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1997 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Image Structure

verfasst von: Luc Florack

Verlag: Springer Netherlands

Buchreihe : Computational Imaging and Vision

Enthalten in: Professional Book Archive

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Über dieses Buch

Despite the fact that images constitute the main objects in computer vision and image analysis, there is remarkably little concern about their actual definition. In this book a complete account of image structure is proposed in terms of rigorously defined machine concepts, using basic tools from algebra, analysis, and differential geometry. Machine technicalities such as discretisation and quantisation details are de-emphasised, and robustness with respect to noise is manifest.
From the foreword by Jan Koenderink:
`It is my hope that the book will find a wide audience, including physicists - who still are largely unaware of the general importance and power of scale space theory, mathematicians - who will find in it a principled and formally tight exposition of a topic awaiting further development, and computer scientists - who will find here a unified and conceptually well founded framework for many apparently unrelated and largely historically motivated methods they already know and love. The book is suited for self-study and graduate courses, the carefully formulated exercises are designed to get to grips with the subject matter and prepare the reader for original research.'

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
A scalar image is the result of a physical observation of some scalar field configuration within some confined region of spacetime, i.e. a set of numbers (“scalars”) that capture the field’s coherent structure1. It may also represent a scalar aspect of another type of field, such as a “scalar density” (density images) or a vector field (vector images 2). Typical examples are proton density in a magnetic resonance scan and grey-tone in a colour image.
Luc Florack
Chapter 2. Basic Concepts
Abstract
In this chapter we discuss some basic physical and mathematical concepts relevant for the description of real-valued images. The focus is on images as instances of physical measurements. The considerations made here are necessary in order to appreciate the precise image definition that will be given in the next chapter.
Luc Florack
Chapter 3. Local Samples and Images
Abstract
An image is a coherent set of local samples. It is the purpose of this chapter to turn this statement into a precise, operational definition. To begin with, we shall take it for granted that spacetime is a continuum, not because it is, but simply because a flotilla of useful mathematical tools is based on this hypothesis. See e.g. Herman Weyl [296]:
“Vom Wesen des Raumes bleibt dem Mathematiker bei solcher Abstraktion nur die eine Wahrheit in Händen: daß er ein dreidimensionales Kontinuum ist.”
Luc Florack
Chapter 4. The Scale-Space Paradigm
Abstract
The conclusion reached at the end of Chapter 3 can be summarised by the following scale-space paradigm.
Luc Florack
Chapter 5. Local Image Structure
Abstract
Local image properties are those that can be associated with a single base point at a fixed inner scale, i.e. that can be defined in terms of derivatives taken at a fixed point in scale-space. Multilocal properties take into account multiple local neighbourhoods. (Note that certain multilocal properties may have a local interpretation at a coarser level of scale or at a higher order of differentiation.) Local properties are the building blocks on the basis of which multilocal expertise must be built. Indeed, the very scale-space construct is intended to encompass global structure as a manifestation of purely local entities that are causally connected in a continuous tree-like structure (“dynamic shape” [162]).
Luc Florack
Chapter 6. Multiscale Optic Flow
Abstract
In the previous chapters we have established two definitions of spatiotemporal images with fundamentally different temporal aspects. The first one does not account for temporal causality. All time instances are treated on equal foot. As such it is useful for off-line image processing on pre-recorded data. The second definition does incorporate causality, and is therefore appropriate for on-line image processing of real-time acquisition data. Both definitions reflect the symmetries that pertain to the classical picture of space and time. However, both models could be called “pseudo-static” in the sense that none of them explicitly accounts for a kinematic relation between local image samples. Such relations naturally arise as a consequence of apparent conservation laws. For this reason we will define a kinematic concept known as optic flow, again—of course—in terms of its actual computation.
Luc Florack
Backmatter
Metadaten
Titel
Image Structure
verfasst von
Luc Florack
Copyright-Jahr
1997
Verlag
Springer Netherlands
Electronic ISBN
978-94-015-8845-4
Print ISBN
978-90-481-4937-7
DOI
https://doi.org/10.1007/978-94-015-8845-4