Издательство Springer, 2003, -470 pp.Scale is not an important parameter in computer vision research. It is an essential parameter. It is an immediate consequence of the process of observation, of measurements. This book is about scale, and its fundamental notion in computer vision, as well as human vision.
Scale-space theory is the theory of apertures. through which we and machines observe the world. The apertures come in an astounding variety. They can be exploited to model the first stages of human vision, and they appear in all aspects of computer vision, such as the extraction of features, the measurement of optic flow and stereo disparity, to do orientation analysis. segmentation, image enhancement etc. They have an essential role in the fundamental processes of differentiation and regularization.
Scale-space theory is named after the space that is fanned by looking at an image at many different scales simultaneously. When stacked, we get one dimension extra, i.e. the scale dimension. The scale-space is the space of the spatial and scale dimensions.
This book is a tutorial course. The level of the book is undergraduate and first level graduate. Its main purpose is to be used as a coursebook in computer vision and front-end vision entry courses. It may also be useful as an entry point for research in biological vision.
Although there are excellent texts appearing on the notion of scale space, most of them are not easy reading for people just entering this field or lacking a solid mathematical background. This book is intended partly to fill this gap, to act as an entry point for the growing literature on scale-space theory. Throughout the book we will work steadily through the necessary mathematics.
The book discusses the many classical papers published over the last two decades, when scale-space theory became mature. The different approaches and findings are put into context. First, linear scale-space theory is derived from first principles, giving it a sound mathematical basis.
The notion that a multi-scale approach is a natural consequence of the process of observation is interwoven in every chapter of this book. E.g. Hom and Schunck's famous optic flow equation gets a new meaning when we 'look at the data'. The concept of a point and local point operators like the derivative operator diffuse into versions with a Gaussian extent, making the process of differentiation well posed. It immediately makes large and mature fields like differential geometry, invariant theory, tensor analysis and singularity theory available for analysis on discrete data, such as images.
We develop ready-to-use applications of differential invariants of second, third and fourth order. The relation between accuracy, differential order and scale of the operator is developed, and an example of very high order derivatives is worked out in the analytical deblurring of Gaussian blur.
Practical examples are also developed in the chapters on multi-scale optic flow and multiscale differential structure of color images. Again, the physics of the observation process forces the analytical solution to be multi-scale. Several examples of ways to come to proper scale-selection are treated underway.Apertures and the notion of scale
Foundations of scale-space
The Gaussian kernel
Gaussian derivatives
Multi-scale derivatives: implementations
Natural limits on observations
Differentiation and regularization
The front-end visual system - the retina
A scale-space model for the retinal sampling
The front-end visual system - LGN and cortex
Deep structure I. watershed segmentation
Deep structure II. catastrophe theory
Deep structure III. topological numbers
Deblurring Gaussian blur
Multi-scale optic flow
Color differential structure
Steerable kernels
Scale-time
Geometry-driven diffusion
Epilog
A. Introduction to Mathematica
B. The concept of convolution
C. Installing the book and packages
D. First Start with Mathematica: Tips & Tricks
