In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

We give infinite lists of translations surfaces with no convex presentations. We classify the surfaces in the stratum H(2) which do not have convex presentations, as well as those with no strictly convex presentations. We show that in H(1, 1), all surfaces in the eigenform loci E4, E9 or E16 have no strictly convex presentation, and that the list of surfaces with no convex presentations in H(1,...

A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular parametrization, called shape-preserving, is found to lead to visually smooth surface approximations.

i x i s = 1, x i s ≥ 0, x ij s ≥ 0 . • x i s ∈ [0, 1]: indicates whether label i is chosen at voxel s • y ij s = x ij s − x s ∈ [−1, 1]: presence of a surface and its direction • ρs: unary term, cost for label i at location s •φij s : convex smoothness term at voxel s for labels i and j • ek ∈ R: k-th canonical basis vector • T : alignment between prior and input data •α: normalization factor f...