Pairs Of Points Research Articles

Sparse-to-Dense Point Cloud Registration Based on Rotation-Invariant Features

Point cloud registration is a critical problem because it is the basis of many 3D vision tasks. With the popularity of deep learning, many scholars have focused on leveraging deep neural networks to address the point cloud registration problem. However, many of these methods are still sensitive to partial overlap and differences in density distribution. For this reason, herein, we propose a method based on rotation-invariant features and using a sparse-to-dense matching strategy for robust point cloud registration. Firstly, we encode raw points as superpoints with a network combining KPConv and FPN, and their associated features are extracted. Then point pair features of these superpoints are computed and embedded into the transformer to learn the hybrid features, which makes the approach invariant to rigid transformation. Subsequently, a sparse-to-dense matching strategy is designed to address the registration problem. The correspondences of superpoints are obtained via sparse matching and then propagated to local dense points and, further, to global dense points, the byproduct of which is a series of transformation parameters. Finally, the enhanced features based on spatial consistency are repeatedly fed into the sparse-to-dense matching module to rebuild reliable correspondence, and the optimal transformation parameter is re-estimated for final alignment. Our experiments show that, with the proposed method, the inlier ratio and registration recall are effectively improved, and the performance is better than that of other point cloud registration methods on 3DMatch and ModelNet40.

Способи побудови розподілу максимальної відстані між випадковими нормальними точками на площині

Many practical problems call for constructing the maximum interpoint distance distribution for random pints in a plane. In the literature, the case of a great number of points is considered, for which an asymptotic distribution is determined. This paper addresses the problem of constructing the maximum interpoint distance distribution for a small number of random points in a plane whose coordinates are independent random quantities that obey the standard normal distribution. The special case of three random points in a plane is considered as the basic one, for which three ways to construct the maximum interpoint distance distribution are studied. The first way is to construct the distribution function from geometrical considerations. To do this, the loci of three points are considered from the condition that the maximum distance between them shall not exceed a certain value. The position of the third point in the plane is determined relative to the two other points: the leftmost and the lowermost one. In this case, the construction of the distribution function involves the successive evaluation of several integrals using numerical methods. The obtained results are in good agreement with those of statistical simulation. The second way is based on studying the distance between pairs of random normal points in a plane. Taken separately, the distances between each pair of random normal points obey one-dimensional Rayleigh distributions, but in the aggregate they prove to be correlated because they are determined from the same pint coordinates. A joint distribution of the squared distances between three points is constructed using the three-dimensional Moran-Downton distribution. Using it, a distribution function of the squared maximum distance between three random normal points, which is identical with the maximum interpoint distance distribution, is obtained. It is found that for small values it underestimates the actual probability of the maximum distance not exceeding a certain value. For great distance values, the above probabilities coincide. The third way uses the Rice distribution (a generalization of the Rayleigh distribution) to approximate the unknown maximum interpoint distance distribution for three random normal points in a plane. The Rice distribution parameters found by the least-squares method are in good agreement with those obtained by statistical simulation. The results for three random normal points are generalized to a greater number of points (up to 30). It is shown that in this case the third way is most efficient.

Cultural relics fragment assembly based on fracture surface contour features

Addressing the issue of registration deviations caused by local fragment loss and shape diversity during the process of cultural relics fragment assembly, this paper proposes a method for assembling cultural relics fragments based on the contour features of fracture surfaces. Initially, the curvature of discrete point clouds is calculated using the quartic surface method and the Weingarten matrix, and curvature discontinuity points are identified using a proportional method as a candidate feature point set. Subsequently, the angle difference between a point and its neighboring points’ directed segments is defined as a neighborhood feature parameter, which further optimizes the feature point set and selects the optimal matching set. Then the 4-points congruent sets (4PCS) algorithm is utilized for the initial registration of the fragments, and the unit quaternion method is employed to calculate the rigid body transformation matrix during the iteration process. Finally, corresponding point pairs are determined by the intersection of a point’s normal with a set of points, improving the iterative closest point (ICP) algorithm to achieve precise assembly of the fragments. The experimental results show that, compared to other assembly algorithms, the proposed method is more accurate in feature point extraction, robust, and effectively enhances the accuracy and efficiency of fragment assembly.

Visibility graph-based covariance functions for scalable spatial analysis in non-convex partially Euclidean domains.

