This edited volume addresses a subject which has been discussed inten sively in the computer vision community for several years. Performance characterization and evaluation of computer vision algorithms are of key importance, particularly with respect to the configuration of reliable and ro bust computer vision systems as well as the dissemination of reconfigurable systems in novel application domains. Although a plethora of literature on this subject is available for certain' areas of computer vision, the re search community still faces a lack of a well-grounded, generally accepted, and--eventually-standardized methods. The range of fundamental problems encoIl passes the value of synthetic images in experimental computer vision, the selection of a representative set of real images related to specific domains and tasks, the definition of ground truth given different tasks and applications, the design of experimental test beds, the analysis of algorithms with respect to general characteristics such as complexity, resource consumption, convergence, stability, or range of admissible input data, the definition and analysis of performance measures for classes of algorithms, the role of statistics-based performance measures, the generation of data sheets with performance measures of algorithms sup porting the system engineer in his configuration problem, and the validity of model assumptions for specific applications of computer vision."

The recent emergence of Local Binary Patterns (LBP) has led to significant progress in applying texture methods to various computer vision problems and applications. The focus of this research has broadened from 2D textures to 3D textures and spatiotemporal (dynamic) textures. Also, where texture was once utilized for applications such as remote sensing, industrial inspection and biomedical image analysis, the introduction of LBP-based approaches have provided outstanding results in problems relating to face and activity analysis, with future scope for face and facial expression recognition, biometrics, visual surveillance and video analysis.

"Computer Vision Using Local Binary Patterns" provides a detailed description of the LBP methods and their variants both in spatial and spatiotemporal domains. This comprehensive reference also provides an excellent overview as to how texture methods can be utilized for solving different kinds of computer vision and image analysis problems. Source codes of the basic LBP algorithms, demonstrations, some databases and a comprehensive LBP bibliography can be found from an accompanying web site.

Topics include: local binary patterns and their variants in spatial and spatiotemporal domains, texture classification and segmentation, description of interest regions, applications in image retrieval and 3D recognition - Recognition and segmentation of dynamic textures, background subtraction, recognition of actions, face analysis using still images and image sequences, visual speech recognition and LBP in various applications.

Written by pioneers of LBP, this book is an essential resource for researchers, professional engineers and graduate students in computer vision, image analysis and pattern recognition. The book will also be of interest to all those who work with specific applications of machine vision.

Provides comprehensive coverage of theory and hands-on implementation of computer vision-based sensors for structural health monitoring This book is the first to fill the gap between scientific research of computer vision and its practical applications for structural health monitoring (SHM). It provides a complete, state-of-the-art review of the collective experience that the SHM community has gained in recent years. It also extensively explores the potentials of the vision sensor as a fast and cost-effective tool for solving SHM problems based on both time and frequency domain analytics, broadening the application of emerging computer vision sensor technology in not only scientific research but also engineering practice. Computer Vision for Structural Dynamics and Health Monitoring presents fundamental knowledge, important issues, and practical techniques critical to successful development of vision-based sensors in detail, including robustness of template matching techniques for tracking targets; coordinate conversion methods for determining calibration factors to convert image pixel displacements to physical displacements; sensing by tracking artificial targets vs. natural targets; measurements in real time vs. by post-processing; and field measurement error sources and mitigation methods. The book also features a wide range of tests conducted in both controlled laboratory and complex field environments in order to evaluate the sensor accuracy and demonstrate the unique features and merits of computer vision-based structural displacement measurement. Offers comprehensive understanding of the principles and applications of computer vision for structural dynamics and health monitoring Helps broaden the application of the emerging computer vision sensor technology from scientific research to engineering practice such as field condition assessment of civil engineering structures and infrastructure systems Includes a wide range of laboratory and field testing examples, as well as practical techniques for field application Provides MATLAB code for most of the issues discussed including that of image processing, structural dynamics, and SHM applications Computer Vision for Structural Dynamics and Health Monitoring is ideal for graduate students, researchers, and practicing engineers who are interested in learning about this emerging sensor technology and advancing their applications in SHM and other engineering problems. It will also benefit those in civil and aerospace engineering, energy, and computer science.

