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

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

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Gradient Descent Flow We minimize (3) with respect to the surface s by introducing . an auxiliary time variable t and deforming the surface s(t) = {P (X, t) : X ∈ s} in time t starting from an initial surface s(0). The evolution is governed by a partial differential equation: Pt = EL(X, s)N, (9) where N is the unit normal to the surface at P and EL(X, s) = 0 is the Euler-Lagrange equation of the cost function (3). Note that in equation (9) we let the surface deform only along the normal direction, because the deforming in the tangent space will not change the shape of the surface (what it changes is the parameterization).

This is actually a very general approach which is valid regardless of the dimension and topology. The key is to consider neighborhoods (or approximations) of the represented object with increasing tolerance. e. manifolds of dimension n−1. For instance, in R3 , both concentric tubes and concentric spheres are bi-dimensional although their limits are curves and points. Finally, those hypersurfaces are conveniently encoded as the iso-hypersurfaces of a scalar function defined on Ω. This implicit representation makes it not too hard to formulate the problem as a variational one.

5 shows a comparison of our detection method with two others on both images containing skin and images not containing skin. Of course, one of the strength of the presented method is that it can be applied with more than three variables and this can be used in order to further enhance the segmentation. For instance, in Fig. | denotes the Euclidean distance. This measure, noted v(L, a, b) accounts somehow to the 14 J. Gomes and A. Mojsilovic Fig. 4. This figure shows the learned shape of the set of human skin colors in the CIE Lab system from different standpoints.

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