The Affine Heat Method

Packet switching of data in networks is done by either the distance-vector or the link-state routing protocols. These protocols use the Bellman-Ford and the Dijkstra's algorithms respectively for the least cost path from a source base station to a destination station. For inter-network transmission, the path-vector routing protocol is in use. With progress of time, the network topologies are becoming huge in size, requiring large demand on book keeping of routing tables and transmission of the data packets dynamically to several other stations of the net-work by broadcast, increasing the load on the network. Here, assuming the router stations to be terrestrially located with links along the ground, a large network is assumed to lie on a spherical surface, and so the shortest geodesic path from source to destination becomes a great circular arc. For fast transmission, the cost of a link to a node is multicast to its neighboring nodes only for selection of the path lying as close as possible to the geodesic line between the source and the destination. As the arrival and dispatch of data packets at a nodal station occurs randomly, the cost of a link is estimated in this paper by the waiting time of a queueing process. This process at a router station is thus modeled by the Markovian M/M/c model, where c is the number of servers at the router station. If other commercial fixed charge is involved for the use of a link, then that can be included in the total cost of a link. Finally, a method of search of a mobile destination is also presented using sphericity of the network. Algorithms for the near geodesic path, costs of links as waiting times and destination search in mobile environment are clearly presented.

This study addresses the challenges associated with incomplete or missing information in obstacle detection methods that employ a single sensor. Additionally, it tackles the issue of motion distortion in LiDAR point cloud data during synchronization and mapping in complex environments. The research introduces two significant contributions. Firstly, a novel obstacle detection method, named the point-map fusion (PMF) algorithm, was proposed. This method integrates point cloud data from the LiDAR, camera, and odometer, along with local grid maps. The PMF algorithm consists of two components: the point-fusion (PF) algorithm, which combines LiDAR point cloud data and camera laser-like point cloud data through a point cloud library (PCL) format conversion and concatenation, and selects the most proximate point cloud to the quadruped robot dog as the valid data; and the map-fusion (MF) algorithm, which incorporates local grid maps acquired using the Gmapping and OctoMap algorithms, leveraging Bayesian estimation theory. The local grid maps obtained by the Gmapping and OctoMap algorithms are denoted as map A and map B, respectively. This sophisticated methodology enables seamless map fusion, which significantly enhances the precision and reliability of the approach. Secondly, a motion distortion removal (MDR) method for LiDAR point cloud data based on odometer readings was proposed. The MDR method utilizes legged odometer data for linear data interpolation of the original distorted LiDAR point cloud data, facilitating the determination of the corresponding pose of the quadruped robot dog. Subsequently, the LiDAR point cloud data are then transformed to the quadruped robot dog coordinate system, efficiently mitigating motion distortion. Experimental results demonstrated that the proposed PMF algorithm achieved a 50% improvement in success rate compared to using only LiDAR or the PF algorithm in isolation, while the MDR algorithm enhanced mapping accuracy by 45.9% when motion distortion was taken into account. The effectiveness of the proposed methods was confirmed through rigorous experimentation.

Experiments were conducted to investigate the nucleate pool boiling heat transfer characteristics and steam carrying phenomena during boiling for different aqueous surfactant solutions, 99% sodium dodecyl sulfate(SDS) and Triton X-114. Bubble behaviour, heat transfer enhancement mechanisms and steam carrying phenomena were discussed for a range of heat flux (24.7-109.1 kW/m2) and mass concentrations (50-8000 ppm for SDS and 20-1000 ppm for Triton X-114). The bubble observations show that, when compared with water, boiling in surfactant solutions is observed to be more vigorous with smaller-sized and fast departure frequency. The surfactant solutions of Triton X-114 is becoming cloudy during boiling at around cmc for its cloud point is much lower than the boiling liquid temperature. The experiments of boiling heat transfer conclude that an optimum heat transfer enhancement is achieved near the critical micelle concentrations (cmc) of the surfactants, and at the same heat flux, the optimum boiling heat transfer enhancement at cmc of SDS is higher than that of Triton X-114 when compared with pure water. The enhancement of boiling heat transfer by the addition of surfactants is the complex effects of surfactant species, the reduction of surface tension, the changes of the contact angel. The experiments of steam carrying show that the amount of surfactants which carried out by steam from solutions during boiling dependeds on the species of surfactant, heat flux and concentration of the initial surfactant aqueous solutions.

