Surface Reconstruction Method Research Articles

Implicit Randomized Progressive-Iterative Approximation for Curve and Surface Reconstruction

In this paper, we propose the implicit randomized progressive-iterative approximation (IR-PIA) method for curve and surface reconstruction. By introducing the effective probability criterion, the IR-PIA method selects the working elements of the collocation matrix to adjust the control coefficients. It is proved that the sequence of curves and surfaces generated by the control coefficients converge to the least-norm results in expectation. The IR-PIA method reduces the computation complexity and speeds up the curve and surface reconstruction compared with the implicit progressive-iterative approximation (I-PIA) method (Hamza et al., 2020). Numerical examples show that the IR-PIA method can be more efficient than the I-PIA method (Hamza et al., 2020). • The IR-PIA method converge to the least-norm solution in expectation. • The IR-PIA method eliminates the extra zero-level sheets effectively. • The working elements are selected to update the control coefficients. • The larger entries of the difference vectors can be annihilated as far as possible.

Restricted Delaunay Triangulation for Explicit Surface Reconstruction

The task of explicit surface reconstruction is to generate a surface mesh by interpolating a given point cloud. Explicit surface reconstruction is necessary when the point cloud is required to appear exactly on the surface. However, for a non-perfect input, such as lack of normals, low density, irregular distribution, thin and tiny parts, and high genus, a robust explicit reconstruction method that can generate a high-quality manifold triangulation is missing. We propose a robust explicit surface reconstruction method that starts from an initial simple surface mesh, alternately performs a Filmsticking step and a Sculpting step of the initial mesh, and converges when the surface mesh interpolates all input points (except outliers) and remains stable. The Filmsticking is to minimize the geometric distance between the surface mesh and the point cloud through iteratively performing a restricted Voronoi diagram technique on the surface mesh, whereas the Sculpting is to bootstrap the Filmsticking iteration from local minima by applying appropriate geometric and topological changes of the surface mesh. Our algorithm is fully automatic and produces high-quality surface meshes for non-perfect inputs that are typically considered to be challenging for prior state of the art. We conducted extensive experiments on simulated scans and real scans to validate the effectiveness of our approach.

A Generative Adversarial Network for Pixel-Scale Lunar DEM Generation from High-Resolution Monocular Imagery and Low-Resolution DEM

Digital elevation models (DEMs) provide fundamental data for scientific and engineering applications in lunar exploration missions. Lunar DEMs have been mainly generated by laser altimetry and stereophotogrammetry. Complementarity to stereo photogrammetry, reflection-based surface reconstruction methods, such as shape from shading (SFS), have been studied and applied in lunar DEM reconstruction from a single image. However, this method often suffers from solution ambiguity and instability. In this paper, we propose a generative adversarial network (GAN)-based method that is able to generate high-resolution pixel-scale DEMs from a single image aided by a low-resolution DEM. We have evaluated the accuracy of the reconstructed high-resolution DEMs from 25 LROC NAC images of four regions using LROC NAC DEMs (2 m/pixel) as ground truth. The experimental results demonstrate good accuracy and adaptability to changes in illumination conditions. The root mean square error (RMSE) can reach about 2 m in areas where the degree of elevation variation is less than 100 m, and the RMSE value ranges from around 3 m to 10 m without considering the degree of the elevation variation in large-area reconstruction. As high-resolution monocular images and low-resolution DEMs are available for the entire lunar surface, the proposed GAN-based method has great potential in high-resolution lunar DEM reconstruction for lunar mapping applications.

Enhanced GPIS Learning Based on Local and Global Focus Areas

Implicit surface learning is one of the most widely used methods for 3D surface reconstruction from raw point cloud data. Current approaches employ deep neural networks or Gaussian process models with the trade-offs across computational performance, object fidelity, and generalization capabilities. We propose a novel method based on Gaussian process regression to build implicit surfaces for 3D surface reconstruction (GPIS), which leads to better accuracy in comparison to the standard GPIS formulation. Our approach encodes local and global shape information from the data to maintain the correct topology of the underlying shape. The proposed pipeline works on dense, sparse, and noisy raw point clouds and can be parallelized to improve computational efficiency. We evaluate our approach on synthetic and real point cloud datasets including data from robot visual and tactile sensors. Results show that our approach leads to high accuracy compared to baselines.