This book presents contributions in the field of computational intelligence for the purpose of image analysis. The chapters discuss how problems such as image segmentation, edge detection, face recognition, feature extraction, and image contrast enhancement can be solved using techniques such as genetic algorithms and particle swarm optimization. The contributions provide a multidimensional approach, and the book will be useful for researchers in computer science, electrical engineering, and information technology.

This book covers dynamic simulation of deformable objects, which is one of the most challenging tasks in computer graphics and visualization. It focuses on the simulation of deformable models with anisotropic materials, one of the less common approaches in the existing research. Both physically-based and geometrically-based approaches are examined. The authors start with transversely isotropic materials for the simulation of deformable objects with fibrous structures. Next, they introduce a fiber-field incorporated corotational finite element model (CLFEM) that works directly with a constitutive model of transversely isotropic material. A smooth fiber-field is used to establish the local frames for each element. To introduce deformation simulation for orthotropic materials, an orthotropic deformation controlling frame-field is conceptualized and a frame construction tool is developed for users to define the desired material properties. The orthotropic frame-field is coupled with the CLFEM model to complete an orthotropic deformable model. Finally, the authors present an integrated real-time system for animation of skeletal characters with anisotropic tissues. To solve the problems of volume distortion and high computational costs, a strain-based PBD framework for skeletal animation is explained; natural secondary motion of soft tissues is another benefit. The book is written for those researchers who would like to develop their own algorithms. The key mathematical and computational concepts are presented together with illustrations and working examples. It can also be used as a reference book for graduate students and senior undergraduates in the areas of computer graphics, computer animation, and virtual reality. Academics, researchers, and professionals will find this to be an exceptional resource.

Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address.

Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

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Accurate Visual Metrology from Single and Multiple Uncalibrated Images presents novel techniques for constructing three-dimensional models from bi-dimensional images using virtual reality tools. Antonio Criminisi develops the mathematical theory of computing world measurements from single images, and builds up a hierarchy of novel, flexible techniques to make measurements and reconstruct three-dimensional scenes from uncalibrated images, paying particular attention to the accuracy of the reconstruction.
This book includes examples of interesting viable applications (eg. Forensic Science, History of Art, Virtual Reality, Architectural and indoor measurements), presented in a simple way, accompanied by pictures, diagrams and plenty of worked examples to help the reader understand and implement the algorithms.

This book thoroughly covers the remote sensing visualization and analysis techniques based on computational imaging and vision in Earth science. Remote sensing is considered a significant information source for monitoring and mapping natural and man-made land through the development of sensor resolutions that committed different Earth observation platforms. The book includes related topics for the different systems, models, and approaches used in the visualization of remote sensing images. It offers flexible and sophisticated solutions for removing uncertainty from the satellite data. It introduces real time big data analytics to derive intelligence systems in enterprise earth science applications. Furthermore, the book integrates statistical concepts with computer-based geographic information systems (GIS). It focuses on image processing techniques for observing data together with uncertainty information raised by spectral, spatial, and positional accuracy of GPS data. The book addresses several advanced improvement models to guide the engineers in developing different remote sensing visualization and analysis schemes. Highlights on the advanced improvement models of the supervised/unsupervised classification algorithms, support vector machines, artificial neural networks, fuzzy logic, decision-making algorithms, and Time Series Model and Forecasting are addressed. This book guides engineers, designers, and researchers to exploit the intrinsic design remote sensing systems. The book gathers remarkable material from an international experts' panel to guide the readers during the development of earth big data analytics and their challenges.

