Color gamut characterization is an essential step in the ICC profile generation for imaging devices. It is also needed as part of evaluation and comparison of image quality achievable by different imaging systems. A novel technique is presented for characterizing the color gamut of an imaging device via ray tracing in the CIELAB color space. Initially, the convex hull of the set of measurement ...

There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected"edge"unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

If F is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.

Let Ω ⊂ R be a bounded open set. Given 2 ≤ m ≤ n, we construct a convex function φ : Ω → R whose gradient f = ∇φ is a Hölder continuous homeomorphism, f is the identity on ∂Ω, the derivative Df has rank m − 1 a.e. in Ω and Df is in the weak L space L. The proof is based on convex integration and staircase laminates.

In this paper, we consider the positive semi-definite space tensor cone constrained convex program, its structure and algorithms. We study defining functions, defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone, give an error bound for the polyhedral outer approximation approach, and thus establish convergence of three polyhedral outer approxi...

Abstract We present recursive formulas that compute the recently defined “higher symplectic capacities” for all convex toric domains. In special case of four-dimensional ellipsoids, we apply homological perturbation theory to associated filtered $\mathcal{L}_\infty $ algebras and prove resulting structure coefficients count punctured pseudoholomorphic curves in cobordisms between ellipsoids. As...

Let L be the space of line transversals to a nite family of pairwise disjoint compact convex sets in R 3. We prove that each connected component of L can itself be represented as the space of transversals to some nite family of pairwise disjoint compact convex sets.

We consider the problem of reporting convex hull points in an orthogonal range query in two dimensions. Formally, let P be a set of n points in R. A point lies on the convex hull of a point set S if it lies on the boundary of the minimum convex polygon formed by S. In this paper, we are interested in finding the points that lie on the boundary of the convex hull of the points in P that also fal...