Image Structure

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.'

1 Introduction. - 2 Basic Concepts. - 3 Local Samples and Images. - 4 The Scale-Space Paradigm. - 5 Local Image Structure. - 6 Multiscale Optic Flow. - A Geometry and Tensor Calculus. - A. 1 Literature. - A. 2 Geometric Concepts. - A. 2. 1 Preliminaries. - A. 2. 2 Vectors. - A. 2. 3 Covectors. - A. 2. 4 Dual Bases. - A. 2. 5 Riemannian Metric. - A. 2. 6 Tensors. - A. 2. 7 Push Forward, Pull Back, Derivative Map. - C Proof of Proposition 5. 4. - D Proof of Proposition 5. 5. - Solutions to Problems. - Symbols.