A key element of any modern video codec is the efficient exploitation of temporal redundancy via motion-compensated prediction. In this book, a novel paradigm of representing and employing motion information in a video compression system is described that has several advantages over existing approaches. Traditionally, motion is estimated, modelled, and coded as a vector field at the target frame it predicts. While this "prediction-centric" approach is convenient, the fact that the motion is "attached" to a specific target frame implies that it cannot easily be re-purposed to predict or synthesize other frames, which severely hampers temporal scalability. In light of this, the present book explores the possibility of anchoring motion at reference frames instead. Key to the success of the proposed "reference-based" anchoring schemes is high quality motion inference, which is enabled by the use of a more "physical" motion representation than the traditionally employed "block" motion fields. The resulting compression system can support computationally efficient, high-quality temporal motion inference, which requires half as many coded motion fields as conventional codecs. Furthermore, "features" beyond compressibility - including high scalability, accessibility, and "intrinsic" framerate upsampling - can be seamlessly supported. These features are becoming ever more relevant as the way video is consumed continues shifting from the traditional broadcast scenario to interactive browsing of video content over heterogeneous networks. This book is of interest to researchers and professionals working in multimedia signal processing, in particular those who are interested in next-generation video compression. Two comprehensive background chapters on scalable video compression and temporal frame interpolation make the book accessible for students and newcomers to the field.

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. Contents Part I Geometric issues in PDE problems related to the infinity Laplace operator Solution of free boundary problems in the presence of geometric uncertainties Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies High-order topological expansions for Helmholtz problems in 2D On a new phase field model for the approximation of interfacial energies of multiphase systems Optimization of eigenvalues and eigenmodes by using the adjoint method Discrete varifolds and surface approximation Part II Weak Monge-Ampere solutions of the semi-discrete optimal transportation problem Optimal transportation theory with repulsive costs Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations On the Lagrangian branched transport model and the equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless Euler equations with maximal density constraint: a time-splitting scheme Convergence of a fully discrete variational scheme for a thin-film equatio Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance

Arobotmustperceivethethree-dimensionalworldifitistobeeffective there. Yet recovering 3-D information from projected images is difficult, and still remains thesubjectofbasic research. Alternatively, onecan use sensorsthatcanprovidethree-dimensionalrangeinformationdirectly. The technique ofprojecting light-stripesstartedto be used in industrialobject recognition systems asearly asthe 1970s, andtime-of-flight laser-scanning range finders became available for outdoor mobile robotnavigation in the mid-eighties. Once range data are obtained, a vision system must still describe the scene in terms of 3-D primitives such as edges, surfaces, and volumes, and recognize objeCts of interest. Today, the art of sensing, extractingfeatures, and recognizing objectsbymeans ofthree-dimensional rangedataisoneofthemostexcitingresearchareasincomputervision. Three-Dimensional Machine Vision is a collection of papers dealing withthree-dimensionalrangedata. Theauthorsarepioneeringresearchers: some are founders and others are bringingnew excitements in thefield. I have tried to select milestone papers, and my goalhas beento make this bookareferenceworkforresearchersinthree-dimensionalvision. The book is organized into four parts: 3-D Sensors, 3-D Feature Extractions, ObjectRecognitionAlgorithms, andSystemsandApplications. Part I includes four papers which describe the development of unique, capable 3-D range sensors, as well as discussions of optical, geometrical, electronic, and computational issues. Mundy and Porter describe asensor systembasedonstructuredilluminationforinspectingmetalliccastings. In order to achieve high-speed data acquisition, it uses multiple lightstripes withwavelength multiplexing. Case, Jalkio, andKim alsopresentamulti stripe system and discuss various design issues in range sensing by triangulation. ThenumericalstereocameradevelopedbyAltschuler, Bae, Altschuler, Dijak, Tamburino, and Woolford projects space-coded grid patterns which are generated by an electro-optical programmable spatial viii PREFACE light modulator. Kanade and Fuhrman present a proximity sensor using multipleLEDswhich areconically arranged. Itcan measurebothdistance andorientationofanobject'ssurface."

