Delaunay Triangulation Algorithm Research Articles

A Fast Modeling Method for BOR–FDTD

Aiming at the inefficiency caused by the optimal design of rotationally symmetric horn feed models, a fast modeling method for rotationally symmetric structures is proposed, which is used to deal with the mesh generation of rotationally symmetric structures and the rapid establishment of computational models. In this paper, the body-of-revolution finite-difference time-domain (BOR–FDTD) method is employed to investigate the radiation performance of the horn feed. Due to the rotational symmetry of the horn antenna, modeling only requires the establishment of a two-dimensional cross-sectional mesh of the horn feed. An optimized Delaunay triangulation algorithm combined with the projection intersection method is utilized to triangulate the horn cross-section of arbitrary polygons and establish the BOR–FDTD computational mesh. Results from both single-medium and multi-medium triangulation algorithms and computational models verify the accuracy of this modeling method. The radiation patterns of a smooth-walled horn were calculated and compared with the modeling time of MATLAB 2017 and the simulation time of CST. The results reveal that the algorithm presented in this paper aligns well with the simulation results from CST; furthermore, the modeling time amounts to only 6.78% of the MATLAB program’s modeling time, while the total simulation time is 31.3% of CST, which demonstrates both the accuracy and efficiency of the proposed method.

Quantitative dispersion characterization of cement particles in hardened cement matrix

Optimizing the cement particle distribution in hardened cement matrix is one of the effective means to utilize cement efficiently, and obtaining information about cement distribution is a prerequisite for this. In view of this, this paper investigates the quantitative dispersion of cement particles in hardened cement paste from an experimental perspective. Cement pastes with different water-binder (W/B) ratios were prepared as the objects. BSE images of these samples were acquired for further analysis, including Delaunay triangulation algorithm, nearest neighbor distance function G(r) and fractal theory. Results showed that when the W/B ratio increases from 0.36 to 0.42, the average cement particle spacing rises from 32.7 μm to 34.9 μm and the proportion of particles with spacing between particle centroids <20 μm decreases from 41.96 % to 25.98 %. Similarly, the increasing W/B ratio causes the nearest neighbor distance function G(r) to shift towards larger distances. When the W/B ratio is 0.34, the median distance between particles (R50) exhibits the most significant change. Additionally, the intricate details of cement particle spacing information can be accurately described by fractal theory. Parameters such as R50 and the proportion of particles with spacing between centroids <20 μm demonstrate strong fits with various fractal parameters. Notably, they exhibit optimal fitting with the spectral width of the generalized fractal spectrum, with an R2 value of 0.99.

Aerial Surveillance Leveraging Delaunay Triangulation and Multiple-UAV Imaging Systems

In aerial surveillance systems, achieving optimal object detection precision is of paramount importance for effective monitoring and reconnaissance. This article presents a novel approach to enhance object detection accuracy through the integration of Delaunay triangulation with multi-unmanned aerial vehicle (UAV) systems. The methodology involves positioning multiple UAVs at pre-specified locations using the Delaunay triangulation algorithm with performance of O (n log n). This is compared with the conventional single UAV approach at a near distance. Our findings reveal that the collaborative efforts of multiple UAVs, guided by Delaunay triangulation, significantly improves object detection accuracy, especially when compared to a single UAV operating in close proximity. This research employs advanced image processing techniques to identify objects in the area under surveillance. Results indicate a substantial enhancement in the collective surveillance capabilities of the multi-UAV system, demonstrating its efficacy in unconstrained scenarios. This research not only contributes to the optimization of aerial surveillance operations but also underscores the potential of spatially informed UAV networks for applications demanding heightened object detection accuracy. The integration of Delaunay triangulation with multi-UAV systems emerges as a promising strategy for advancing the capabilities of aerial surveillance in scenarios ranging from security and emergency response to environmental monitoring.