We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not guaranteed to be positive definite on such domains, while existing non-Euclidean approaches fail to respect the partially Euclidean nature of these domains where the geodesic distance agrees with the Euclidean distances for some pairs of points. Using a visibility graph on the domain, we propose a class of covariance functions that preserve Euclidean-based covariances between points that are connected in the domain while incorporating the non-convex geometry of the domain via conditional independence relationships. We show that the proposed method preserves the partially Euclidean nature of the intrinsic geometry on the domain while maintaining validity (positive definiteness) and marginal stationarity of the covariance function over the entire parameter space, properties which are not always fulfilled by existing approaches to construct covariance functions on non-convex domains. We provide useful approximations to improve computational efficiency, resulting in a scalable algorithm. We compare the performance of our method with those of competing state-of-the-art methods using simulation studies on synthetic non-convex domains. The method is applied to data regarding acidity levels in the Chesapeake Bay, showing its potential for ecological monitoring in real-world spatial applications on irregular domains.

Diameter of Compact Riemann Surfaces

AbstractDiameter is one of the most basic properties of a geometric object, while Riemann surfaces are one of the most basic geometric objects. Surprisingly, the diameter of compact Riemann surfaces is known exactly only for the sphere and the torus. For higher genuses, only very general but loose upper and lower bounds are available. The problem of calculating the diameter exactly has been intractable since there is no simple expression for the distance between a pair of points on a high-genus surface. Here we prove that the diameters of a class of simple Riemann surfaces known as generalized Bolza surfaces of any genus greater than 1 are equal to the radii of their fundamental polygons. This is the first exact result for the diameter of a compact hyperbolic manifold.

A new look at the myopia control efficacy of orthokeratology

PurposeTo evaluate the efficacy of orthokeratology contact lens wear in slowing the axial elongation of the eye in myopic children. MethodsData from three prospective studies, which evaluated the use of orthokeratology for slowing myopia progression in children in comparison to a parallel control group of distance, single-vision spectacle lens wearers over a 2-year period, were pooled together for analysis. ResultsCollectively, data from 125 orthokeratology and 118 control subjects were analyzed in this study. Of these, 101 (81 %) and 88 (75 %) orthokeratology and control subjects completed the 2-year follow-up period, respectively. Statistically significant differences in the change in axial length from baseline were found over time, between groups and for the time*group interaction (all p < 0.001), indicating that the rate of increase in axial length over time was significantly lower in the orthokeratology versus the control group. The lower axial elongation of the orthokeratology versus the control group was statistically significant at all time points (all p < 0.001), with significant differences being also present between each of the different pairs of time points (all p < 0.001). The interactions of group with age, gender, mean spherical refractive error and ethnicity at baseline were not significant (p > 0.05). The change in axial length at the 2-year visit in comparison to baseline for the orthokeratology and control groups were 0.41 ± 0.25 and 0.65 ± 0.30 mm, respectively, thus providing a treatment effect following 2-years of lens wear of 0.24 mm (95 % confidence intervals: 0.15 to 0.34 mm). About 40 % and 25 % of the orthokeratology subjects experienced remarkably low and high levels of myopia progression, respectively (2-years axial elongation: ≤0.30 mm and >0.59 mm, respectively). ConclusionsOrthokeratology lens wear slows the axial elongation of the eye in comparison to spectacle lens wear in myopic children. The use of these lenses for slowing myopia progression appears to be very effective and not effective at all in 40% and 25% of orthokeratology lens wearers, respectively.

Pose estimation algorithm based on point pair features using PointNet + +

This study proposes an innovative deep learning algorithm for pose estimation based on point clouds, aimed at addressing the challenges of pose estimation for objects affected by the environment. Previous research on using deep learning for pose estimation has primarily been conducted using RGB-D data. This paper introduces an algorithm that utilizes point cloud data for deep learning-based pose computation. The algorithm builds upon previous work by integrating PointNet + + technology and the classical Point Pair Features algorithm, achieving accurate pose estimation for objects across different scene scales. Additionally, an adaptive parameter-density clustering method suitable for point clouds is introduced, effectively segmenting clusters in varying point cloud density environments. This resolves the complex issue of parameter determination for density clustering in different point cloud environments and enhances the robustness of clustering. Furthermore, the LineMod dataset is transformed into a point cloud dataset, and experiments are conducted on the transformed dataset to achieve promising results with our algorithm. Finally, experiments under both strong and weak lighting conditions demonstrate the algorithm's robustness.

