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Bildregistrierung zur Verbrennungsanalyse
Abstract
In der plastischen Chirurgie ist es zur Bestimmung der Therapie notwendig, den Schweregrad einer Verbrennung genau einzusch
ätzen. Hierzu ist ein Verfahren entwickelt worden, das auf der Verarbeitung visueller Aufnahmen der Wunde in unterschiedlichen
Farbspektren beruht. Diese müssen zur Weiterverarbeitung unbedingt deckungsgleich sein, so dass ein Registrierungsproblem
gegeben ist. Zur Lösung dieses Problems präsentieren wir einen parametrischen Registrierungsansatz, der auf einer speziellen
Vorverarbeitung und der Modifikation eines bekannten Distanzmaßes beruht. Die einzelnen Schritte und Bausteine werden erläutert.
Das Verfahren ist an 50 Datensätzen aus der klinischen Praxis getestet worden, wobei es sich als besonders geeignet erwiesen
hat.
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This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter XII. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.
This book really shows how registration works: the flip-book appearing at the top right corners shows a registration of a human knee from bent to straight position (keeping bones rigid). Of course, the book also provides insight into concepts and practical tools. The presented framework exploits techniques from various fields such as image processing, numerical linear algebra, and optimization. Therefore, a brief overview of some preliminary literature in those fields is presented in the introduction (references [1–51]), and registration-specific literature is assembled at the end of the book (references [52–212]). Examples and results are based on the FAIR software, a package written in MATLAB. The FAIR software, as well as a PDF version of this entire book, can be freely downloaded from www.siam.org/books/fa06.
This book would not have been possible without the help of Bernd Fischer, Eldad Haber, Claudia Kremling, Jim Nagy, and the Safir Research Group from Lübeck: Sven Barendt, Björn Beuthin, Konstantin Ens, Stefan Heldmann, Sven Kabus, Janine Olesch, Nils Papenberg, Hanno Schumacher, and Stefan Wirtz. I'm also indebted to Sahar Alipour, Reza Heydarian, Raya Horesh, Ramin Mafi, and Bahram Marami Dizaji for improving the manuscript.
One of the remaining challenges in image registration arises for multi-modal images taken from different imaging devices and/or modalities. Starting in 1995, mutual information has shown to be a very successful distance measure for multi-modal image registration. However, as it is well-known, mutual information also has a number of drawbacks. Here, we present an alternative image similarity measure which is also capable to handle multi-modal images but better suited for optimization. As we show, the alternative normalized gradient based approach is deterministic, much simpler, easier to interpret, fast and straightforward to implement, faster to compute, and also much more suitable to optimization.
We present a noninvasive imaging method for objective determination of the depth of burn wounds. The method is easy to use and enables even the nonspecialized physician to determine the burn depth at a very early time and to make available an objective documentation for quality management.