Exploring Low-Speed Marine Diesel Engine Parameters through Advanced 3D Visualization with Delaunay Triangulation

The article presents an algorithm for creating software leading to the optimization of the combustion process of marine engines. Parameters determining the Existing Ships Energy Efficiency Index (EEXI) related to ship type, capacity, and propulsion principle are considered. Test data on the characteristics of a two-stroke main engine, model HYUNDAI 6S60MC-C for six types of loads were used as the basis. To present the working field of the engine, the necessary calculations have been carried out and dependencies have been derived for the power and the specific fuel consumption as a function of the revolutions. The implementation includes the development of a small software program using Delaunay's triangulation algorithm to create 3D graphics, as well as Python libraries and methods.

Three-Axes Mems Calibration Using Kalman Filter and Delaunay Triangulation Algorithm

MEMS-IMUs are widely used in research, industry, and commerce. A proper calibration technique must reduce their innate errors. In this study, a turntable-based IMU calibration approach was presented. Parameters such as the bias, lever arm, and scale factor, in addition to misalignment, are included in the general nonlinear model of the IMU output. Accelerometer error parameters were estimated using the transformed unscented Kalman filter (TUKF) with triangulation algorithm is suggested for calibrating inertial measurement unit (MPU6050) three-axes accelerometer. In contrast to the present methods, the suggested method uses the gravitational signal as a constant reference and necessitates no external equipment. The technique requires that the sensor be positioned in a rough orientation and that basic rotations be adopted. This technology also offers a quicker and easier calibration. Comparing the experimental findings with other works, Allan deviation shows significant improvements for the bias instability, where a bias instability of (0.116 μg) is achieved at temperatures between (−15°C) and (80°C).

Voronoi discretization to improve the meshless local Petrov–Galerkin method in 3D-computational fracture mechanics

Purpose1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.Design/methodology/approachUsing appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).FindingsBy doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.Originality/valueThe present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].

Underwater Wireless Sensor Network-Based Delaunay Triangulation (UWSN-DT) Algorithm for Sonar Map Fusion

Abstract Robust and fast image recognition and matching is an important task in the underwater domain. The primary focus of this work is on extracting subsea features with sonar sensor for further Autonomous Underwater Vehicle navigation, such as the robotic localization and landmark mapping applications. With the assistance of high-resolution underwater features in the Side Scan Sonar (SSS) images, an efficient feature detector and descriptor, Speeded Up Robust Feature, is employed to seabed sonar image fusion task. In order to solve the nonlinear intensity difference problem in SSS images, the main novelty of this work is the proposed Underwater Wireless Sensor Network-based Delaunay Triangulation (UWSN-DT) algorithm for improving the performances of sonar map fusion accuracy with low computational complexity, in which the wireless nodes are considered as underwater feature points, since nodes could provide sufficiently useful information for the underwater map fusion, such as the location. In the simulated experiments, it shows that the presented UWSN-DT approach works efficiently and robustly, especially for the subsea environments where there are few distinguishable feature points.

Evolution of pore structure in nanoparticle deposits from unimodal to bimodal pore size distributions: Focus on structural features of dendritic structures

Nanoparticle deposits can exhibit various structures, including compact and dendritic structures, depending on the deposition conditions. While previous studies have characterized deposit structures using factors such as porosity and spatial autocorrelation index, the pore size distribution (PSD), which is an essential structural property, has only been explored in compact structures. In this study, we investigate the PSDs of the entire nanoparticle deposits, ranging from compact to dendritic structures. Deposits are formed using an off-lattice Monte Carlo simulation, and deposition conditions are represented by two dimensionless numbers (KnD, χF). The diffusive Knudsen number (KnD) ranges from 10−1.5 to 101.5, while the dimensionless translational energy of a particle (χF) ranges from 10−3 to 101.5. We use the Delaunay triangulation algorithm for fast PSD calculation, and validate the calculation method using theoretical values of ideal structures and experimental literature data. Our results show that bimodal PSDs appear under thermally-dominated conditions with high values of KnD, while unimodal PSDs with a constant mode radius (∼2.5 rp) are observed under highly advective conditions with high values of χF. We present the geometric mean radii and mode radii of pores as color-filled contours to show their variation trends with KnD and χF. Additionally, we propose a simple model that predicts dendrite width by combining the overall porosity and mode radii of pores. Our model's predictions reasonably match the dendrite width data obtained using a density-based clustering algorithm.