A dual watermarking algorithm for trajectory data based on robust watermarking and fragile watermarking

Digital watermarking technology plays a crucial role in securing trajectory data. However, as trajectory data usage scenarios continue to expand, the security requirements for it have changed from a single copyright protection to one that takes into account data integrity. Existing digital watermarking algorithms for trajectory data can only choose between implementing copyright protection or ensuring integrity, unable to simultaneously achieve both functionalities. This limitation impedes the sharing and utilization of trajectory data. A dual watermarking algorithm that combines robust and fragile watermarking was innovatively proposed to solve this problem based on the geometric domain. Firstly, a set of feature points is extracted from the trajectory, and the farthest point pair of the minimum convex hull of the feature points is set as fixed points. The robust watermark is then embedded in the angles constructed by the feature points and the fixed points using quantization index modulation. Meanwhile, the trajectory points are grouped based on the angle and distance ratio constructed from the trajectory points to the fixed points. In each group, the spatiotemporal attributes of the trajectory points are mapped to the fragile watermark, which is then embedded into the distance ratios constructed by the trajectory points. Experimental results show that the proposed algorithm achieves both copyright protection and integrity verification for trajectory data and exhibits stronger robustness and tampering localization ability. This research can provide security and privacy protection for trajectory data and contribute positively to the application of trajectory data.

When Four Cyclic Antipodal Pairs Are Ordered Counterclockwise in Euclidean and Hyperbolic Geometry

A cyclic antipodal pair of a circle is a pair of points that are the intersection of the circle with the diameter of the circle. In this article, a recent proof of Ptolemy’s Theorem—simultaneously in both (i) Euclidean geometry and (ii) the relativistic model of hyperbolic geometry (also known as the Klein model)—motivates the study of four cyclic antipodal pairs of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Identities that extend the Pythagorean identity in both Euclidean and hyperbolic geometry are obtained.

Thermoelectric transport of a topological semimetal with a pair of Weyl points and a nodal ring in the quantum limit

Thermoelectric transport of a topological semimetal with a pair of Weyl points and a nodal ring in the quantum limit

Measurement of outer diameter parameters of manual grinding cable joints based on 3D point cloud processing

For the problems associated with low measurement accuracy caused by surface shrinkage, uneven grinding, and irregular shapes in manual grinding cable joints, as well as the limitations of existing machine vision measurement techniques for the outer diameter parameters, this paper proposes a non-contact outer diameter parameters measurement method of manual grinding cable joints based on three-dimensional (3D) point cloud processing. Firstly, statistical filtering is used to remove discrete noise, and coordinate transformation preprocessing is conducted to ordered the point cloud. Secondly, a bidirectional point cloud slicing method is proposed based on the cable joint structure and point cloud distribution to preserve the original features for effective measurement. Subsequently, the normalized mean curvature is utilized as the weight of point cloud coordinate averaging to construct key points for surface slices, which reduces the amount of data in the sliced point cloud and improves the matching efficiency. Finally, the key points are matched according to the position of the surface slices, and the distance of point pairs is calculated to complete the measurement of the outer diameter parameters. Experiments and error analysis are conducted on multiple manual grinding 110 kV and 500 kV real cable joints. The absolute error in the measurement of the outer diameter is less than 0.2 mm, with a relative error within 1 %. The absolute error of the XY-axis outer diameter deviation is less than 0.1 mm. The experiments demonstrate that the proposed method exhibits superior performance in cable joint outer diameter measurement.

Computer Vision and Augmented Reality for Human-Centered Fatigue Crack Inspection.

A significant percentage of bridges in the United States are serving beyond their 50-year design life, and many of them are in poor condition, making them vulnerable to fatigue cracks that can result in catastrophic failure. However, current fatigue crack inspection practice based on human vision is time-consuming, labor intensive, and prone to error. We present a novel human-centered bridge inspection methodology to enhance the efficiency and accuracy of fatigue crack detection by employing advanced technologies including computer vision and augmented reality (AR). In particular, a computer vision-based algorithm is developed to enable near-real-time fatigue crack detection by analyzing structural surface motion in a short video recorded by a moving camera of the AR headset. The approach monitors structural surfaces by tracking feature points and measuring variations in distances between feature point pairs to recognize the motion pattern associated with the crack opening and closing. Measuring distance changes between feature points, as opposed to their displacement changes before this improvement, eliminates the need of camera motion compensation and enables reliable and computationally efficient fatigue crack detection using the nonstationary AR headset. In addition, an AR environment is created and integrated with the computer vision algorithm. The crack detection results are transmitted to the AR headset worn by the bridge inspector, where they are converted into holograms and anchored on the bridge surface in the 3D real-world environment. The AR environment also provides virtual menus to support human-in-the-loop decision-making to determine optimal crack detection parameters. This human-centered approach with improved visualization and human-machine collaboration aids the inspector in making well-informed decisions in the field in a near-real-time fashion. The proposed crack detection method is comprehensively assessed using two laboratory test setups for both in-plane and out-of-plane fatigue cracks. Finally, using the integrated AR environment, a human-centered bridge inspection is conducted to demonstrate the efficacy and potential of the proposed methodology.