Abstract. Photorealistic 3D models play an important role in various applications related to smart cities. Texture mapping plays a crucial role as the last step of 3D reconstruction. The texture of the model directly reflects the visualization and realism of the model. In complex city scenes, objects often have varying degrees of occlusion from one another. Traditional methods to circumvent occlusion by image or model data are not very effective. In this paper, we propose an automatic texture mapping method for 3D models to circumvent occlusion through 3D spatial through-view relationships between images, models, and point clouds. First of all, calculate the density and voxel resolution of the point clouds, the point clouds here can be either dense matching point clouds or laser point clouds. Voxelization is based on point clouds, voxels generated by voxelization can reflect the spatial location of the point clouds. Secondly, to determine whether there is an occlusion of voxels between the image and the model vertices based on the spatial through-view relationship between the image, the model, and the voxels, and filter out the unobstructed images. Finally, by optimizing the data items of the Markov random field, the shading function is added to the original data items for evaluating the shading condition, based on which the most suitable image is selected for texture mapping of a triangular surface of the model. Loop computation to complete the unobstructed texture mapping of the entire model. In this paper, the public test datasets released by the International Society for Photogrammetry and Remote Sensing (ISPRS) and several urban area datasets collected by ourselves are incorporated to test the performance of the proposed method. Both qualitative and quantitative cross-sectional comparisons with existing texture mapping algorithms are conducted and presented. Experimental results indicate that our method can effectively circumvent occlusion for automated texture mapping, and generate 3D models with fewer obstructed textures, which largely improves the visual quality and realism of the models.

With the rapid development of 3D vision applications based on point clouds, point cloud quality assessment(PCQA) is becoming an important research topic. However, the prior PCQA methods ignore the effect of local quality variance across different areas of the point cloud. To take an advantage of the quality distribution imbalance, we propose a no-reference point cloud quality assessment (NR-PCQA) method with local area correlation analysis capability, denoted as COPP-Net. More specifically, we split a point cloud into patches, generate texture and structure features for each patch, and fuse them into patch features to predict patch quality. Then, we gather the features of all the patches of a point cloud for correlation analysis, to obtain the correlation weights. Finally, the predicted qualities and correlation weights for all the patches are used to derive the final quality score. Experimental results show that our method outperforms the state-of-the-art benchmark NR-PCQA methods. The source code for the proposed COPP-Net can be found at https://github.com/philox12358/COPP-Net.

<title>Abstract</title> Wheels are critical components of railway vehicles, and the dynamic measurement of wheel parameters is of paramount importance for the safe operation of trains.To enhance the matching accuracy in the existing dynamic measurement processes for train wheel parameters, this paper proposes an improved point cloud registration algorithm based on key point fusion of the Super-4PCS(Super Four-Points Congruent Sets) and ICP (Iterative Closest Point) algorithm. Firstly, point cloud filtering and normal estimation are performed on the wheel point cloud data to obtain source and target point clouds with normal information. Subsequently, the ISS algorithm is employed to extract key points, and the FPFH(Fast Point Feature Histograms) point cloud feature descriptor is utilized to characterize the extracted key points. Then, a two-level registration strategy is used to improve registration accuracy, in which the Super-4PCS algorithm is applied for primary coarse registration and the ICP algorithm is used for the secondary fine registration, respectively. Finally, the experiment is conducted to validate the proposed algorithm and the performance of the algorithm is further comparative analyzed through the listed registration evaluation metrics. Experimental results demonstrate that the proposed algorithm exhibits significant improvements in registration accuracy and robustness for wheel point cloud data compared to the traditional algorithms.