Progressive bridge collapse analysis under both scour and floods by coupling simulation in structural and hydraulic fields. Part Ⅰ: Numerical solver

Hydraulic bridge failures have become the greatest threat to the structural safety of bridges. Combined numerical simulations are rare due to the high computational cost of structural nonlinear finite element analysis (NLFEA) and computing fluid dynamics (CFD). Structural analysis and design for extreme hydrological hazards are challenging due to complicated hydrodynamics-soil-structure interactions. This paper proposes a numerical solver to simulate hydraulic bridge failures through coupling simulations. The solver applies hydrodynamic load and updates scour boundary in a structural model by utilizing a scatter linear interpolation method based on the Delaunay triangulation algorithm in each loop solution. Then, a simplified sediment stress model considering external forces in the vertical plane and a complex model with an arbitrary slope in three-dimensional coordinates are introduced into the basic incipient motion model of sediment, resulting in a more realistic stress state of sediment. Finally, the numerical solver is adapted to provide an accessible method to investigate the influence of such a modified model on the scour process and structure response. Meanwhile, the validation of this numerical solver is conducted in a companion paper based on the comparison between the numerical result of the hybrid model and the field data.

FDTD Complex Terrain Modeling Method Based on Papery Contour Map

This study aims to develop a finite difference time-domain (FDTD) modeling method for complex terrain using a paper contour map. First, the image preprocessing technology is employed to segment, denoise, and number the drawing area to arrive at independent figures and curve matrices. Subsequently, the support vector machine (SVM) classifier is implemented to identify the number and obtain the elevation value pertinent to the curve in the figure. Finally, the scattered points in the curve matrix are meshed by the Delaunay triangulation algorithm, and a three-dimensional triangular mesh model is established according to the recognition results. The FDTD calculation model is established by the method of intersection of Yee cell grid lines and triangle projection. The simulation results reveal that the recognition rate of the SVM classification model in this study is close to 100% for printed numerals. This approach is capable of quickly and accurately establishing the FDTD-based calculation model for complex terrain on the basis of the paper contour map.

Outlier Detection of Crowdsourcing Trajectory Data Based on Spatial and Temporal Characterization

As an emerging type of spatio-temporal big data based on positioning technology and navigation devices, vehicle-based crowdsourcing data has become a valuable trajectory data resource. However, crowdsourcing trajectory data has been collected by non-professionals and with multiple measurement terminals, resulting in certain errors in data collection. In these cases, to minimize the impact of outliers and obtain relatively accurate trajectory data, it is crucial to detect and clean outliers. This paper proposes an efficient crowdsourcing trajectory outlier detection (CTOD) method that detects outliers from the trajectory sequence data in both spatial view and temporal view. Specifically, we first use the adaptive spatial clustering algorithm based on the Delaunay triangulation (ASCDT) algorithm to remove the location offset points in the trajectory sequence. After that, based on the most basic attributes of the trajectory points, a 6-dimensional movement feature vector is constructed for each point as an input. The feature-rich trajectory sequence data is reconstructed using the proposed temporal convolutional network autoencoder (TCN-AE), and the Squeeze-and-Excitation (SE) channel attention mechanism is introduced. Finally, the effectiveness of the CTOD method is experimentally verified.