This book offers a comprehensive introduction to advanced methods for image and video analysis and processing. It covers deraining, dehazing, inpainting, fusion, watermarking and stitching. It describes techniques for face and lip recognition, facial expression recognition, lip reading in videos, moving object tracking, dynamic scene classification, among others. The book combines the latest machine learning methods with computer vision applications, covering topics such as event recognition based on deep learning,dynamic scene classification based on topic model, person re-identification based on metric learning and behavior analysis. It also offers a systematic introduction to image evaluation criteria showing how to use them in different experimental contexts. The book offers an example-based practical guide to researchers, professionals and graduate students dealing with advanced problems in image analysis and computer vision.

Data visualization is currently a very active and vital area of research, teaching and development. The term unites the established field of scientific visualization and the more recent field of information visualization. The success of data visualization is due to the soundness of the basic idea behind it: the use of computer-generated images to gain insight and knowledge from data and its inherent patterns and relationships. A second premise is the utilization of the broad bandwidth of the human sensory system in steering and interpreting complex processes, and simulations involving data sets from diverse scientific disciplines and large collections of abstract data from many sources.
These concepts are extremely important and have a profound and widespread impact on the methodology of computational science and engineering, as well as on management and administration. The interplay between various application areas and their specific problem solving visualization techniques is emphasized in this book. Reflecting the heterogeneous structure of Data Visualization, emphasis was placed on these topics:

-Visualization Algorithms and Techniques;
-Volume Visualization;
-Information Visualization;
-Multiresolution Techniques;
-Interactive Data Exploration. Data Visualization: The State of the Art presents the state of the art in scientific and information visualization techniques by experts in this field. It can serve as an overview for the inquiring scientist, and as a basic foundation for developers. This edited volume contains chapters dedicated to surveys of specific topics, and a great deal of original work not previously published illustrated by examples from awealth of applications. The book will also provide basic material for teaching the state of the art techniques in data visualization. The companion CD-ROM contains all chapters in digital form with illustrations in color, as well as additional high-quality images and movies.
Data Visualization: The State of the Art is designed to meet the needs of practitioners and researchers in scientific and information visualization. This book is also suitable as a secondary text for graduate level students in computer science and engineering.

Vision chips, or smart visual sensors, are those sensors that have integrated image acquisition and parallel processing, often at the pixel level, using dedicated analog and digital circuits. Vision Chips presents a systematic approach to the design and analysis of vision chips using analog VLSL. It presents algorithmic level implementation issues, from both the VLSI and computer vision points of view. It reviews the VLSI technologies and general analog VLSI design methodologies, in the context of suitability for vision chips. It describes chip-level architectural issues, including tessellation structures, pixel-processor interaction, and data read-out. It presents detailed analysis of building-blocks necessary in vision chips, including photodetectors, photocircuits, and spatial and temporal processing circuits. It addresses other important design issues, such as testing, digital noise, and mismatch. In addition Vision Chips reviews some of the past and existing implementations of smart vision sensors. It contains condensed information on more than fifty vision chips, designed by research laboratories all over the world. Novel and interesting features of each vision chip have been highlighted through informative diagrams and concise descriptions. This book is a valuable asset for researchers in the area, engineers working on the design of vision sensors, graduate students working in analog VLSI and vision, and computer vision and biological vision researchers and scientists.

Digital Functions and Data Reconstruction: Digital-Discrete Methods provides a solid foundation to the theory of digital functions and its applications to image data analysis, digital object deformation, and data reconstruction. This new method has a unique feature in that it is mainly built on discrete mathematics with connections to classical methods in mathematics and computer sciences. Digitally continuous functions and gradually varied functions were developed in the late 1980s. A. Rosenfeld (1986) proposed digitally continuous functions for digital image analysis, especially to describe the "continuous" component in a digital image, which usually indicates an object. L. Chen (1989) invented gradually varied functions to interpolate a digital surface when the boundary appears to be continuous. In theory, digitally continuous functions are very similar to gradually varied functions. Gradually varied functions are more general in terms of being functions of real numbers; digitally continuous functions are easily extended to the mapping from one digital space to another. This will be the first book about digital functions, which is an important modern research area for digital images and digitalized data processing, and provides an introduction and comprehensive coverage of digital function methods. Digital Functions and Data Reconstruction: Digital-Discrete Methods offers scientists and engineers who deal with digital data a highly accessible, practical, and mathematically sound introduction to the powerful theories of digital topology and functional analysis, while avoiding the more abstruse aspects of these topics.

