Error Analysis: Analytical Approaches
The chapter discusses analytical approaches for analysis of errors of approximating Euclidean metrics by digital metrics. Toward this, various analytical error measures have been defined and their upper-bounds in integral and real spaces are discussed. It
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Approximation of Euclidean Metric by Digital Distances
Approximation of Euclidean Metric by Digital Distances
Jayanta Mukhopadhyay
Approximation of Euclidean Metric by Digital Distances
123
Jayanta Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology Kharagpur Kharagpur, West Bengal, India
ISBN 978-981-15-9900-2 ISBN 978-981-15-9901-9 https://doi.org/10.1007/978-981-15-9901-9
(eBook)
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
To my father Shree Dulal Krishna Mukherjee with deep gratitude, love, and respect.
Preface
In this monograph, different types of distance functions in an n-D integral space are discussed to consider their usefulness in approximating Euclidean metric. It discusses the properties of these distance functions and presents various approaches to error analysis in approximating Euclidean metrics. The main emphasis of this book is to present the mathematical treatises for performing error analysis of a digital metric with reference to the Euclidean metric in an integral coordinate space of arbitrary dimension. I hope that the monograph will be useful to researchers and postgraduate students in areas of digital geometry, pattern recognition, and image processing. The theory and results on the properties of different distance functions presented may have applications in various pattern recognition techniques. Analytical approaches discussed in the book would be useful in solving related problems in digital and distance geometry. As a prerequisite, the author expects that the readers have gone through first-level cour
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