Noncontact Detection Method for Food Texture Assessment Based on Air Puff Combined With Structured Light Imaging

Given the shortcomings of subjectivity and destructiveness associated with traditional methods of measuring food texture parameters (such as fruit firmness and meat tenderness) when using a texture meter, a non-contact measurement method utilizing an Air-puff combined with Structured Light Imaging (ASLI) was proposed in this study. First, the finite element simulation method was used to simulate the airflow impact model and optimize the ranges of the angle and distance parameters. The detection device was then developed, and binocular 3D phenotype acquisition and 3D feature extraction algorithms were investigated. Denoising, point cloud segmentation, greedy projection triangulation, Delaunay triangulation, and surface fitting algorithms were used to process the point cloud, and concave parameters such as depth, mapping area, surface area, and volume of the concave area on the beef surface were obtained. Finally, four typical samples with different meat (beef and chicken) and fruit (kiwifruit and peach) parameters were tested. Five machine learning methods were used to model and analyze the correlation among texture parameters. The results revealed that the model established by the ensemble learning modeling method with extracted concave parameters possessed the highest accuracy. The prediction accuracy of the shear force values of the beef and chicken samples were 0.92 and 0.91. The accuracy of meat and fruit grading was 0.942 and 1.0. Therefore, the non-contact detection method proposed in this study to determine food texture characteristics based on airflow can be used to replace the traditional texture analyzer in food engineering and exhibits good application potential.

A PARALLELED DELAUNAY TRIANGULATION ALGORITHM FOR PROCESSING LARGE LIDAR POINTS

Abstract. LiDAR is an important data source for disaster prevention and mitigation, its advantages include speediness, penetration, initiative, high-density and high-precision, high efficiency, information-richness. In this paper, we address the design and implementation of a practical parallel algorithm for Delaunay triangulation that works on massive point cloud data acquired by airborne LiDAR. The algorithm is based on the divide and conquer algorithm, Bowyer-Watson algorithm and triangulation-growth and can be easily extended to multi-core or cluster environment. It first divides the point cloud data into blocks at the MapReduce’s Map phase; then the triangulation network of each block is simultaneously constructed using Bowyer-Watson algorithm on different CPU cores; at the reduction phase, the triangular network of each block is merged and optimized using triangulation-growth and Local Optimization Procedure (LOP). Experimental results show that the speed of the paralleled triangulation algorithm can be improved significantly compared to the sequential algorithm on multi-core desktop computer. The speedup depends on partition of the dataset and the number of CPU cores used, and is usually 2–3 times that of sequential algorithms.

Rapeseed Leaf Estimation Methods at Field Scale by Using Terrestrial LiDAR Point Cloud

Exploring the key technologies of agricultural robots is an inevitable trend in the development of smart agriculture. It is significant to continuously transplant and develop novel algorithms and models to update agricultural robots that use light detection and ranging (LiDAR) as a remote sensing method. This paper implements a method for extracting and estimating rapeseed leaves through agricultural robots based on LiDAR point cloud, taking leaf area (LA) measurement as an example. Firstly, the three-dimensional (3D) point cloud obtained with a terrestrial laser scanner (TLS) were used to extract crop phenotypic information. We then imported the point cloud within the study area into a custom hybrid filter, from which the rapeseed point cloud was segmented. Finally, a new LA estimation model, based on the Delaunay triangulation (DT) algorithm was proposed, namely, LA-DT. In this study, a crop canopy analyzer, LAI-2200C, was used to measure rapeseed LA in farmland. The measured values were employed as standard values to compare with the calculated results obtained using LA-DT, and the differences between the two methods were within 3%. In addition, 100 individual rapeseed crops were extracted, and the output of the LA-DT model was subjected to linear regression analysis. The R² of the regression equation was 0.93. The differences between the outputs of the LAI-2200C and LA-DT in these experiments passed the paired samples t-test with significant correlation (p &lt; 0.01). All the results of the comparison and verification showed that the LA-DT has excellent performance in extracting LA parameters under complex environments. These results help in coping with the complex working environment and special working objects of agricultural robots. This is of great significance for expanding the interpretation methods of agricultural 3D information.

