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Introduction

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Local Features in Natural Images via Singularity Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2165))

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Abstract

In this monograph we consider a basic problem in computer imaging for natural images, which are images of objects obtained by projection of their reflected light rays onto a viewing plane, which might be a camera lens or a viewer’s eye. The goal for natural images is to detect the objects in the image and determine their geometric features such as edges, creases, corners, and “marking curves” separating regions of an object with distinct visual properties.

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Notes

  1. 1.

    Earlier versions had the title Characterizing Stable Local Features of Illuminated Surfaces and Their Generic Transitions from Viewer Movement and this was the way in which we referred to the present work in two articles [DGH1, DGH2]. These articles highlighted the main results without any of the mathematical details.

  2. 2.

    We are grateful to the following for permission to use the photographs: for Hassler Whitney, to his daughter Sally Thurston; for René Thom to the director of L’Institut des Hautes Études Scientifiques; for Bernard Malgrange, to Yousuke Ohyama; for Vladimir Arnol’d to Svetlana Tretyakova. The photograph of John Mather was taken by James Damon.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA

    James Damon

  2. Dept. of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Peter Giblin

  3. Ainsdale, UK

    Gareth Haslinger

Authors
  1. James Damon
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  2. Peter Giblin
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  3. Gareth Haslinger
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Damon, J., Giblin, P., Haslinger, G. (2016). Introduction. In: Local Features in Natural Images via Singularity Theory. Lecture Notes in Mathematics, vol 2165. Springer, Cham. https://doi.org/10.1007/978-3-319-41471-3_1

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