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.

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

Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence

2010 ◽  
Vol 646 ◽  
pp. 517-526 ◽  
Author(s):  
ANNALISA BRACCO ◽  
JAMES C. MCWILLIAMS
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Large Scale ◽  
Velocity Structure ◽  
Stokes Equations ◽  
Turbulent Transport ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Random Forcing ◽  
Statistical Measures

Turbulent solutions of the two-dimensional Navier–Stokes equations are a paradigm for the chaotic space–time patterns and equilibrium distributions of turbulent geophysical and astrophysical ‘thin’ flows on large horizontal scales. Here we investigate how homogeneous, stationary two-dimensional turbulence varies with the Reynolds number (Re) in stationary solutions with large-scale, random forcing and viscous diffusion, also including hypoviscous diffusion to limit the inverse energy cascade. This survey is made over the computationally feasible range in Re ≫ 1, approximately between 1.5 × 103 and 5.6 × 106. For increasing Re, we witness the emergence of vorticity fine structure within the filaments and vortex cores. The energy spectrum shape approaches the forward-enstrophy inertial-range form k−3 at large Re, and the velocity structure function is independent of Re. All other statistical measures investigated in this study exhibit power-law scaling with Re, including energy, enstrophy, dissipation rates and the vorticity structure function. The scaling exponents depend on the forcing properties through their influences on large-scale coherent structures, whose particular distributions are non-universal. A striking result is the Re independence of the intermittency measures of the flow, in contrast with the known behaviour for three-dimensional homogeneous turbulence of asymptotically increasing intermittency. This is a consequence of the control of the tails of the distribution functions by large-scale coherent vortices. Our analysis allows extrapolation towards the asymptotic limit of Re → ∞, fundamental to geophysical and astrophysical regimes and their large-scale simulation models where turbulent transport and dissipation must be parameterized.

scholarly journals 2D Sub-Pixel Disparity Measurement Using QPEC / Medicis

2016 ◽  
Vol XLI-B1 ◽  
pp. 291-298
Author(s):  
M. Cournet ◽  
A. Giros ◽  
L. Dumas ◽  
J. M. Delvit ◽  
D. Greslou ◽  
...  
Keyword(s):  
Earth Observation ◽  
Block Matching ◽  
Disparity Estimation ◽  
Estimation Methods ◽  
Two Dimensional ◽  
Disparity Map ◽  
Matching Algorithm ◽  
Block Matching Algorithm ◽  
Statistical Measures ◽  
Digital Elevation

In the frame of its earth observation missions, CNES created a library called QPEC, and one of its launcher called Medicis. QPEC / Medicis is a sub-pixel two-dimensional stereo matching algorithm that works on an image pair. This tool is a block matching algorithm, which means that it is based on a local method. Moreover it does not regularize the results found. It proposes several matching costs, such as the Zero mean Normalised Cross-Correlation or statistical measures (the Mutual Information being one of them), and different match validation flags. QPEC / Medicis is able to compute a two-dimensional dense disparity map with a subpixel precision. Hence, it is more versatile than disparity estimation methods found in computer vision literature, which often assume an epipolar geometry. <br><br> CNES uses Medicis, among other applications, during the in-orbit image quality commissioning of earth observation satellites. For instance the Pléiades-HR 1A & 1B and the Sentinel-2 geometric calibrations are based on this block matching algorithm. Over the years, it has become a common tool in ground segments for in-flight monitoring purposes. For these two kinds of applications, the two-dimensional search and the local sub-pixel measure without regularization can be essential. This tool is also used to generate automatic digital elevation models, for which it was not initially dedicated. <br><br> This paper deals with the QPEC / Medicis algorithm. It also presents some of its CNES applications (in-orbit commissioning, in flight monitoring or digital elevation model generation). Medicis software is distributed outside the CNES as well. This paper finally describes some of these external applications using Medicis, such as ground displacement measurement, or intra-oral scanner in the dental domain.

Stochastic Analysis of Vertical Wave Loads on Deck

2008 ◽  
Author(s):  
Ravikiran S. Kota ◽  
Torgeir Moan
Keyword(s):  
Impact Load ◽  
Added Mass ◽  
Two Dimensional ◽  
Wave Loads ◽  
Random Waves ◽  
Statistical Measures ◽  
Model Following ◽  
Wave Slamming ◽  
Stationary Gaussian Processes ◽  
Maximum Minimum

Vertical loads on a platform deck due to incident random waves — long-crested and Gaussian, are studied. Loads on the deck are due to wave-slamming, added-mass over the wetted length and nonlinear Froude-Krylov components. Reliable estimation of these loads and their duration is important in evaluating their effects on platform response (global or local). Emphasis of the present work is to study statistical measures such as expected maximum/minimum impact load and its duration. Gaussian waves are numerically simulated over several points of a two-dimensional deck in time-domain and each deck-wetting event identified and tracked from its inception to expiry. Forces are modeled using a simplified two-dimensional slamming model following Kaplan’s (1987) approach. Use of von Ka´rma´n method, and hence instantaneous wave profile, enables multiple slamming regions to be considered. Simulated results for expected deck-wetting duration and expected maximum wetted length are then compared against analytical results for one- and two-dimensional stationary Gaussian processes.

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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