Matching algorithms for finite point sets in plane

On the maximum area pentagon in a planar point set

Efficient point pattern matching algorithm for planar point sets under transform of translation, rotation and scale

Point pattern matching is an important topic of computer vision and pattern recognition. In this paper, we propose a point pattern matching algorithm for two planar point sets under Euclidean transform. We view a point set as a complete graph, establish the relation between the point set and the complete graph, and solve the point pattern matching problem by finding congruent complete graphs. Experiments are conducted to show the effectiveness and robustness of the proposed algorithm.

In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The proposed algorithm is a hybrid approach in which a depth-first search using hill-climbing strategies and dynamic programming techniques are combined. The algorithm starts with an initial (feasible) lower bound computed by solving a series of single bounded knapsack problems. In order to enhance the first-level lower bound, we introduce an incremental procedure which is used within a top-down branch-and-bound procedure. We also propose some hill-climbing strategies in order to produce a good trade-off between the computational time and the solution quality. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approach. The obtained results are compared to the results published by Alvarez-Valdes et al. (2002).

We show the existence of $\varepsilon$-nets of size $O\left(\frac{1}{\varepsilon}\log\log\frac{1}{\varepsilon}\right)$ for planar point sets and axis-parallel rectangular ranges. The same bound holds for points in the plane and “fat” triangular ranges and for point sets in $\boldsymbol{R}^3$ and axis-parallel boxes; these are the first known nontrivial bounds for these range spaces. Our technique also yields improved bounds on the size of $\varepsilon$-nets in the more general context considered by Clarkson and Varadarajan. For example, we show the existence of $\varepsilon$-nets of size $O\left(\frac{1}{\varepsilon}\log\log\log\frac{1}{\varepsilon}\right)$ for the dual range space of “fat” regions and planar point sets (where the regions are the ground objects and the ranges are subsets stabbed by points). Plugging our bounds into the technique of Brönnimann and Goodrich or of Even, Rawitz, and Shahar, we obtain improved approximation factors (computable in expected polynomial time by a randomized algorithm) for the hitting set or the set cover problems associated with the corresponding range spaces.

In the paper, we present and prove Castle Theorem of Convex Hull, design and realize the Fast Rampart Searching Algorithm. The algorithm can be treated as the preprocess of Convex Hull calculation of very large planar point set. When calculating the Convex Hull of a very large planar point set, we can use the Fast Rampart Searching Algorithm to get a very small part points as candidate point set, and then we can get the Convex Hull of the whole planar point set from the candidate point set through other algorithms. Keywords-fast rampart searching algorithm; castle theorem; convex hull; computational geometry

Establishing correct links among the coreference ontology instances is critical to the success of Linked Open Data (LOD) cloud. However, because of the high level heterogeneity and large scale instance set, matching the coreference instances in LOD cloud is an error prone and time consuming task. To this end, in this work, we present an asymmetrical profile-based similarity measure for instance matching task, construct new optimal models for schema-level and instance-level matching problems, and propose a compact hybrid evolutionary algorithm based ontology matching approach to solve the large scale instance matching problem in LOD cloud. Finally, the experimental results of comprising our approach with the states of the art systems on the instance matching track of OAEI 2015 and real-world datasets show the effectiveness of our approach.

This paper introduced points and directed line segment relation judgment method, the characteristics of generation and Graham method using the original convex hull generation algorithm of convex hull discrete points of the convex hull, an improved algorithm for planar discrete point set is proposed. The main idea is to use quadrilateral to divide planar discrete point set into five blocks, and then by judgment in addition to the four district quadrilateral internally within the point is in a convex edge. The result shows that the method is relatively simple program, high computational efficiency.

A non-parametric approach to shape reconstruction from planar point sets through Delaunay filtering

Instance matching acts as a significant part of information integration in semantic web research. While ontology matching focuses on the schema level of data, instance matching deals with massive instances objects. Ambiguation is a common problem which may lead to error matching when different instances share the same names or descriptions. To cope with this problem structural approach is used by many matching systems for disambiguation. However, existing structural approach has a hidden problem named 'error propagation' which would affect the precision of matching result. In this paper, we investigate instance matching techniques and propose a new instance matching framework. It is based on a novel structural matching algorithm which calculates similarity separately on sub graphs. The structural information is fully taken advantage of to realize disambiguation and several indexing strategies are used to cut down the computing overhead. We have conducted experiments on instance matching benchmark and results show that our proposed matching approach is comparable to state-of-art systems. And experiment on real dataset has proved the validity of our approach in instance disambiguation.

Traditional geometric algorithms are often presented as if input imprecision does not exist, even though it is often unavoidable. We argue that in some cases, it may be desirable for geometric algorithms to treat this imprecision as an explicit component of the input, and to reflect this imprecision in the output. Starting with three problems from computational geometry whose inputs are planar point sets (Voronoi diagrams, convex hulls, and smallest bounding discs), we recast these as problems where each input point’s location is imprecise, but known to lie within a particular region of uncertainty. Where algorithms to solve each of the original problems produce a single geometric object as output, the algorithms that we present typically produce either guaranteed or possible output objects. A guaranteed object represents qualities that can be guaranteed for every point set that is consistent with the uncertain regions, and a possible object represents qualities that exist for at least one such point set. By dealing with input imprecision explicitly, these guaranteed and possible objects can represent a more accurate view of what can be reliably inferred from the input data.

Triangulating with high connectivity

We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity rho(S) of S is given by the smallest number of reflex vertices in a simple polygonalization of S. We prove various combinatorial bounds and provide efficient algorithms to compute reflexivity, both exactly (in special cases) and approximately (in general). Our study considers also some closely related quantities, such as the convex cover number kappa_c(S) of a planar point set, which is the smallest number of convex chains that cover S, and the convex partition number kappa_p(S), which is given by the smallest number of convex chains with pairwise-disjoint convex hulls that cover S. We have proved that it is NP-complete to determine the convex cover or the convex partition number and have given logarithmic-approximation algorithms for determining each.

LetS be a set ofn points in ℝ d . A setW is aweak e-net for (convex ranges of)S if, for anyT⊆S containing en points, the convex hull ofT intersectsW. We show the existence of weak e-nets of size\(O((1/\varepsilon ^d )\log ^{\beta _d } (1/\varepsilon ))\), whereβ2=0,β3=1, andβ d ≈0.149·2d-1(d-1)!, improving a previous bound of Alonet al. Such a net can be computed effectively. We also consider two special cases: whenS is a planar point set in convex position, we prove the existence of a net of sizeO((1/e) log1.6(1/e)). In the case whereS consists of the vertices of a regular polygon, we use an argument from hyperbolic geometry to exhibit an optimal net of sizeO(1/e), which improves a previous bound of Capoyleas.

An algorithm is presented which directly computes the 3-D coordinates of the vertices of a quadrangle relative to the camera frame. This method is extended to determine the camera's exterior orientation in a world coordinate system. A shape restoration procedure is designed to reduce the effects of noise and thereby improve the accuracy of the algorithm.