Surface reconstruction algorithm using a modified Allen–Cahn equation

In this paper, we propose a novel efficient surface reconstruction method from unorganized point cloud data in three-dimensional Euclidean space. The proposed method is based on the Allen–Cahn partial differential equation, with an edge indicating function to restrict the evolution. We applied the explicit Euler’s method to solve the discrete equation, and use the operator splitting technique to split the governing equation. Furthermore, we also modify the double well form to a periodic potential. Then we find that the proposed model can reconstruct the surface well even in the case of insufficient data. After selecting the appropriate parameters, we carried out various numerical experiments to demonstrate the robustness and accuracy of the proposed method. We adopt the proposed method to reconstruct the surfaces on simple, irregular and complex models, respectively, and can obtain smooth three-dimensional surfaces and visual effects. In addition, we also perform comparison tests to show the superiority of the proposed model. Statistic metrics such as the [Formula: see text], [Formula: see text], [Formula: see text], CPU time, and vertex numbers are evaluated. Results show that our model performs better than the other methods in statistical metrics even use far less point cloud data, and with the faster CPU computing speed.

Topology-controllable Implicit Surface Reconstruction Based on Persistent Homology

In geometric design, reconstructing an implicit surface with high-quality geometry and expected topology from point clouds has been a challenging problem. However, traditional topological invariants, such as Betti numbers, are not easily used in controlling topology in implicit surface reconstruction. Persistent homology provides a quantitative measurement, i.e. , persistence diagram (PD), and allows tracking of pairs of key points that generate and destroy topological holes. In this study, we propose a topology-controllable implicit surface reconstruction method from point clouds based on persistent homology. Specifically, given a point cloud with normals, the signed distance field is first constructed, and then a B-spline function represented distance function is generated by fitting the signed distance values through progressive iterative approximation. By designing a topological target function using the persistent pairs in PDs according to topological priors, the control coefficients of the B-spline function are optimized to extract an implicit surface, i.e. , an iso-surface of the B-spline function, with expected topology. Experiments show that the proposed method can reconstruct surfaces with higher topological quality than other reconstruction methods. Moreover, the proposed method can be used to edit the topology of an implicit surface. • The topology-controllable framework for implicit B-spline surface reconstruction improves geometric quality and ensures the desired topology of the extracted surface. • Principles of designing the topological target function for implicit surface reconstruction are proposed. • Reconstruction on sparse point clouds and the application of topology editing are explored.

Connectivity-aware Graph: A planar topology for 3D building surface reconstruction

Multi-view Stereo (MVS) meshes suffer from occlusions or missing data, making most surface reconstruction methods invalid. Due to data imperfections, existing methods, just like PolyFit, have made a trade-off between reconstruction accuracy and time consumption. We propose a novel approach that automatically reconstructs a building surface model from raw triangular mesh with data incompleteness. Unlike existing methods that extract high-quality primitives, our method focuses on assemblies of primitives to control the level of geometric detail in the reconstructed models. We design a topological relationship of the primitives to form a plane connection graph. To be precise, we first combine the scalability of shapes with plane primitives. Then strong and soft connections between primitives are constructed by calculating the confidence of the plane intersection in space. Furthermore, the topological relations of all primitives are encoded into an undirected graph. Finally, a watertight and manifold model is extracted from the faces of a candidate set by energy minimization. Experiments on the Helsinki 3D dataset demonstrate the superiority of our method in time consumption and reconstruction error, as measured by Hausdorff distance. Our method outperforms other primitive-based algorithms in handling non-planar structures. Even when dealing with imperfect data, a watertight model is still obtained.