Application of Rotationally Symmetrical Triangulation Stereo Vision Sensor in National Dance Movement Detection and Recognition

Information acquisition is an important branch of information science. It is the product of the development and cross-integration of traditional sensing technology and other multidisciplines. It is characterized by the high precision, high speed, integration, and intelligence of information acquisition. An important part of information acquisition, it studies how to acquire the geometric structure and scale information of objects in three-dimensional space. With the continuous development of the level, the acquisition of 3D information has become more and more important in scientific research and industrial production. This paper takes 3D information acquisition technology as the main line. From the perspectives of fusion, effectiveness, physical limit, and measurement efficiency, high-resolution 3D information acquisition techniques are studied. In this paper, the upper and lower limb movements of each behavioral segment are segmented according to the difference. An omnidirectional stereo vision sensor composed of a single camera and two secondary conical mirrors is designed, which solves the problems of large size, narrow field of view, and asynchronous image acquisition of traditional binocular vision sensors, effectively ensuring image perspective. The invariance of projection avoids image distortion caused by curved mirror imaging and reduces the difficulty of subsequent work. The three-dimensional Delaunay triangulation algorithm is used to replace the traditional Poisson reconstruction algorithm to generate the triangular mesh model. The triangular mesh model obtained by the multiview stereo reconstruction algorithm is relatively rough. This article uses Zbrush’s ZRemesher and geometric-divide functions to smooth and simplify the model. The results show that the accuracy of the algorithm proposed in this paper is as high as 89.25% in the motion recognition of body elements. The dynamic mapping method is used to map the texture of the triangular mesh model, so that the realism of the model reaches 91.23%.

A Generalization of Self-Improving Algorithms

Ailon et al. [SICOMP’11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances x 1 , ... , x n follow some unknown product distribution . That is, x i is drawn independently from a fixed unknown distribution 𝒟 i . After spending O ( n 1+ε ) time in a learning phase, the subsequent expected running time is O (( n + H )/ε), where H ∊ { H S , H DT }, and H S and H DT are the entropies of the distributions of the sorting and DT output, respectively. In this article, we allow dependence among the x i ’s under the group product distribution . There is a hidden partition of [1, n ] into groups; the x i ’s in the k th group are fixed unknown functions of the same hidden variable u k ; and the u k ’s are drawn from an unknown product distribution. We describe self-improving algorithms for sorting and DT under this model when the functions that map u k to x i ’s are well-behaved. After an O (poly( n ))-time training phase, we achieve O ( n + H S ) and O ( n α ( n ) + H DT ) expected running times for sorting and DT, respectively, where α (⋅) is the inverse Ackermann function.

PIMesh: An automatic point cloud and unstructured mesh generation algorithm for meshless methods and finite element analysis-with applications in surgical simulations.

We propose a point cloud and mesh generation algorithm, particle injection mesh generator (PIMesh), that can be used to generate optimized high-quality point clouds and unstructured meshes for domains in any shape with minimum (or even no) user intervention. The domains can be scanned images in OBJ format in 2D and 3D or just a line drawing in 2D. Mesh grading can also be easily controlled. The PIMesh is robust and easy to be implemented and is useful for a variety of applications, ranging from generating point clouds for meshless methods, mesh generation for finite element methods, computer graphics applications and surgical simulators. The core idea of the PIMesh is that a mesh domain is considered as an "airtight container" into which particles are "injected" at one or multiple selected interior points. The motion of the particles is controlled by a pseudo-molecular dynamics (PMD) formulation with a pairwise purely repelling "force" moderated by an absolute velocity dependent drag force. The particles repel each other and occupy the whole domain somewhat like blowing up a balloon. When the container is full of particles and the motion is stopped (the particles can be considered as a point cloud), a Delaunay triangulation algorithm is employed to link the particles together to generate an unstructured mesh. The performance of the PIMesh and the comparison with other unstructured mesh generation approaches are demonstrated through generating node distributions and meshes for several 2D and 3D object domains including a scanned image of bones and others.

