Computer Vision is a rapidly growing field of research investigating computational and algorithmic issues associated with image acquisition, processing, and understanding. It serves tasks like manipulation, recognition, mobility, and communication in diverse application areas such as manufacturing, robotics, medicine, security and virtual reality. This volume contains a selection of papers devoted to theoretical foundations of computer vision covering a broad range of fields, e.g. motion analysis, discrete geometry, computational aspects of vision processes, models, morphology, invariance, image compression, 3D reconstruction of shape. Several issues have been identified to be of essential interest to the community: non-linear operators; the transition between continuous to discrete representations; a new calculus of non-orthogonal partially dependent systems.

Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.

The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

this gap. In sixteen survey articles the most important theoretical results, algorithms and software methods of computer algebra are covered, together with systematic references to literature. In addition, some new results are presented. Thus the volume should be a valuable source for obtaining a first impression of computer algebra, as well as for preparing a computer algebra course or for complementary reading. The preparation of some papers contained in this volume has been supported by grants from the Austrian "Fonds zur Forderung der wissenschaftlichen For schung" (Project No. 3877), the Austrian Ministry of Science and Research (Department 12, Dr. S. Hollinger), the United States National Science Foundation (Grant MCS-8009357) and the Deutsche Forschungsgemeinschaft (Lo-23 1-2). The work on the volume was greatly facilitated by the opportunity for the editors to stay as visitors at the Department of Computer and Information Sciences, University of Delaware, at the General Electric Company Research and Development Center, Schenectady, N. Y. , and at the Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, N. Y. , respectively. Our thanks go to all these institutions. The patient and experienced guidance and collaboration of the Springer-Verlag Wien during all the stages of production are warmly appreciated. The editors of the Cooperative editor of Supplementum Computing B. Buchberger R. Albrecht G. Collins R. Loos Contents Loos, R. : Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 1 Buchberger, B. , Loos, R. : Algebraic Simplification . . . . . . . . . . 11 Neubiiser, J. : Computing with Groups and Their Character Tables. 45 Norman, A. C. : Integration in Finite Terms. . . . . . . . . . . . . .

This volume contains mainly a collection of the invited lectures which were given during a conference on "Fundamentals of Numerical Computation," held in June, 5 - 8, 1979, on the occasion of the centennial of the Technical University of Berlin. About hundred scientists from several countries attended this conference. A preceding meeting on "Fundamentals of Computer-Arithmetic" was held in August, 1975, at the "Mathematisches Forschungsinstitut Oberwolfach." The lectures of this conference have been published as Supplementum 1 of Computing (Editors R. Albrecht, U. Kulisch). After a period of four years of active research the purpose of the Berlin-Conference was to give a broad survey of the present status of the closely connected topics Interval Analysis, Mathematical Foundation of Computer Arithmetic, Rounding Error Analysis and Stability of Numerical Algorithms and to give prospects of future activities in these fields. Besides the invited lectures 35 short com munications, each of 20 minutes length, were given. We gratefully acknowledge the support of the President of the Technical University and of his Aussenreferat as well as of the Department of Mathematics. Besides these institutions financial support was given by AEG-Telefunken, Berlin, Allianz Lebensversicherungs A.G., Stuttgart, CDC, Hamburg/Berlin, DAT A 100, Munchen, Gesellschaft von Freunden der TU Berlin e.V., Berlin and Siemens AG., Berlin. Finally we express our thanks to Mrs. G. Froehlich and Mrs. B. Trajanovic, who managed the paper work before, during and after the conference."

Obwohl man annehmen kann, daB das gerundete Rechnen so alt ist wie das Rechnen mit Zahlen iiberhaupt, hat es eine ausgedehnte und systematische Anwendung erst durch die neuzeitlichen Digitalrechenanlagen gefunden. Die zwangslliufige Begrenzung sowohl des Gesamtspeichers wie der Bitanzahl der einzelnen Speicherzellen und Register bedingt bei jeder Zahldarstellung eine Einschrlinkung eines theoretischen, idealisierten, unendlichen Zahlenbereiches auf eine endliche Teilmenge, in der die realen arithmetischen Operationen konstruktiv erfolgen. Infolgedessen stimmen die Regeln fiir dieses "gerundete" Rechnen im realen Bereich mit denen des Rechnens im idealen Bereich nicht iiberein und verschiedene der klassischen Eigenschaften arithmetischer Ver- kniipfungen, beispielsweise im Korper der rationalen Zahlen die Assoziativitlit und Distributivitlit, gehen bei Rundung verloren. Der gerundete Bereich sowie die konstruktiv auszufiihrenden arithmetischen Operationen sind natiirlich nicht Selbstzweck, sondem sie sollen in zu definierendem Sinne eine Approximation zunI idealen Bereich und zu den idealen arithmetischen Operationen darstellen. Seit einigen lahren bestehen nun Versuche und Teilergebnisse zu einer axio- matischen Begriindung und einer Theorie des gerundeten Rechnens. Diese bezie- hen sich einerseits auf die Konstruktionsvorschrift und deren Realisierung, nach der den idealen Zahlen bzw. einer konstruktiv darstellbaren Untermenge hier- von gerundete Zahlen zuzuordnen sind, urn gewisse Kriterien zu erfiiIlen, z. B. Minimisierung der Abweichung des Nliherungsergebnisses yom exakten Ergeb- nis bei Auswertung eines arithmetischen Ausdruckes mit verschiedenen Daten im statistischen Mittel, Ausgabe eines moglichst "kleinen" Zahlenbereiches, in dem das Ergebnis einer idealen Rechnung mit Sicherheit (Intervall-Arithmetik) oder mit vorgegebener Wahrscheinlichkeit liegt.