The application of intelligent imaging techniques to industrial vision problems is an evolving aspect of current machine vision research. Machine vision is a relatively new technology, more concerned with systems engineering than with computer science, and with much to offer the manufacturing industry in terms of improving efficiency, safety and product quality. Beginning with an introductory chapter on the basic concepts, the authors develop these ideas to describe intelligent imaging techniques for use in a new generation of industrial imaging systems. Sections cover the application of AI languages such as Prolog, the use of multi-media interfaces and multi-processor systems, external device control, and colour recognition. The text concludes with a discussion of several case studies that illustrate how intelligent machine vision techniques can be used in industrial applications.

Computer Vision for Multimedia Applications: Methods and Solutions includes the latest developments in computer vision methods applicable to various problems in multimedia computing. This publication presents discussions on new ideas, as well as problems in computer vision and multimedia computing. It will serve as an important reference in multimedia and computer vision for academicians, researchers, and academic libraries.

The concept of ridges has appeared numerous times in the image processing liter ature. Sometimes the term is used in an intuitive sense. Other times a concrete definition is provided. In almost all cases the concept is used for very specific ap plications. When analyzing images or data sets, it is very natural for a scientist to measure critical behavior by considering maxima or minima of the data. These critical points are relatively easy to compute. Numerical packages always provide support for root finding or optimization, whether it be through bisection, Newton's method, conjugate gradient method, or other standard methods. It has not been natural for scientists to consider critical behavior in a higher-order sense. The con cept of ridge as a manifold of critical points is a natural extension of the concept of local maximum as an isolated critical point. However, almost no attention has been given to formalizing the concept. There is a need for a formal development. There is a need for understanding the computation issues that arise in the imple mentations. The purpose of this book is to address both needs by providing a formal mathematical foundation and a computational framework for ridges. The intended audience for this book includes anyone interested in exploring the use fulness of ridges in data analysis."

Computer vision is one of the most complex and computationally intensive problem. Like any other computationally intensive problems, parallel pro cessing has been suggested as an approach to solving the problems in com puter vision. Computer vision employs algorithms from a wide range of areas such as image and signal processing, advanced mathematics, graph theory, databases and artificial intelligence. Hence, not only are the comput ing requirements for solving vision problems tremendous but they also demand computers that are efficient to solve problems exhibiting vastly dif ferent characteristics. With recent advances in VLSI design technology, Single Instruction Multiple Data (SIMD) massively parallel computers have been proposed and built. However, such architectures have been shown to be useful for solving a very limited subset of the problems in vision. Specifically, algorithms from low level vision that involve computations closely mimicking the architec ture and require simple control and computations are suitable for massively parallel SIMD computers. An Integrated Vision System (IVS) involves com putations from low to high level vision to be executed in a systematic fashion and repeatedly. The interaction between computations and information dependent nature of the computations suggests that architectural require ments for computer vision systems can not be satisfied by massively parallel SIMD computers."