The prevalence of computer graphics technology boosts the development of point clouds, which offer advantages over T riangular I rregular N etworks , i.e., TIN s, in proximity queries. All existing on-the-fly shortest path query algorithms and oracles on a TIN are expensive, and no algorithms can answer shortest path queries on a point cloud directly. Thus, we propose two types of efficient shortest path oracles on a point cloud. They answer the shortest path query between (1) a pair of P oints- O f- I nterests ( POIs ), and (2) any point and a POI, respectively. We propose four adaptations of them to answer the query between any point and a POI (or any point if no POIs are given). We also propose two efficient proximity query algorithms using these oracles. Our two oracles and their proximity query algorithms outperform the best-known adapted oracle by 12 to 42,000 times in terms of the oracle construction time, oracle size and proximity query time, respectively.

Heat flow in adiabatic calorimeters of various shapes and materials is described in terms of linear partial differential equations. From these equations it is deduced that in the intermittent heating method the heat exchange between the calorimeter and the adiabatic shield due to transients at the beginning and end of the heating period can be made to cancel. The remaining heat exchange is the same for intermittent or continuous heating methods and can be treated as the sum of effects due to gradients set up by heat flow (1) from the shield to the environment and (2) from the shield and calorimeter heaters to raise the temperatures of the shield and calorimeter, respectively. The first effect can be accounted for by measurements during fore and after periods in intermittent calorimetry and by varying the heating rate in continuous calorimetry. Under certain conditions the second effect can be accounted for by measurements with the empty calorimeter. Variation in heating rate fails as a test for the magnitude of the second effect.

We introduce the first learning-based method for recovering shapes from Laplacian spectra. Our model consists of a cycle-consistent module that maps between learned latent vectors of an auto-encoder and sequences of eigenvalues. This module provides an efficient and effective linkage between Laplacian spectrum and geometry. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Our learning model applies without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh super-resolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and point-to-point matching.

• A novel foundation for topological pattern recognition of point cloud data, through persistent homology of graph approximations. • An extension of persistent homology to point cloud data of metric trees, including theoretical and experimental verification. • The first charting of cell trajectory data sets that explains some of the difficulties this field is confronted with. The rising field of Topological Data Analysis (TDA) provides a new approach to learning from data through persistence diagrams , which are topological signatures that quantify topological properties of data in a comparable manner. For point clouds, these diagrams are often derived from the Vietoris-Rips filtration—based on the metric equipped on the data—which allows one to deduce topological patterns such as components and cycles of the underlying space. In metric trees these diagrams often fail to capture other crucial topological properties, such as the present leaves and multifurcations. Prior methods and results for persistent homology attempting to overcome this issue mainly target Rips graphs, which are often unfavorable in case of non-uniform density across our point cloud. We therefore introduce a new theoretical foundation for learning a wider variety of topological patterns through any given graph . Given particular powerful functions defining persistence diagrams to summarize topological patterns, including the normalized centrality or eccentricity , we prove a new stability result, explicitly bounding the bottleneck distance between the true and empirical diagrams for metric trees. This bound is tight if the metric distortion obtained through the graph and its maximal edge-weight are small. Through a case study of gene expression data, we demonstrate that our newly introduced diagrams provide novel quality measures and insights into cell trajectory inference.

Magnetically inferred regional heat flow and geological structures in parts of Chad Basin, Nigeria and their implications for geothermal and hydrocarbon prospects

Automatic pairwise registration for unordered terrestrial laser scanner (TLS) point clouds is the pre-requisite for many applications, including 3D model reconstruction, cultural heritage management and landslide monitoring. However, most of the existing registration methods are still suffering from several limitations: (1) difficult to find the correct corresponding point pairs from the source and target point cloud, (2) low accuracy of pairwise registration and (3) the iterative process of registration is time-consuming. To overcome these challenges, based on the covariance matrix, this paper presents a robust and descriptive feature descriptor vector (FDV) to locally describe a point, by which the corresponding point pairs are obtained and the registration matrix is calculated. First, the FDVs of the original point cloud’s keypoints are calculated. Second, the corresponding point pairs are found via their FDVs. Third, the coarse transformation matrix is calculated by the corresponding point pairs using the singular value decomposition (SVD) algorithm, and which is further refined by the iterative closest point (ICP) algorithm to get a better result. Finally, the experiments are conducted on the Autonomous Systems Lab (ASL) and ISPRS datasets; our results show that the proposed algorithm can obtain good registration performance, and outperforms the compared methods.

