scholarly journals On some remarkable properties of the two-dimensional Hammersley point set in base 2

2006 ◽  
Vol 18 (1) ◽  
pp. 203-221 ◽  
Author(s):  
Peter Kritzer
Keyword(s):  
Two Dimensional ◽  
Hammersley Point Set ◽  
Point Set

Statistical measures of two dimensional point set uniformity

2012 ◽  
Vol 56 (6) ◽  
pp. 2159-2181 ◽  
Author(s):  
Meng Sang Ong ◽  
Ye Chow Kuang ◽  
Melanie Po-Leen Ooi
Keyword(s):  
Two Dimensional ◽  
Statistical Measures ◽  
Point Set

Study on Automatic Tracking Method of Marking Points in Sports Image Sequence

2021 ◽  
Vol 14 ◽  
Author(s):  
Cong Hua Pan ◽  
Gaurav Dhiman
Keyword(s):  
Real Time ◽  
Human Model ◽  
Two Dimensional ◽  
Current Frame ◽  
Automatic Tracking ◽  
Tracking Method ◽  
Motion Data ◽  
Registration Process ◽  
Rigid Deformation ◽  
Point Set

: The effect of teaching and training in physical sports is improved by the sport demonstration system. The two-dimensional sport demonstration system is widely applied for the training of practical athletic. In the accurate motion positioning, a certain visual deficiency exists, and the two-dimensional sport demonstration system is analyzed by the kinematic. Methodology: Aiming at the problems in the real-time tracking of fast moving targets in sports images, an automatic tracking method of sports images, based on the registration of landmark points of the passive optical motion capture system, is proposed. First, build a human model and divide the human model into several limb segments. Then, find a corresponding relationship between the first frame of motion data and template data to complete the first frame of motion data registration; based on the smallest non-rigid deformation and point, set matching error to find the corresponding relationship between the current frame of motion data and the previous frame of registered motion data. Finally, through the mark points, follow up to complete the registration process of the marker. Results: Experiments show that the average processing accuracy of this algorithm can reach over 85%, and the processing time of a single frame of motion data is t<1/60s, which can meet real-time requirements. Conclusion: The multi-point set least squares matching algorithm is used to correct the registered landmark data rigidly. No manual intervention is required for the entire mark registration process.

On one-sided densities of arcs of positive two-dimensional measure

1964 ◽  
Vol 60 (3) ◽  
pp. 517-524
Author(s):  
A. S. Besicovitch
Keyword(s):  
Two Dimensional ◽  
Common Value ◽  
Dimensional Measure ◽  
Closed Disc ◽  
Point Set ◽  
The Right ◽  
Lower Limits ◽  
Simple Arc

1. Let AB be a plane simple arc, which, considered as a point-set, has a positive two-dimensional measure. If x be a point of AB, a point x′ ≠ x is said to be to the left or to the right from x according as it belongs to the arc Ax or xB. The upper and the lower limits of the ratio [m2{Ax C(x, r)}]/πr2, where C(x, r) denotes the closed disc with centre x and radius r, as r → 0 define the upper and the lower left densities at the point x. When the two densities are equal their common value defines the left density. The right densities are defined similarly.

On the -Discrepancy of the Hammersley Point Set

2002 ◽  
Vol 136 (1) ◽  
pp. 67-79 ◽  
Author(s):  
Friedrich Pillichshammer
Keyword(s):  
Hammersley Point Set ◽  
Point Set

scholarly journals AUTOMATIC MONITORING OF TUNNEL DEFORMATION BASED ON HIGH DENSITY POINT CLOUDS DATA

2017 ◽  
Vol XLII-2/W7 ◽  
pp. 353-360 ◽  
Author(s):  
L. Du ◽  
R. Zhong ◽  
H. Sun ◽  
Q. Wu
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Point Clouds ◽  
Central Axis ◽  
Two Dimensional ◽  
Density Point ◽  
Point Set ◽  
The Cross ◽  
Projection Point ◽  
Dimensional Surface

