Counting Non-Convex 5-Holes in a Planar Point Set

Let S be a set of n points in the general position, that is, no three points in S are collinear. A simple k-gon with all corners in S such that its interior avoids any point of S is called a k-hole. In this paper, we present the first algorithm that counts the number of non-convex 5-holes in S. To our best knowledge, prior to this work there was no known algorithm in the literature except a trivial brute force algorithm. Our algorithm runs in time O(T+Q), where T denotes the number of 3-holes, or empty triangles, in S and Q that denotes the number of non-convex 4-holes in S. Note that T+Q ranges from Ω(n2) to O(n3), while its expected number is Θ(n2logn) when the points in S are chosen uniformly and independently at random from a convex and bounded body in the plane.

Pairwise Registration Algorithm for Large-Scale Planar Point Cloud Used in Flatness Measurement

In this paper, an optimized three-dimensional (3D) pairwise point cloud registration algorithm is proposed, which is used for flatness measurement based on a laser profilometer. The objective is to achieve a fast and accurate six-degrees-of-freedom (6-DoF) pose estimation of a large-scale planar point cloud to ensure that the flatness measurement is precise. To that end, the proposed algorithm extracts the boundary of the point cloud to obtain more effective feature descriptors of the keypoints. Then, it eliminates the invalid keypoints by neighborhood evaluation to obtain the initial matching point pairs. Thereafter, clustering combined with the geometric consistency constraints of correspondences is conducted to realize coarse registration. Finally, the iterative closest point (ICP) algorithm is used to complete fine registration based on the boundary point cloud. The experimental results demonstrate that the proposed algorithm is superior to the current algorithms in terms of boundary extraction and registration performance.

THEORETICAL-EXPERIMENTAL POSSIBILLITIES OF MICROSTRUCTURE QUANTIFICATION OF DISPERSION STRENGTHENED MATERIALS

The present paper is devoted to the possibilities to classify the spatial arrangement of the elements (features) of a stochastic process with geometrical objects. The fundamental quantities describing point processes were introduced. Experimental possibilities of structural objects determination, possibilities of evaluation of the size distribution of the secondary phases, testing of planar point structures (estimation of the process intensity, square method and characteristics of the second order) were estimated. Interparticle distances, namely mean interparticle distance, mean minimum distance, mean visibility and mean path of spherical contact were defined. Selected processes were described and demonstrated from simulated realizations on Al-Al4C3 dispersion strengthened material, prepared by a powder metallurgy method of reaction milling. Interparticle distances of Al4C3 particles were evaluated. Polygonal methods and quadrant counts method were used for characterization of the particle arrangement.

A Novel Indoor Structure Extraction Based on Dense Point Cloud

Herein, we propose a novel indoor structure extraction (ISE) method that can reconstruct an indoor planar structure with a feature structure map (FSM) and enable indoor robot navigation using a navigation structure map (NSM). To construct the FSM, we first propose a two-staged region growing algorithm to segment the planar feature and to obtain the original planar point cloud. Subsequently, we simplify the planar feature using quadtree segmentation based on cluster fusion. Finally, we perform simple triangulation in the interior and vertex-assignment triangulation in the boundary to accomplish feature reconstruction for the planar structure. The FSM is organized in the form of a mesh model. To construct the NSM, we first propose a novel ground extraction method based on indoor structure analysis under the Manhattan world assumption. It can accurately capture the ground plane in an indoor scene. Subsequently, we establish a passable area map (PAM) within different heights. Finally, a novel-form NSM is established using the original planar point cloud and the PAM. Experiments are performed using three public datasets and one self-collected dataset. The proposed plane segmentation approach is evaluated on two simulation datasets and achieves a recall of approximately 99%, which is 5% higher than that of the traditional plane segmentation method. Furthermore, the triangulation performance of our method compared with the traditional greedy projection triangulation show that our method performs better in terms of feature representation. The experimental results reveal that our ISE method is robust and effective for extracting indoor structures.