Analytic Combinatorics for Multiple Object Tracking
The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking—without information loss—into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to
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alytic Combinatorics for Multiple Object Tracking
Analytic Combinatorics for Multiple Object Tracking
Roy Streit Robert Blair Angle Murat Efe •
•
Analytic Combinatorics for Multiple Object Tracking
123
Roy Streit Metron, Inc Reston, VA, USA
Robert Blair Angle Metron, Inc Reston, VA, USA
Murat Efe Department of Electrical and Electronics Engineering Ankara University Golbasi, Ankara, Turkey
ISBN 978-3-030-61190-3 ISBN 978-3-030-61191-0 https://doi.org/10.1007/978-3-030-61191-0
(eBook)
© Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my loving wife, Nancy Roy Streit To Dorothy and Parker, my all Robert Blair Angle To Gülşah, Oğuzhan and Ali Emre Murat Efe
Preface
Solving simple enumeration problems is fun and natural for most folks. When the problems become complicated or subtle, however, solving them becomes tedious and the fun disappears. At the end of a long and difficult enumeration, a seed of doubt often floats unhappily to mind, “Did I/we overlook any terms, or double count them?” It takes time and patience, and careful (bordering sometimes on fanatical) attention to detail, to convince oneself that everything is fine. And then comes the task of convincing others the solution is correct, a necessary step if solving the problem is part of your job. Problems posed in the language of analytic combinatorics (AC) and generating functions (GFs) do not suffer from this “enumeration doubt” because the enumerations are embedded—exactly—in the derivatives of the GF, and the GF is determined by the fundamental assumptions of the problem, that is, from first principles. The doubt is focused where it belongs, on the fidelity of the GF model of the probl
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