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Über dieses Buch

Much of our understanding of the relationships among geometric struc­ tures in images is based on the shape of these structures and their relative orientations, positions and sizes. Thus, developing quantitative methods for capturing shape information from digital images is an important area for computer vision research. This book describes the theory, implemen­ tation, and application of two multi resolution image shape description methods. The author begins by motivating the need for quantitative methods for describing both the spatial and intensity variations of struc­ tures in grey-scale images. Two new methods which capture this informa­ tion are then developed. The first, the intensity axis of symmetry, is a collection of branching and bending surfaces which correspond to the skeleton of the image. The second method, multiresolution vertex curves, focuses on surface curvature properties as the image is blurred by a sequence of Gaussian filters. Implementation techniques for these image shape descriptions are described in detail. Surface functionals are mini­ mized subject to symmetry constraints to obtain the intensity axis of symmetry. Robust numerical methods are developed for calculating and following vertex curves through scale space. Finally, the author demon­ strates how grey-scale images can be segmented into geometrically coher­ ent regions using these shape description techniques. Building quantita­ tive analysis applications in terms of these visually sensible image regions promises to be an exciting area of biomedical computer vision research. v Acknowledgments This book is a corrected and revised version of the author's Ph. D.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction and Background

Abstract
Quantitative analysis is the primary motivation for digital image processing in many applications. For example, locating and measuring anatomical structures in medical images is an important first step in diagnosis and treatment planning. In biology and other scientific disciplines, the analysis of structures in images often leads to better understanding of the underlying mechanisms in the systems being studied. Often the shape of structures within images plays an important role in this identification and analysis process. For example, we might distinguish different types of blood cells by their shape and perhaps gain an understanding of blood disorders by an analysis of shape variations. For this reason, determining how the shape of image structures should be best represented to facilitate quantitative analysis is one of the central problems in computer-aided image analysis. To answer this difficult question requires an understanding of what shape is and how shape information should be extracted from grey-scale images.
John M. Gauch

Chapter 2. The Intensity Axis of Symmetry

Abstract
The previous chapter reviewed existing shape and image description methods and identified the symmetric axis and the intensity stack as the most promising methods in these respective categories. This chapter defines a new image shape description called the intensity axis of symmetry (IAS) which shares the advantages of both these methods. This is accomplished by describing simultaneously the shape of the whole collection of level curves which comprise the image. A discussion of the important descriptive properties of the IAS then follows.
John M. Gauch

Chapter 3. Computing the Intensity Axis of Symmetry

Abstract
The previous chapter defined the intensity axis of symmetry (IAS) and described certain desirable properties of this image shape description. This chapter describes our approach for calculating a discrete representation of the IAS given an arbitrary grey scale image. The emphasis is on calculating an accurate and robust approximation of the IAS; questions of efficiency are of secondary interest here and will be discussed only briefly.
John M. Gauch

Chapter 4. Segmentation via the Intensity Axis of Symmetry

Abstract
The previous chapter described how the IAS can be calculated for an image. This chapter explains how the IAS can be used to segment an image into sensible image regions. Before this is demonstrated, several methods for displaying the IAS are illustrated. The chapter concludes with an analysis of the effects of preprocessing the image before computing the IAS and its induced image segmentation.
John M. Gauch

Chapter 5. Multiresolution Analysis of the Intensity Axis of Symmetry

Abstract
The previous three chapters defined the intensity axis of symmetry (IAS), described an implementation of the IAS and illustrated the application of this shape description to the problem of image segmentation. This chapter describes the multiresolution behavior of the IAS and outlines two methods for calculating a quasi-hierarchical shape description based on this information. The first method uses the close relationship between symmetry and maximal curvature while the second approach makes use of the approximate relationship between symmetry and watershed boundaries. This chapter concludes with a summary of unsolved problems and suggestions for future work.
John M. Gauch

Chapter 6. Conclusions

Abstract
The principal objective of our research was to extend the analysis of shape to grey-scale images. This goal was accomplished by designing and implementing a new structural shape description called the intensity axis of symmetry (IAS) and an associated curvature—based description called vertex curves. Both of these descriptions focus on properties of individual level curves of the image and combine this information across intensities to obtain representations which capture both spatial and intensity properties of shape in an image. To demonstrate the effectiveness of this image shape description, an interactive image segmentation program was implemented which identifies and displays image regions associated with individual components of the IAS. These regions often correspond to sensible anatomical structures in medical images. An analysis of the multiresolution behavior of the IAS reveals that it is possible to impose a quasi-hierarchy on IAS sheets by focusing on the multiresolution properties of much simpler geometric structures: vertex curves approximated by watershed boundaries. The next four sections expand on these accomplishments.
John M. Gauch

Backmatter

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