily Clinical Practice....Pages 165-183
Colour Images....Pages 185-191
....