PDE-based surface reconstruction in automotive styling design

Surface reconstruction is an important part in automotive styling design. Existing reconstruction methods mainly rely on the proficiency of digital modelers who manually modify the surface shape to approximate the scanned data. Apart from manual modifications, the reconstructed surfaces cannot well reflect the design intent of designers since the feature curves of clay models have not been preserved accurately. In this paper, we propose a partial differential equation (PDE) based surface reconstruction method to analytically generate optimal surfaces with Cn continuity under the constraint of the feature curves. The proposed method accurately preserves automotive feature curves and achieves automatic reconstruction of Class-A surfaces without time-consuming manual work. The effectiveness of the proposed method is demonstrated by a number of experiments that reconstruct main parts of automotive exteriors.

Co-gradient Li-rich cathode relieving the capacity decay in Lithium-ion batteries

Lithium-rich layered oxides (LLOs) are one of the promising cathode materials for next generation energy storage devices, but structural degradation and severe capacity decay during cycling have hindered applications. Here, we find cobalt effectively mitigate structural degradation and develop a simple and novel metal organic framework (MOF) treatment and surface reconstruction method to fabricate Co gradient layer on LLOs. In situ and ex situ microstructural studies show the capacity decay is mainly originated from the formation of microstructural defects such as voids and pores, continuous oxygen release and formation of spinel and rock-salt structure initiated from the surface. The reconstruction leads to the formation of an artificial layer of Co rich and Li poor spinel (Co3O4) and rock-salt (CoO) structure on surface, suppressing the diffusion of cations and O−1/O−2 anions toward the surface during cycling. The LLO-Co cathode exhibits enhanced cycling stability with a capacity retention of 94.4% at 0.2 C after 100 cycles and a high capacity of 183 mAh g−1 at 1 C, in comparison with those of untreated LLO (80.5% and 153 mAh g−1). This work sheds lights on better utilize rare Co resource in the development of high capacity and cyclability cathode materials for lithium-ion batteries.

An improved FFT method for shot peening surface reconstruction

Shot peening is the efficient method for metal surface modification and performance improvement. However, there is still no effective way to establishing the mathematical model for shot peening surface reconstruction, resulting in restricting the correlation study between shot peening surface properties and morphology. The difficulty of shot peening surface reconstruction lies in how to accurately characterize the roughness surface height and texture features. Therefore, a novel method of generating non-Gaussian sequences with specified height roughness parameters is proposed in this paper. Fast Fourier transform (FFT) method gets improved combined with the new method, which overcome the predicament that the unimproved FFT cannot ensure the height features in the reconstructed shot peening surfaces. In addition, a new autocorrelation function in shot peening surfaces is proposed to accurately characterize the reconstructed surface texture. The experimental results show that with the improved FFT method and the new autocorrelation function introduced to shot peening surface reconstruction, the maximum error of the seven height roughness parameters in the reconstructed surface is 2.201%. And the texture features and height distribution of the reconstructed surface are in good agreement with the measured surface.

Terrestrial Laser Scanning to Assess Eucalyptus Aboveground Biomass: A Surface Reconstruction Approach

Terrestrial laser scanners (TLS) provide an alternative to traditional field sampling for gathering accurate volumetric data about vegetations without destroying the tree samples. However, popular volumetric modeling approaches (e.g., those cylindrical methods) oversimplify vegetation structure by underutilizing surface undulations provided by the point cloud. Thus, this study aimed to test the capability of two specialized surface reconstruction methods against a traditional cylindrical method to obtain the stem volumes and masses from 3D-cloud points generated by terrestrial laser scanners under relatively controlled conditions in a eucalyptus plantation in Muang, Nakornratchasima Province, Thailand. The TLS point data were collected from the test plots, and then three algorithms, the Poisson Surface Reconstruction (PSR), the Screen Poisson Surface Reconstruction (SPSR), and the traditional Quantitative Structure Model (QSM) were applied in order to build volumetric models of the sample eucalyptus trees. It is notable that this is the first study to test the SPSR method on real tree samples (N=40). The results were then compared with the reference values measured by a water replacement method. The root means square errors (RMSE) were estimated between the xylometric referenced aboveground biomass (AGB) and the TLS three methods. The SPSR approach yielded the most accurate results (RMSE of 0.49 kg or 6.91%), while the PSR method resulted in an RMSE of 0.60 kg (8.37%). The QSM method had the worst results, with an RMSE of 1.09 kg (15.31%). Despite the occlusion problem that caused 20% systematic error, this outcome provides evidence that the use of two Poisson reconstruction methods (e.g., PSR and SPSR) provides effective alternatives to accurately quantify aboveground biomass for eucalyptus trees.