Regional application of C1 finite element interpolation method in modeling of ionosphere total electron content over Europe

• A novel approach for regional ionosphere grid model with high spatial-temporal resolution is suggested. • The results of the new model is analyzed at different disturb geomagnetic and solar conditions. • A comparative analysis between the results of new model, GIM, NeQuick and GPS-TEC is made. In this paper, a novel approach based on C 1 finite element (FE) interpolation is used to construct a regional ionospheric grid model (RIGM) with high spatio-temporal resolution over Europe. The spatial resolution of the new model is 0.5 0 for a longitude and latitude and a temporal resolution is 15 min. Observations of 38 GPS stations at different days and seasons with different geomagnetic and solar activity conditions are used to evaluate the new method. All stations are used to discretize the whole domain of the problem into separate triangular patches using a Delaunay triangulation algorithm. In this case, GPS stations would be the vertices of the triangular patches. Also, the position of stations in sun-fixed coordinate system with coordinates of latitude and longitude are chosen in order to consider the temporal variations of vertical total electron content (VTEC). To model the behavior of VTEC in each triangular patch, a particular shape function is defined which is fitted to VTEC values at three vertices of each triangle while it satisfies C 1 continuity of VTEC at the common edges of the adjacent triangles. The results of the new model are compared with the VTEC of GPS at 4 control stations as well as global ionosphere map (GIM) and NeQuick models. Statistical parameters, including correlation coefficient, root mean square error (RMSE), standard deviation and dVTEC = |VTEC GPS - VTEC model | have been used to evaluate the error of the models. In low geomagnetic activity (KP < 4), the average RMSE at 4 control stations for FE, GIM and NeQuick models are 0.89, 1.05 and 6.42 TECU, respectively, while in the high geomagnetic activity (KP > 4), they are 1.24, 1.68 and 7.62 TECU, respectively. For further analysis, the accuracy of three models in precise point positioning (PPP) has been also evaluated. In PPP method, there is an improvement of about 1–16 mm compared to GIM and NeQuick models at coordinate components of control stations in high geomagnetic activity. The results of the analysis performed in this paper show that the FE model has a very high capability and accuracy in regional VTEC modeling in high and low geomagnetic conditions. The regional accuracy of this model is higher than GIM and NeQuick models and therefore can be considered as a new model for the ionosphere.

The method for accurate acquisition of pavement macro-texture and corresponding finite element model based on three-dimensional point cloud data

To establish the accurate pavement macro-texture finite element (FE) model used for tire-pavement interaction FE analysis, a novel processing and modelling procedure was proposed based on point cloud data obtained by the laser texture scanner. At first, drop-outs were removed using the linear interpolation technique, and a binary linear function was fitted to correct the pavement texture tilt. Besides, the spikes were detected and removed via bilateral test and linear interpolation based on asymmetric generalized Gaussian distribution. The effectiveness of proposed tilt correction and the spike detection method were verified based on the reference plate and the comparison with existing spike detection methods respectively. Subsequently, the Delaunay triangulation algorithm was employed to triangulate the processed point cloud data. Then, the reverse engineering modelling technique was used to generate the accurate three-dimensional (3D) pavement macro-texture FE model. To evaluate the effectiveness of the established FE model, a revised sand patch method was proposed, and the correlation between the calculated mean texture depth (MTD′) and the measured MTD was analyzed. The results show that the mean relative error between MTD′ and the measured MTD is 5.97%, and the correlation coefficient R is equal to 0.9873, demonstrating that the processed point cloud data could characterize the actual pavement macro-texture precisely. Moreover, the generated pavement macro-texture FE model could be easily imported to Abaqus as well. Therefore, it could be concluded that the processing and modelling methods proposed in this study are effective for the establishment of 3D pavement macro-texture FE model.

A Depth Map Generation Method for Path Planning of Mobile Robot

Recently, the unmanned mobile robots have received broad applications, such as industrial and security inspection, disinfection and epidemic prevention, warehousing logistics, agricultural picking, etc. In order to drive autonomously from departure to destination, an unmanned mobile robot mounts different sensors to collect information around it and further understand its surrounding environment based on the perceptions. Here we proposed a method to generate high-resolution depth map for given sparse LiDAR point cloud. Our method fits the point cloud into a 3D curve and projects LiDAR data onto the curve surface, and then we make appropriate interpolations of the curve and finally implement the Delaunay triangulation algorithm to all the data points on the 3D curve. The experimental results show that our approach can effectively improve the resolution of depth maps from sparse LiDAR measurements.