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Applications of Singularity Theory and 3D Modelling in Arts and Retail

In: UK Success Stories in Industrial Mathematics

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  • Peter Giblin

    (The University of Liverpool, Department of Mathematical Sciences)

Abstract

When a camera moves with known motion and orientation past an object, modelled as a smooth surface M, it is possible to deduce the geometry of M from measurements of the apparent contours in the camera image. When the camera motion is not known then it is still possible in principle to recover the geometry of M through the use of ‘frontier points’. The theoretical framework is described in this chapter; it was formulated in the 1990s by several people, including K. Åström, R. Cipolla and the author [7]. The theory has been successfully implemented in real-world situations, with real data and using optimization algorithms to solve the equations; the specific applications referred to here are by Cipolla and his co-workers in Cambridge. Two practical applications, which formed the basis of the Impact Case, are described briefly in Section “Two Applications of the Theory”, but the details of the implementation are not included here.

Suggested Citation

  • Peter Giblin, 2016. "Applications of Singularity Theory and 3D Modelling in Arts and Retail," Springer Books, in: Philip J. Aston & Anthony J. Mulholland & Katherine M.M. Tant (ed.), UK Success Stories in Industrial Mathematics, edition 1, pages 265-270, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-25454-8_34
    DOI: 10.1007/978-3-319-25454-8_34
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