Titlebook: Approximation of Euclidean Metric by Digital Distances; Jayanta Mukhopadhyay Book 2020 The Author(s), under exclusive license to Springer

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cs by digital distances from the mid-sixties of the previous century. The book also contains an in-depth presentation of recent progress, and new research problems in this area.?.978-981-15-9900-2978-981-15-9901-9

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Organization

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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 also considers the empirical analysis of approximation errors.

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Conclusion,The chapter concludes the discussion of error analysis in this book by presenting a comparative study on performances of various representative distances in approximating Euclidean metrics.

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P. Frick,G.-A. Harnack,A. Praderf distance functions, and many of the results derived for them are shown as special cases of the properties of the general class of distance function. It includes discussion on m-neighbor distances, t-cost distances, generalized octagonal distances, chamfering weighted distances, weighted t-cost dis

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https://doi.org/10.1007/978-3-642-69841-5are discussed. It defines different types of geometric errors using those properties for evaluating the proximity of distance functions to Euclidean metrics. Finally, it presents a hybrid approach of computing analytical error from geometric measurements on hyperspheres.