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2014 | Buch

Topology of Digital Images: Basic Ingredients Kapitel lesen Erstes Kapitel lesen

Topology of Digital Images

Visual Pattern Discovery in Proximity Spaces

verfasst von: James F. Peters

Verlag: Springer Berlin Heidelberg

Buchreihe : Intelligent Systems Reference Library

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book carries forward recent work on visual patterns and structures in digital images and introduces a near set-based a topology of digital images. Visual patterns arise naturally in digital images viewed as sets of non-abstract points endowed with some form of proximity (nearness) relation. Proximity relations make it possible to construct uniform topologies on the sets of points that constitute a digital image. In keeping with an interest in gaining an understanding of digital images themselves as a rich source of patterns, this book introduces the basics of digital images from a computer vision perspective. In parallel with a computer vision perspective on digital images, this book also introduces the basics of proximity spaces. Not only the traditional view of spatial proximity relations but also the more recent descriptive proximity relations are considered. The beauty of the descriptive proximity approach is that it is possible to discover visual set patterns among sets that are non-overlapping and non-adjacent spatially. By combining the spatial proximity and descriptive proximity approaches, the search for salient visual patterns in digital images is enriched, deepened and broadened. A generous provision of Matlab and Mathematica scripts are used in this book to lay bare the fabric and essential features of digital images for those who are interested in finding visual patterns in images. The combination of computer vision techniques and topological methods lead to a deep understanding of images.

