Visual Motion of Curves and Surfaces

<p>The world is full of objects, many of which are visible to us as surfaces. Examples are people, cars, machines, computers and bananas. Exceptions are such things as clouds and trees, which have a more detailed, fuzzy structure. Computer vision aims to detect and reconstruct features of surfaces from the images produced by cameras, in some ways mimicking the way in which humans reconstruct features of the world around them by using their eyes. This book describes how the 3D shape of surfaces can be recovered from image sequences of outlines. Cipolla and Giblin provide all the necessary background in differential geometry (assuming knowledge of elementary algebra and calculus) and in the analysis of visual motion, and emphasizes intuitive visual understanding of the geometric techniques with computer-generated illustrations. They also give a thorough introduction to the mathematical techniques and the details of the implementations, and apply the methods to data from real images.</p>

Computers & Technology

Cipolla, Roberto

Giblin, Peter

Computer Science

Cambridge University Press

<p>These proceedings collect the papers accepted for presentation at the bien nial IMA Conference on the Mathematics of Surfaces, held in the University of Cambridge, 4-7 September 2000. While there are many international con ferences in this fruitful borderland of mathematics, computer graphics and engineering, this is the oldest, the most frequent and the only one to concen trate on surfaces. Contributors to this volume come from twelve different countries in Eu rope, North America and Asia. Their contributions reflect the wide diversity of present-day applications which include modelling parts of the human body for medical purposes as well as the production of cars, aircraft and engineer ing components. Some applications involve design or construction of surfaces by interpolating or approximating data given at points or on curves. Others consider the problem of 'reverse engineering'-giving a mathematical descrip tion of an already constructed object. We are particularly grateful to Pamela Bye (at the Institue of Mathemat ics and its Applications) for help in making arrangements; Stephanie Harding and Karen Barker (at Springer Verlag, London) for publishing this volume and to Kwan-Yee Kenneth Wong (Cambridge) for his heroic help with com piling the proceedings and for dealing with numerous technicalities arising from large and numerous computer files. Following this Preface is a listing of the programme committee who with the help of their colleagues did much work in refereeing the papers for these proceedings.</p>

The Mathematics of Surfaces IX: Proceedings of the Ninth IMA Conference on the Mathematics of Surfaces

Crafts, Hobbies & Home

Gardening & Landscape Design

Springer

This monograph is devoted to the problem of inferring geometric information about arbitrarily curved surfaces from visual cues; this is a central problem in computer vision with immediate relevance for robot manipulation and navigation.The author develops computational theories and techniques relating visual information arising from viewer movements to the differential geometry of visible surfaces. The theories developed have been implemented and tested using a real-time tracking system based on deformable contours. Applications of the techniques to geometric modelling, obstacle avoidance, navigation, and object manipulation are presented.

Active Visual Inference of Surface Shape (Lecture Notes in Computer Science, 1016)

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