In this paper we introduce the notion of virtual occluders. Given a scene and a viewcell, a virtual occluder is a view-dependent (simple) convex object, which is guaranteed to be fully occluded from any given point within the viewcell and which serves as an effective occluder from the given viewcell. Virtual occluders are a compact intermediate representation of the aggregate occlusion for a gi...

In this paper we investigate the strict convexity and the di erentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly elliptic case). We prove that it is always di erentiable in totally irrational directions, while in other directions, it is di erentiable if and only if the corre...

We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we investigate its strict convexity and differentiability properties.

Aspheric optical components are the indispensable part of modern optics systems. With the constant development of aspheric optical fabrication technique, the systems with large aperture convex aspheric optical components are widely used in astronomy and space optics. Thus, the measurement of the figure error of the whole convex aspherical surface with high precision comes to be a challenge in t...

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

In this paper, we describe a new vector similarity measure associated with a convex cost function. Given two vectors, we determine the surface normals of the convex function at the vectors. The angle between the two surface normals is the similarity measure. Convex cost function can be the negative entropy function, total variation (TV) function and filtered variation function. The convex cost ...

We present a new proof for the existence of a simple closed geodesic on a convex surface M . This result is due originally to Poincaré. The proof uses the 2k-dimensional Riemannian manifold kΛM = (briefly) Λ of piecewise geodesic closed curves on M with a fixed number k of corners, k chosen sufficiently large. In Λ we consider a submanifold ≈ Λ0 formed by those elements of Λ which are simple re...

If a convex body K in R is contained in a convex body L of elliptic type (a curvature image), then it is known that the affine surface area of K is not larger than the affine surface area of L. We prove that the affine surface areas of K and L can only be equal if K = L. 2010 Mathematics Subject Classification: primary 52A10; secondary 53A15