Inhaltsverzeichnis

Frontmatter
Topology of Digital Images: Basic Ingredients
Abstract
This chapter not only introduces some of the basics of digital image processing, it also introduces the idea of image structures such as various neighbourhoods of points in the topology of digital images. A recognition of image structures ushers in a topological view of images and leads to the discovery of visual patterns.
James F. Peters
Structures Arising from Sets of Pixels
Abstract
The real input side of intelligence is perception in a much broader sense, the analysis of all the noisy incomplete signals which you can pick up from the world through natural or artificial senses. Such signals typically display a mix of distinctive patterns which tend to repeat with many kinds of variations and which are confused by noisy distortions and extraneous clutter. The interesting and important structure of the world is thus coded in these signals, using a code which is complex but not perversely so (David Mumford, ICM 2002, Beijing [184]).
James F. Peters
Visualisations and Covers
Abstract
This chapter introduces various ways to visualise digital images. For example, the distribution of pixel orientations in a tree nymph butterfly (genus idea, species I.leuconoe, family nymphalidae) is shown in Fig. 3.1.1 and the distribution of pixel orientations for a red admiral butterfly (genus vanessa, species atalanta, family nymphalidae) is shown in Fig. 3.1.2 (see MathScript 6 in Appendix A.3 for the Mathematica script used to produce these distributions). By itself, the distribution in Fig. 3.1.1 is interesting, since it indicates the dominance of negative pixel orientations in the tree nymph butterfly (at rest). By contrast, the pixel orientations of the red admiral butterfly (at rest) in Fig. 3.1.2 aremarkedly less negative.This form of visualisation is useful in the case where a pair of images are compared and classified, based on pixel orientations.
James F. Peters
Linear Filtering and Visual Patterns in Images
Abstract
This chapter introduces linear spatial filters and visual patterns in digital images. Previously, the focus was manipulating the dynamic range to improve, sharpen and increase the contrast of image features. By contrast, image filtering is based on weighted sums of local neighbourhood pixel values. As a result, we obtain a means of removing image noise, sharpening image features (enhancing image appearance), and achieve edge and corner detection. A filtered image provides a workspace for the study of near sets and visual patterns in a digital image as well as different forms of uniform topologies in digital images.
James F. Peters
Edges, Lines, Ridges, and Nearness Structures
Abstract
This chapter focuses on the detection of edges, lines, ridges and corners in digital images. Interest in ridges in digital images began in the early 1980s with the study by R. Haralick on zero crossing second derivative edge detection [97] and the subsequent work by T. Lindeberg in the late 1990s [157]. In nature, a ridge is a long, narrow hilltop, mountain range or watershed. Descriptive uniform topologies and new forms of visual patterns are natural byproducts of the study of edges, lines and ridges.
James F. Peters
Corners and Symmetric Proximity
Abstract
This chapter further explores approaches to edge detection stemming from the isotropic edge detection proposed by D. Marr and E. Hildreth [174] and its alternative, namely, anisotropic (direction dependent) edge detection. This chapter also considers Harris-Stephens corner detection. This further study of edge detection leads rather naturally to a consideration of the nearness of sets of pixels, the notion of symmetric proximity and proximal neighbourhoods in digital images.
James F. Peters
Separation of Image Regions and Set Patterns
Abstract
This chapter focuses on segmenting digital images and the separation axioms from topology. Segmentation of an image results from partitioning an image to obtain disjoint sets of homogeneous pixels called segments. Mathematical morphology (MM) is a mainstay in the study of image segmentation. MM was introduced by G. Matheron (founder of geostatistics [175]) and J. Serra [258] during the 1960s (Matheron was Serra’s Ph.D. supervisor). Two basic operations (erosion and dilation denoted by ⊝ , ⊕, respectively) establish the foundations of MM. Digital images are viewed as sets of objects (dark areas) that are either thinned (eroded) or expanded (dilated). Combinations of erosion and dilation operations lead to closing and opening operations. Eventually, what is known as watershed segmentation was introduced as a means of delineating the boundaries of image objects as closed contours.
James F. Peters
Descriptive Raster Spaces
Abstract
Recall that a raster is a rectangular pattern of scanning lines followed by an electron beam on a television screen or computer monitor. A raster image is a 2D array of numbers. Each row of numbers in a raster image, where each number is a pixel intensity, is one of the lines in a raster. In a vector representation of a digital image (also called vector image), each pixel p is represented by a n × 1 vector p. A pixel vector is a column of n real numbers,
James F. Peters
Component Analysis and Uniform Spaces
Abstract
This chapter introduces a number of selected topics that serve to strengthen the overall view of a topology of digital images. There is interest in identifying those parts of each image with uniform as well as interesting characteristics. This interest leads us to consider an introduction to what are known as principle axes in a division of image spaces into four quadrants (image niches) containing sets of pixel clusters and with the origin located at the centre of mass of an image.
James F. Peters
Shapes and Shape Set Patterns
Abstract
This chapter introduces shape descriptors and uniform coverings of shapes found in digital images. Shape descriptors are useful in representing and extracting shape information from images. In general, a digital image shape descriptor is an expression that describes, identifies or indexes an image region. Shape descriptors are usually mathematical expressions used to extract image region shape feature values. The basic approach is to use shape descriptors to represent, extract and quantify information about image shapes.
James F. Peters
Texture and Texture Set Patterns
Abstract
The chapter introduces local pixel neighbourhood-based texture features. An image texture is a small, elementary pattern that is repeated periodically or almost periodically in a digital image (see, e.g., the corrugated (honeycomb-like) configuration of the dragonfly wings in Fig. 11.1). A texture feature provides a basis for separating an object from the background of an image. Examples of texture features are contrast, correlation, entropy, homogeneity, local orientation (gradient), local range, local variance and uniformity.
James F. Peters
Pattern-Based Picture Classification
Abstract
In this work, pattern-based classification will be governed by the selection of a motif set that is a generator for a set pattern. A motif set pattern serves as a representative of a class of images and also makes it possible to identify salient test images. A test image is salient, provided it has a set pattern that is descriptively close enough to the class set pattern.
James F. Peters
Backmatter
Metadaten
Titel
Topology of Digital Images
verfasst von
James F. Peters
Copyright-Jahr
2014
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-53845-2
Print ISBN
978-3-642-53844-5
DOI
https://doi.org/10.1007/978-3-642-53845-2

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