Automated building extraction from multi-source data has attracted great attention in recent years. This paper presents an approach to automated building extraction by fusion of image data, height data and 2D ground plans. In this approach buildings are detected using ground plans and height data. A split-and-merge process is applied to fuse image and height data and derive the parametric forms...

that contains the famous 19-face monostatic polyhedron polyhedra of this class allow to efficiently scan them , with a computer program, whether the class contains a .

The SQAP-polytope was associated to quadratic assignment problems with a certain symmetric objective function structure by Rijal (1995) and Padberg and Rijal (1996). We derive a technique for investigating the SQAP-polytope that is based on projecting the (low-dimensional) polytope into a lower dimensional vector-space, where the vertices have a “more convenient” coordinate structure. We exploi...

Ordinary polytopes were introduced by Bisztriczky as a (nonsimplicial) generalization of cyclic polytopes. We show that the colex order of facets of the ordinary polytope is a shelling order. This shelling shares many nice properties with the shellings of simplicial polytopes. We also give a shallow triangulation of the ordinary polytope, and show how the shelling and the triangulation are used...

The hyperdeterminant of format 2 × 2 × 2 × 2 is a polynomial of degree 24 in 16 unknowns which has 2894276 terms. We compute the Newton polytope of this polynomial and the secondary polytope of the 4-cube. The 87959448 regular triangulations of the 4-cube are classified into 25448 Dequivalence classes, one for each vertex of the Newton polytope. The 4-cube has 80876 coarsest regular subdivision...

The order polytope O(P ) and the chain polytope C(P ) associated to a partially ordered set P are studied. In this paper, we introduce the convex polytope Γ(O(P ),−C(Q)) which is the convex hull of O(P ) ∪ (−C(Q)), where both P and Q are partially ordered sets with |P | = |Q| = d. It will be shown that Γ(O(P ),−C(Q)) is a normal and Gorenstein Fano polytope by using the theory of reverse lexico...

Let S be a convex polytope. The set of all valid inequalities carries the structure of a convex polytope S, called the polar (polytope) of S. The facial structure of the polar provides information for each of its points: two points a and b are in the same face of S if and only if the faces of S obtained by intersecting it with the hyperplanes given respectively by a and b coincide. Suppose now ...

This theoretical paper is inspired by an integer linear programming (ILP) approach to learning the structure of decomposable models. We intend to represent decomposable models by special zeroone vectors, named characteristic imsets. Our approach leads to the study of a special polytope, defined as the convex hull of all characteristic imsets for chordal graphs, named the chordal graph polytope....

The monomial initial ideals of a graded polynomial ideal are in bijection with the vertices of a convex polytope known as the state polytope of the ideal. The Grr obner fan of the ideal is the normal fan of its state polytope. In this paper we present a software system called TiGERS (Toric Grr obner bases Enumeration by Reverse Search) for computing the Grr obner fan of a toric ideal by enumera...

We study the problem of how to obtain an integer realization of a 3d polytope when an integer realization of its dual polytope is given. We focus on grid embeddings with small coordinates and develop novel techniques based on Colin de Verdière matrices and the Maxwell–Cremona lifting method. We show that every truncated 3d polytope with n vertices can be realized on a grid of size O(n). Moreove...