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The structure on symmetry sets of images as a family of iso-contours

All the results produced by the Liverpool team are theoretical, as envisaged in the original proposal. In Deliverable 23 we gave the latest information on the symmetry sets of isophote curves in all the generic cases.

These matters have not been investigated before. We obtained a new subdivision of the hyperbolic region of a surface into two sub-regions separated by the 'vertex transition curve'. This separates the two generic behaviours of the vertices (maxima/minima of curvature) of sections of a surface at a given hyperbolic point. No global definition of this curve is known, and in fact this question has been taken up by other mathematicians at INRIA in France following a visit by myself to INRIA in December 2005. I hope indeed to pursue it myself.

These theoretical results are not directly applicable to technology. That will be a later stage for someone else to consider.

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The University of Liverpool
Department of Mathematical Sciences, Peach Street
L69 7ZL Liverpool
United Kingdom
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