Computer Vision — ECCV 2002: 7th European Conference on by José Gomes, Aleksandra Mojsilovic (auth.), Anders Heyden,

By José Gomes, Aleksandra Mojsilovic (auth.), Anders Heyden, Gunnar Sparr, Mads Nielsen, Peter Johansen (eds.)

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Extra resources for Computer Vision — ECCV 2002: 7th European Conference on Computer Vision Copenhagen, Denmark, May 28–31, 2002 Proceedings, Part II

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28. K. Sobottka and I. Pitas. Extraction of facial regions and features using color and shape information. In Proceedings of the International Conference on Pattern Recognition, volume 3, pages C421–C425, Vienna, Austria, 1996. 29. R. Szelisky, D. Tonnesen, and D. Terzopoulos. Modelling surfaces of arbitrary topology with dynamic particles. In Proceedings of the Conference on Computer Vision and Pattern Recognition, pages 82–87, New York, June 1993. 30. Gabriel Taubin. A signal processing approach to fair surface design.

1 Cost Functional Inverting the integral in equation (1) based on measurements I is an ill-posed problem. Furthermore, often (1) is only an approximation of the model that generates the data. We will therefore look for solutions that minimize a suitable optimization criterion. In [6] Csisz´ar presents a derivation of “sensible” optimization criteria for the problem above, and concludes that the only two that satisfy a set of consistency axioms are the L2 norm – when the quantities at play are unconstrained – and the information-divergence – when both the radiance and the kernel are constrained to be non-negative.

The minimization of the first one enforces that M passes through P. In effect it is null if and only if u(P) = {0}. Minimizing the second one prevents M from passing through other points than those of P. e. in Ω/P. Finally, minimizing the third one enforces the smoothness of u hence, to some extent1 , that of Sα . e. the null function, elsewhere in Ω. As for the fourth integral, it is minimized by non-concave functions but this is not as straightforward and we are going to develop this point further.

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