Integration of autonomous maximal smile 3D image with digital 3D dental model and investigation of its accuracy.

This study aims to establish an approach to integrate autonomous maximal smile (AMS) 3D facial image with digital 3D dental models to demonstrate the digital orthodontic set-up in the 3D facial context. Using Geomagic Studio software, the AMS 3D facial image and pre-treatment dental model were manually and globally registered. Subsequently, the pre-treatment dental model was substituted with the predicted post-treatment dental model. The intraoral region of the AMS 3D facial image was removed, achieving a conjunctive display of the AMS 3D facial image and the post-treatment dental set-up. The distances between four groups of corresponding landmark pairs on the AMS 3D facial image and the pre-treatment dental set-up were calculated, and the accuracy of the registration operation was evaluated by paired t-test. The novel approach effectively facilitated the integration of AMS 3D facial images with the pre-treatment and predicted post-treatment 3D dental models. The average distances between the pairs of points were (1.19±0.55) mm and (1.55±0.59) mm for the two registrations, respectively. Notably, no statistically significant difference was observed between the two measurements (P>0.05), indicating a high agreement (intraclass correlation coefficient=0.914). This study established an approach to integrate AMS 3D facial images with digital 3D dental models. Through this approach, the digital orthodontic set-up design can be displayed in the context of a 3D facial image, which may help to improve the quality of outcome set-up in digital orthodontics, such as clear aligner therapy.

A note on the 2-colored rectilinear crossing number of random point sets in the unit square

Let S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document} be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document} with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S$$\\end{document} defines a pair of crossing edges of the same color is equal to 1/4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/4$$\\end{document}. This is connected to a recent result of Aichholzer et al. [1] who showed that by 2-colouring the edges of a geometric graph and counting monochromatic crossings instead of crossings, the number of crossings can be more than halved. Our result shows that for the described random drawings, there is a coloring of the edges such that the number of monochromatic crossings is in expectation 12-750\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{2}-\\frac{7}{50}$$\\end{document} of the total number of crossings.

Single Image Dehazing via Regional Saturation-Value Translation

This paper proposes an image dehazing prior, called Regional Saturation-Value Translation (RSVT), in order to address the color distortion issues produced by prevailing prior-based dehazing methods when processing hazy images with large sky regions. The proposed RSVT prior is derived from statistical analyses of the correlation between hazy points and respective haze-free points in the HSV color space. The prior is based upon two key observations in the sky areas. First, the difference in terms of hue for a pair of hazy and haze-free points is very small, raising an assumption that the variability of pixel values caused by haze mostly occurs in the saturation and value spaces. This leads to the second observation that, in the 2D saturation-value coordinate system, almost all the lines passing through corresponding pairs of hazy-clean points, termed S-V lines, are likely to intersect around the airlight coordinates. A hybrid refined dark channel is introduced in order to decompose the input hazy image into sky and non-sky regions and to estimate the global atmospheric light. Combining the prior with the hybrid refined dark channel, a novel single image dehazing framework is proposed. Haze removal is performed separately for the sky and non-sky regions by adopting the proposed RSVT prior and Koschmieder's law, respectively. The experimental results have shown that the proposed dehazing method can restore visually compelling sky color and effectively handle the color distortion issues associated with large sky regions.

Geometric random intersection graphs with general connection probabilities

Abstract Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}^d$ . A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points (v, u) with $v\in\mathcal{V}$ and $u\in\mathcal{U}$ independently with probability $g(v-u)$ , where g is a non-increasing radial function, and then connecting two points $v_1,v_2\in\mathcal{V}$ if and only if they have a joint neighbor $u\in\mathcal{U}$ . This gives rise to a random intersection graph on $\mathbb{R}^d$ . Local properties of the graph, including the degree distribution, are investigated and quantified in terms of the intensities of the underlying Poisson processes and the function g. Furthermore, the percolation properties of the graph are characterized and shown to differ depending on whether g has bounded or unbounded support.