An automated method for tunnel deformation monitoring using high density point clouds data is presented. Firstly, the 3D point clouds data are converted to two-dimensional surface by projection on the XOY plane, the projection point set of central axis on XOY plane named U<sub>xoy</sub> is calculated by combining the Alpha Shape algorithm with RANSAC (Random Sampling Consistency) algorithm, and then the projection point set of central axis on YOZ plane named Uyoz is obtained by highest and lowest points which are extracted by intersecting straight lines that through each point of U<sub>xoy</sub> and perpendicular to the two -dimensional surface with the tunnel point clouds, U<sub>xoy</sub> and U<sub>yoz</sub> together form the 3D center axis finally. Secondly, the buffer of each cross section is calculated by K-Nearest neighbor algorithm, and the initial cross-sectional point set is quickly constructed by projection method. Finally, the cross sections are denoised and the section lines are fitted using the method of iterative ellipse fitting. In order to improve the accuracy of the cross section, a fine adjustment method is proposed to rotate the initial sectional plane around the intercept point in the horizontal and vertical direction within the buffer. The proposed method is used in Shanghai subway tunnel, and the deformation of each section in the direction of 0 to 360 degrees is calculated. The result shows that the cross sections becomes flat circles from regular circles due to the great pressure at the top of the tunnel

Construction of Curve Network on the Multi-Line Contour Based on Convex-Hull

2013 ◽  
Vol 753-755 ◽  
pp. 1291-1294
Author(s):  
Yue Hong Tang ◽  
Yu Ping Gu ◽  
Hao Liu ◽  
Pan Qian
Keyword(s):  
Convex Hull ◽  
Incremental Algorithm ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Design Of Algorithms ◽  
Line Contour ◽  
Analysis And Design ◽  
Initial Network ◽  
Feature Line ◽  
Point Set

An algorithm is proposed to weave curve network on the multi-line contour, which refers to analysis and design of algorithms in computational geometry and uses convex hull to construct network on the surface of multi-line contour. First of all, with the incremental algorithm, a convex hull of point set, composed of the first and the last point of the feature line segment, is constructed. Then, by using the mapping from convex hull to fitting surface, an initial network is formed which meets the rules of the two-dimensional manifold. At last, a two-dimensional manifold network of feature curves is acquired by modifying connection of the curve network on the multi-line contour. In conclusion, the algorithm this paper put forward is intuitive, concise and easy to be implemented, and the woven curve network can precisely reflect the shape and the topology of the multi-line contour.

scholarly journals CAD Model Segmentation Algorithm Using the Fusion of PERT and Spectral Technology

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Li Hao ◽  
Rong Mo ◽  
Binbin Wei
Keyword(s):  
Human Cognition ◽  
Cad Model ◽  
Two Dimensional ◽  
Segmentation Method ◽  
Topological Information ◽  
Model Segmentation ◽  
Model Retrieval ◽  
Cad Models ◽  
Point Set ◽  
Cluster Points

For complex CAD models, model segmentation technology is an important support for model retrieval and reuse. In this article, we first propose a novel CAD model segmentation method that uses the fusion of the program/project evaluation and review technique (PERT) and the Laplacian spectrum theory. By means of PERT, spectral theory, and the CAD models’ geometrical and topological information, we transform the b-rep model faces into two-dimensional coordinate points corresponding to the nodes of the attributed adjacent graph (AAG). The k-means approach with the Silhouette coefficient was employed to conduct unsupervised learning of the coordinate points. The experimental results demonstrate that (1) the proposed approach can effectively transform the b-rep model into a two-dimensional coordinate point set; (2) the k-means algorithm can efficiently cluster points to achieve segmentation; and (3) in view of human cognition, the segmentation results are more reasonable. It can effectively divide the point set into several groups to achieve the model segmentation.

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