Electrochemically Activated Surface Reconstruction of PdCu Nanotubes for Improved Ethanol Oxidation Electrocatalysis

Boosting the stability of anodic electrocatalysts is of prominent importance for direct ethanol fuel cells. Precise control of the surface structure at the atomic level can effectively tune the electrocatalytic performance of materials. Here, an in situ electrochemical post‐treatment technique to rebuild a highly crystalline and stable multilayered Pd‐skin structure on Pd47Cu53 nanotubes (NTs) via dealloying and atomic rearrangement is reported. The structural and compositional evolution of Pd47Cu53 NTs is tracked through the whole post‐treatment process, involving sequential cyclic voltammetry (CV) and potentiostatic chronoamperometry (PC) treatments. The post‐treated Pd47Cu53 NTs not only preserve the original tubular structure of the pristine materials, as‐prepared Pd47Cu53 NTs, but also extensively improve the crystallinity of discrete nanoparticles (NPs) along the NTs. By comparing their catalytic performance toward ethanol oxidation reaction (EOR), the construction of a multilayered Pd‐skin surface is capable of greatly enhancing the catalytic stability of Pd47Cu53 NTs. Such in situ electrochemical processing features and significant stabilization effects show a bright future of being a universal surface reconstruction method for alloy electrocatalysts.

Free-form surface form error evaluation based on smaller-scale sampling points in touch-trigger probing

Surface reconstruction is an essential operation in the evaluation of free-form surface form error. As a feasible technology in free-form surface sampling, touch-trigger probing has been widely used in on-machine measurement and coordinate measurement machine. However, surface reconstruction quality is influenced by limited sampling point size. This study proposes a surface reconstruction method based on surface position error and deformation error model. Surface form error is decomposed into surface position error and deformation error. Then, the design surface is taken as a rigid body, and a point-to-surface function-based iterative algorithm is conducted to adjust surface location and orientation to best match the sampling points. The advantage of this algorithm is that it considers the probe dimension, so further compensation of probe radius is not required. The geometry of the adjusted design surface is modified based on thin plate energy minimization and point-to-surface function. Due to the inherent feature of the proposed method, geometric features of the design surface are kept. Experiments are conducted to verify the effectiveness of the proposed method, and results show that the proposed method can achieve lower error compared with existing methods.

Adjusting videoendoscopic 3D reconstruction results using tomographic data

Videoendoscopic and tomographic research are the two leading medical imaging solutions for detecting, classifying and characterizing a wide array of pathologies and conditions. However, source information from these types of research is very different, making it hard to cross-correlate them. The paper proposes a novel algorithm for combining results of based on 3D surface reconstruction methods. This approach allows to align separate parts of two input 3D surfaces: surface obtained by applying bundle adjustment-based 3D surface reconstruction algorithm to the endoscopic video sequence, and surface reconstructed directly from separate tomographic cross-section slice projections with regular density. Proposed alignment method is based on using local feature extractor and descriptor algorithms by applying them to the source surface normal maps. This alignment allows both surfaces to be equalized and normalized relative to each other. Results show that such an adjustment allows to reduce noise, correct reconstruction artifacts and errors, increase representative quality of the resulting model and establish correctness of the reconstruction for hyperparameter tuning.

