Related papers: A Facet Enumeration Algorithm for Convex Polytopes
We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.
We discuss a new memory-efficient depth-first algorithm and its implementation that iterates over all elements of a finite locally branched lattice. This algorithm can be applied to face lattices of polyhedra and to various generalizations…
This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap's faces are quadrilaterals, with vertices…
We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…
We introduce Sieve-SDP, a simple facial reduction algorithm to preprocess semidefinite programs (SDPs). Sieve-SDP inspects the constraints of the problem to detect lack of strict feasibility, deletes redundant rows and columns, and reduces…
The calculation of the volume enclosed by curved surfaces discretized into triangular elements, and a cube is of great importance in different domains, such as computer graphics and multiphase flow simulations. We propose a robust…
One may associate several frames to a given polytope, such as its collection of vertices, edges, or facet normal vectors. In this note, we use these frames to generate geometric inequalities for the simplex in $\mathbb{R}^d$ and polytopes…
In the modern world, facial identification is an extremely important task in which many applications rely on high performing algorithms to detect faces efficiently. Whilst classical methods of SVM and k-NN commonly used may perform to a…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
In the convex covering problem, we are given a convex polygon with holes $P$ and the goal is to cover $P$ using a small number of convex polygons that lie inside $P$. In this paper, we solve the problem using the following strategy. We find…
Clustering face images according to their identity has two important applications: (i) grouping a collection of face images when no external labels are associated with images, and (ii) indexing for efficient large scale face retrieval. The…
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is…
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
In this paper we state a full classification for Coxeter polytopes in $\mathbb{H}^{n}$ with $n+3$ facets which are non-compact and have precisely one non-simple vertex.
Despite significant recent advances in the field of face recognition, implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet,…
Finding faces in images is one of the most important tasks in computer vision, with applications in biometrics, surveillance, human-computer interaction, and other areas. In our earlier work, we demonstrated that it is possible to tell…
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer…
Face clustering is an essential tool for exploiting the unlabeled face data, and has a wide range of applications including face annotation and retrieval. Recent works show that supervised clustering can result in noticeable performance…
"Frontalization" is the process of synthesizing frontal facing views of faces appearing in single unconstrained photos. Recent reports have suggested that this process may substantially boost the performance of face recognition systems.…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…