Mountainous road vector data update method based on matching point pair grouping

ABSTRACT The vector information of mountainous roads is great significance, including regional economics, emergency response, disaster management, among others. Nevertheless, there are irregular deformations in existing vector data, coupled with incomplete extraction results for mountainous roadways. These issues pose challenges in establishing a matching model between road extraction results and existing vector data, significantly reducing the efficiency of automated updates for the current vector data. Targeting roads as a distinct artificial feature and leveraging their topological connectivity, we propose a vector data updating method based on matching point pair grouping. Firstly, we employ the SDUNet model to extract mountainous road and utilize the Superglue model to match road binary images with vector binary images, resulting in sets of initial matching point pairs. Subsequently, we propose a road line extraction model that groups matching point pairs, eliminates misaligned pairs based on road topological connectivity, and establishes a mapping relationship between road lines and vector lines. Ultimately, through road line optimization and vector line optimization methods, we accomplish the automatic updating of vector data for mountainous roadways. Through a comprehensive analysis of over 2600 vector data, our method demonstrates substantial advantages in terms of both F1 and IoU compared to alternative methods.

Constructing topology‐constrained distance cartograms with application on spatial interaction data

AbstractA distance cartogram is a deformed map where the distance between points conforms to a specific proximity indicator. Its readability is crucial, requiring a similar spatial arrangement of points between the original map and cartogram. Previous studies mainly incorporated angle changes of point pairs into the optimization objective. However, this soft constraint fails to provide high readability for spatial interaction data with numerous points and links. This study emphasizes the significance of maintaining Delaunay triangulation during deformation. To achieve this, topology‐constrained particle swarm optimization (TC‐PSO) is proposed, in which triangle intersections and flipping are prevented during optimization. Additionally, a topology error is introduced to evaluate the difference in triangulation between the original and deformed maps. TC‐PSO outperforms previous approaches by exhibiting the smallest topology error and producing more readable cartograms in simulation experiments and Baidu index data. These show TC‐PSO's advantage as a cartographic tool.

Mesoscopic simulation of uniaxial compression fracture of concrete via the nonlocal macro–meso-scale consistent damage model

To capture the uniaxial compression fracture of concrete composite is still a great challenging problem. To this end, the newly proposed nonlocal macro–meso-scale consistent damage (NMMD) model is extended to simulate uniaxial compression fracture of concrete composites. In the NMMD model, a mesoscopic structure composed of material point pairs is attached to each material point. A decomposition scheme suitable for masonry-like materials is adopted to decompose the elongation quantity of point pairs. The topologic damage is defined as the weighted summation of mesoscopic damage in neighboring material point pairs driven by the decomposed elongation quantity. The physically-based energetic degradation function is employed to bridge the geometric discontinuity in solids and the energy dissipation, and thus the topologic damage is integrated into the framework of continuum damage mechanics. The Monte-Carlo method and two-phase random field model are employed to generate stochastic circular and irregular aggregates representing the meso structure of concrete, respectively. The interface transition zone is prescribed by reducing the critical value of interface point pairs. Numerical results indicate that both the crack patterns and stress–strain curves of the uniaxial compression experiments on concrete panels can be well captured by the proposed NMMD model without mesh size sensitivity. The influence of horizontal constraints on the top and bottom surfaces is investigated and shown to have an effect on the crack patterns, strength and deformation capability of the specimen. The necessity of decomposition is also illustrated.

Adaptive parameter local consistency automatic outlier removal algorithm for area-based matching

Abstract. Due to the influence of image differences and matching methods, geometric calibration of remote sensing images often results in the extraction of control points with inevitable outliers. Moreover, it is susceptible to limitations imposed by locally constrained outlier rejection methods, making it challenging to automatically remove relatively small gross errors. This paper introduces an adaptive parameter local consistency automatic outlier removal algorithm, referred to as APLC. Initially, we construct k-nearest neighbors for each pair of matching points, deriving distance and topological uncertainty based on the accuracy of point matching. Subsequently, we conduct cross-validation on the uncertainty between the two pairs of vectors formed by points within the neighborhood, aiming for parameter adaptation. Finally, a cost-defined function is introduced to assess the consistency of local structures. Through a two-stage outlier removal strategy, matching points that do not maintain local structural consistency are eliminated. To assess the effectiveness of the proposed algorithm, we conduct experimental comparisons using region-based initial matching results from the FY-3D remote sensing dataset, demonstrating its superiority compared to three state-of-the-art methods.