Point cloud registration is a fundamental problem in robotics, critical for tasks such as localization and mapping. Most approaches to this problem use feature-based techniques. However, these approaches have issues when dealing with unstructured environments where meaningful features are difficult to extract. Recently, an innovative global point cloud registration algorithm, PHASER, which does not rely on geometric features or point correspondences, has been introduced. It leverages Fourier transforms to identify the optimal rigid transform that maximizes cross-correlation between source and target point clouds. PHASER can also incorporate additional data channels, like LiDAR intensity, to enhance registration results. Because it does not rely on local features and because of its ability to exploit additional data, PHASER is particularly useful when dealing with very noisy point clouds or with many outliers. For this reason, we propose an extension to PHASER that considers multiple plausible rototranslation hypotheses. Our extended approach outperforms the original PHASER algorithm, especially in challenging scenarios where point clouds are widely separated. We validate its effectiveness on the DARPA SubT, and the Newer College datasets, showcasing its potential for improving registration accuracy in complex environments.

We present a novel no-reference quality assessment metric, the image transferred point cloud quality assessment (IT-PCQA), for 3D point clouds. For quality assessment, deep neural network (DNN) has shown compelling performance on no-reference metric design. However, the most challenging issue for no-reference PCQA is that we lack large-scale subjective databases to drive robust networks. Our motivation is that the human visual system (HVS) is the decision-maker regardless of the type of media for quality assessment. Leveraging the rich subjective scores of the natural images, we can quest the evaluation criteria of human perception via DNN and transfer the capability of prediction to 3D point clouds. In particular, we treat natural images as the source domain and point clouds as the target domain, and infer point cloud quality via unsupervised adversarial domain adaptation. To extract effective latent features and minimize the domain discrepancy, we propose a hierarchical feature encoder and a conditional-discriminative network. Considering that the ultimate pur-pose is regressing objective score, we introduce a novel con-ditional cross entropy loss in the conditional-discriminative network to penalize the negative samples which hinder the convergence of the quality regression network. Experi-mental results show that the proposed method can achieve higher performance than traditional no-reference metrics, even comparable results with full-reference metrics. The proposed method also suggests the feasibility of assessing the quality of specific media content without the expensive and cumbersome subjective evaluations. Code is available at https://github.com/Qi-Yangsjtu/IT-PCQA.

We consider the problem of finding a rectilinear path between two designated points in the presence of rectilinear obstacles subject to various optimization functions in terms of the number of bends and the total length of the path. Specifically we are interested in finding a minimum bend shortest path, a shortest minimum bend path or a least-cost path where the cost is defined as a function of both the length and the number of bends of the path. We provide a unified approach by constructing a path-preserving graph. guaranteed to preserve all these three kinds of paths and give an O(K+e log e) algorithm to find them, where e is the total number of obstacle edges, and K is the number of intersections between tracks from extreme point and other tracks (defined in the text). K is bounded by O(et), where t is the number of extreme edges. In particular, if the obstacles are rectilinearly convex, then K is O(ne), where n is the number of obstacles. Extensions are made to find a shortest path with a bounded number of bends and a minimum-bend path with a bounded length. When a source point and obstacles are pre-given, queries for the assorted paths from the source to given points can be handled in O( log e+k) time after O(K+e log e) preprocessing, where k is the size of the goal path. The trans-dichotomous algorithm of Fredman and Willard8 and the running time for these problems are also discussed.