Bounding overwatch

About: Bounding overwatch is a research topic. Over the lifetime, 966 publications have been published within this topic receiving 15156 citations.

Method and apparatus for training a character detector based on weak supervision, system and medium

Abstract: A method and apparatus for training a character detector based on weak supervision, a character detection system and a computer readable storage medium are provided, wherein the method includes: inputting coarse-grained annotation information of a to-be-processed object, wherein the coarse-grained annotation information including a whole bounding outline of a word, text bar or line of the to-be-processed objected; dividing the whole bounding outline of the coarse-grained annotation information, to obtain a coarse bounding box of a character of the to-be-processed object; obtaining a predicted bounding box of the character of the to-be-processed object through a neural network model from the coarse-grained annotation information; and determining a fine bounding box of the character of the to-be-processed object as character-based annotation of the to-be-processed object, according to the coarse bounding box and the predicted bounding box.

Creation of bounding boxes on a 3d modeled assembly

Abstract: It is proposed a computer-implemented method for creating a set of bounding boxes on a three-dimensional modeled assembly in a three-dimensional scene. The method comprises providing three-dimensional modeled objects forming a three-dimensional modeled assembly in a three-dimensional scene; computing a main bounding box encompassing the three-dimensional modeled assembly; creating a set of three-dimensional modeled objects that meet at least one property of the three-dimensional modeled assembly; computing two or more bounding boxes encompassed by the main bounding box, one of the two or more bounding boxes comprising the three-dimensional modeled objects of the set.

Linearly χ‐bounding (P6, C4)‐free graphs*

Abstract: Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no induced subgraph isomorphic to H1 or H2. Let Pt and Cs be the path on t vertices and the cycle on s vertices, respectively. In this paper we show that for any (P6, C4)-free graph G it holds that χ(G) ≤ 3 2 ω(G), where χ(G) and ω(G) are the chromatic number and clique number of G, respectively. Our bound is attained by several graphs, for instance, the five-cycle, the Petersen graph, the Petersen graph with an additional universal vertex, and all 4-critical (P6, C4)-free graphs other than K4 (see [17]). The new result unifies previously known results on the existence of linear χ-binding functions for several graph classes. Our proof is based on a novel structure theorem on (P6, C4)-free graphs that do not contain clique cutsets. Using this structure theorem we also design a polynomial time 3/2-approximation algorithm for coloring (P6, C4)-free graphs. Our algorithm computes a coloring with 3 2 ω(G) colors for any (P6, C4)-free graph G in O(n m) time.

High dimensional Hoffman bound and applications in extremal combinatorics

Abstract: One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound is sharp on the tensor power of a graph whenever it is sharp for the original graph. In this paper, we introduce the related problem of upper-bounding independent sets in tensor powers of hypergraphs. We show that many of the prominent open problems in extremal combinatorics, such as the Turan problem for (hyper-)graphs, can be encoded as special cases of this problem. We also give a new generalization of the Hoffman bound for hypergraphs which is sharp for the tensor power of a hypergraph whenever it is sharp for the original hypergraph. As an application of our Hoffman bound, we make progress on the problem of Frankl on families of sets without extended triangles from 1990. We show that if $\frac{1}{2}n\le2k\le\frac{2}{3}n,$ then the extremal family is the star, i.e. the family of all sets that contains a given element. This covers the entire range in which the star is extremal. As another application, we provide spectral proofs for Mantel's theorem on triangle-free graphs and for Frankl-Tokushige theorem on $k$-wise intersecting families.