By Rhodri H. Davies, Carole J. Twining, Tim F. Cootes, John C. Waterton, Chris J. Taylor (auth.), Anders Heyden, Gunnar Sparr, Mads Nielsen, Peter Johansen (eds.)

Premiering in 1990 in Antibes, France, the eu convention on laptop imaginative and prescient, ECCV, has been held biennially at venues throughout Europe. those meetings were very profitable, making ECCV an enormous occasion to the pc imaginative and prescient neighborhood. ECCV 2002 used to be the 7th within the sequence. The privilege of organizing it was once shared by means of 3 universities: The IT college of Copenhagen, the college of Copenhagen, and Lund college, with the convention venue in Copenhagen. those universities lie ¨ geographically shut within the shiny Oresund sector, which lies in part in Denmark and in part in Sweden, with the newly outfitted bridge (opened summer season 2000) crossing the sound that previously divided the nations. we're more than pleased to file that this year’s convention attracted extra papers than ever sooner than, with round six hundred submissions. nonetheless, including the convention board, we determined to maintain the culture of retaining ECCV as a unmarried music convention. every one paper was once anonymously refereed via 3 assorted reviewers. For the nal choice, for the rst time for ECCV, a procedure with region chairs used to be used. those met with this system chairsinLundfortwodaysinFebruary2002toselectwhatbecame45oralpresentations and 181 posters.Also at this assembly the choice was once made with no wisdom of the authors’identity.

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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 III

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38 S. J. Yezzi . As we have anticipated, we choose either E(hi ) = ∆(gi (µ), γi ) or E(hi ) = ψ(gi (µ), γi ). Therefore, abusing the notation as anticipated before Def. 1, we can write the problem above as an unconstrained minimization gˆ, µ ˆ = arg min φ(γ1 , γ2 ) g,µ where . φ(γ1 , γ2 ) = E(µ, γ1 ) + E(g(µ), γ2 ) (7) and E is either ∆ or ψ. The estimate gˆ defines the motion between γ1 and γ2 , and the estimate µ ˆ defines the average of the two contours. If one thinks of contours and their interior, represented by a characteristic function χ, as a binary image, then the cost functional above is just a particular case of a more general cost functional where each term is obtained by integrating a function inside and a function outside the contours 2 φ= i=1 µ ¯ in fin (x, γi )dx + µ ¯ out fout (x, γi )dx (8) where the bar in µ ¯ indicates that the integral is computed on a region inside or outside µ and we have emphasized the fact that the function f depends upon the contour γi .

However, these choices can be easily changed without altering the nature of the contribution of this paper. Naturally, since shape and motion are computed as the solution of a nonlinear optimization problem, the algorithms we propose are only guaranteed to converge to local minima and, in general, no conclusions can be drawn on uniqueness. Indeed, it is quite simple to generate pathological examples where the setup we have proposed fails. In the experimental section we will highlight the limitations of the approach when used beyond the assumptions for which it is designed.

J. Taylor, “An Information Theoretic Approach to Statistical Shape Modelling”, in British Machine Vision Conference - BMVC’01, p 3-12, 2001 10. , S. Lavalee, “Building a Complete Surface Model from Sparse Data Using Statistical Shape Models: Application to Computer Assisted Knee Surgery”, in MICCAI’98, p878-887, 1998 11. M. H. Hansen and B. J. 1998. 12. , A. J. Taylor, “Model based interpretation of 3D medical images”, in British Machine Vision Conference, BMVC’93, p339-348, 1993 13. Joshi et. al , “Gaussian Random Fields on Sub-Manifolds for Characterizing Brain Surfaces”, in IPMI’97, p381-386, 1997 14.

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