The research book is focused on the recent advances in computer vision methodologies and innovations in practice. The Contributions include: * Human Action Recognition: Contour-Based and Silhouette-based Approaches. * The Application of Machine Learning Techniques to Real Time Audience Analysis System. * Panorama Construction from Multi-view Cameras in Outdoor Scenes. * A New Real-Time Method of Contextual Image Description and Its Application in Robot Navigation and Intelligent Control. * Perception of Audio Visual Information for Mobile Robot Motion Control Systems. * Adaptive Surveillance Algorithms Based on the Situation Analysis. * Enhanced, Synthetic and Combined Vision Technologies for Civil Aviation. * Navigation of Autonomous Underwater Vehicles Using Acoustic and Visual Data Processing. * Efficient Denoising Algorithms for Intelligent Recognition Systems. * Image Segmentation Based on Two-dimensional Markov Chains. The book is directed to the PhD students, professors, researchers and software developers working in the areas of digital video processing and computer vision technologies.

Computer systems that analyze images are critical to a wide variety of applications such as visual inspections systems for various manufacturing processes, remote sensing of the environment from space-borne imaging platforms, and automatic diagnosis from X-rays and other medical imaging sources. Professor Azriel Rosenfeld, the founder of the field of digital image analysis, made fundamental contributions to a wide variety of problems in image processing, pattern recognition and computer vision. Professor Rosenfeld's previous students, postdoctoral scientists, and colleagues illustrate in Foundations of Image Understanding how current research has been influenced by his work as the leading researcher in the area of image analysis for over two decades. Each chapter of Foundations of Image Understanding is written by one of the world's leading experts in his area of specialization, examining digital geometry and topology (early research which laid the foundations for many industrial machine vision systems), edge detection and segmentation (fundamental to systems that analyze complex images of our three-dimensional world), multi-resolution and variable resolution representations for images and maps, parallel algorithms and systems for image analysis, and the importance of human psychophysical studies of vision to the design of computer vision systems. Professor Rosenfeld's chapter briefly discusses topics not covered in the contributed chapters, providing a personal, historical perspective on the development of the field of image understanding. Foundations of Image Understanding is an excellent source of basic material for both graduate students entering the field and established researchers who require a compact source for many of the foundational topics in image analysis.

Advancements in digital sensor technology, digital image analysis techniques, as well as computer software and hardware have brought together the fields of computer vision and photogrammetry, which are now converging towards sharing, to a great extent, objectives and algorithms. The potential for mutual benefits by the close collaboration and interaction of these two disciplines is great, as photogrammetric know-how can be aided by the most recent image analysis developments in computer vision, while modern quantitative photogrammetric approaches can support computer vision activities. Devising methodologies for automating the extraction of man-made objects (e.g. buildings, roads) from digital aerial or satellite imagery is an application where this cooperation and mutual support is already reaping benefits. The valuable spatial information collected using these interdisciplinary techniques is of improved qualitative and quantitative accuracy. This book offers a comprehensive selection of high-quality and in-depth contributions from world-wide leading research institutions, treating theoretical as well as implementational issues, and representing the state-of-the-art on this subject among the photogrammetric and computer vision communities.

With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index

Gaussian scale-space is one of the best understood multi-resolution techniques available to the computer vision and image analysis community. It is the purpose of this book to guide the reader through some of its main aspects. During an intensive weekend in May 1996 a workshop on Gaussian scale-space theory was held in Copenhagen, which was attended by many of the leading experts in the field. The bulk of this book originates from this workshop. Presently there exist only two books on the subject. In contrast to Lindeberg's monograph (Lindeberg, 1994e) this book collects contributions from several scale space researchers, whereas it complements the book edited by ter Haar Romeny (Haar Romeny, 1994) on non-linear techniques by focusing on linear diffusion. This book is divided into four parts. The reader not so familiar with scale-space will find it instructive to first consider some potential applications described in Part 1. Parts II and III both address fundamental aspects of scale-space. Whereas scale is treated as an essentially arbitrary constant in the former, the latter em phasizes the deep structure, i.e. the structure that is revealed by varying scale. Finally, Part IV is devoted to non-linear extensions, notably non-linear diffusion techniques and morphological scale-spaces, and their relation to the linear case. The Danish National Science Research Council is gratefully acknowledged for providing financial support for the workshop under grant no. 9502164."