Views of illuminated surfaces

DIKU-talk with professor Peter Giblin, University of Liverpool

Program:

15.15 - 16.30 Talk - Views of illuminated surfaces

The talk is followed by a reception. All are welcome!
Scientific Host: The Image Group at DIKU

Abstract:

This is joint work with James Damon (UNC Chapel Hill) and Gareth Haslinger (Liverpool).
We consider the mutual interactions of apparent contours, marking curves, shade and cast shadow boundaries, on surfaces which are smooth or piecewise smooth, such as valley/ridge creases and corners of various types. We consider only stable illumination but allow up to codimension 2 in the viewing.

The most complete results are codimension 1, which amounts to a `flypast' of a surface. We use the methods of singularity theory to derive rigorously the abstract classification of view projections and then apply geometrical arguments to realise the various possibilities or, in many cases, to prove that realisation is not possible. Our work corrects several errors in
earlier attempts to do this classification, which depended on applying theorems of singularity theory to situations where they are not valid, leading to incorrect results.

Short bio:

Peter Giblin is professor of mathematics at the University of Liverpool, where he has worked since 1967 and served as head of the Department of Mathematical Sciences. His research interests are in singularity theory and its application to differential geometry and computer vision. Professor Giblin has collaborated with the Image group at the University of Copenhagen through the EU project 'Deep Structure, Singularities and Computer Vision'.