3D Printed hair modeling from strand-level hairstyles

Recent advances in the design and fabrication of personalized figurines have made the creation of high-quality figurines possible for ordinary users with the facilities of 3D printing techniques. The hair plays an important role in gaining the realism of the figurines. Existing hair reconstruction methods suffer from the high demand for acquisition equipment, or the result is approximated very coarsely. Instead of creating hairs for figurines by scanning devices, we present a novel surface reconstruction method to generate a 3D printable hair model with geometric features from a strand-level hairstyle, thus converting the exiting digital hair database to a 3D printable database. Given a strand-level hair model, we filter the strands via bundle clustering, retain the main features, and reconstruct hair strands in two stages. First, our algorithm is the key to extracting the hair contour surface according to the structure of strands and calculating the normal for each vertex. Next, a close, manifold triangle mesh with geometric details and an embedded direction field is achieved with the Poisson surface reconstruction. We obtain closed-manifold hairstyles without user interactions, benefiting personalized figurine fabrication. We verify the feasibility of our method by exhibiting a wide range of examples.

Surface reconstruction method for measurement data with outlier detection by using improved RANSAC and correction parameter

The moving least squares (MLS) and moving total least squares (MTLS) are two of the most popular methods used for reconstructing measurement data, on account of their good local approximation accuracy. However, their reconstruction accuracy and robustness will be greatly reduced when there are outliers in measurement data. This article proposes an improved MTLS method (IMTLS), which introduces an improved random sample consensus (RANSAC) algorithm and a correction parameter in the support domain, to deal with the outliers and random errors. Based on the nodes within the support domain, firstly the improved RANSAC is used to generate a model for establishing the group of pre-interpolation and calculating the residual of each node. Subsequently, the abnormal degree of the node with the largest residual is evaluated by the correction parameter associated with the node residual and random errors. The node with certain abnormal degree will be eliminated and the remaining nodes are used to obtain the approximation coefficients. The correction parameter can be used for data reconstruction without insufficient or excessive elimination. The results of numerical simulation and measurement experiment show that the reconstruction accuracy and robustness of the IMTLS method is superior to the MLS and MTLS method.

Efficient Lightweight Surface Reconstruction Method from Rock-Mass Point Clouds

As for rock numerical calculation and stability analysis, it is essential to build a numerical model of rock mass with concise and accurate structure information through the three-dimensional surface reconstruction of rock-mass point clouds. However, the current research on lightweight surface reconstruction of non-artificial objects is very limited. In this paper, an efficient lightweight surface reconstruction method for rock-mass point clouds is proposed. Firstly, the input point cloud is segmented to obtain the plane primitives. In this process, the recognition of texture information and the complete over-segmentation of effective information play a vital role in the high-precision segmentation of rock surfaces. Secondly, the boundaries of all planes are reorganized according to the obvious connectivity in the segmentation results, so as to realize the assembly of the model, while solving all collision problems. Finally, an integer programming model is constructed to screen the best closure scheme of each plane, thus ensuring the best outcome of the reconstruction. In this study, seven groups of natural rock-mass point clouds are used to validate the proposed method. As suggested by the experimental results, this algorithm is effective in compressing the point cloud data of rock mass, to generate a watertight numerical model that can be directly used for simulation calculation. In addition, this method has strong robustness to noise and can effectively deal with highly corrupted rock-mass point cloud data.

A Two-Step Surface Reconstruction Method Using Signed Marching Cubes

In this paper, we explore a new approach, a two-step surface reconstruction method to extract the target isosurface from a given implicit function efficiently. Our main contribution is that we improve the surface reconstruction process by accelerating the speed of evaluation using signed marching cubes. The basic strategy is to filter the invalid voxels that do not intersect with the target isosurface in a low-cost manner, and to evaluate the valid voxels that intersect with the target isosurface accurately. The improved signed marching cubes method consists of a rough evaluation step and an exact evaluation step. The coarse evaluation step evaluates the points of all voxels using the fast multipole method with a lower order. After the rough evaluation step, the voxels that intersect with the target isosurface are screened out. Then, the exact evaluation step evaluates the points of filtered voxels using the fast multipole method with a higher order. The experimental results show that, compared with the traditional marching cubes method, the improved reconstruction method reduces the amounts of calculation for invalid voxels that do not intersect with the target isosurfaces, which is useful to improve the efficiency of surface reconstruction.

A Novel Learning Based Non-Lambertian Photometric Stereo Method for Pixel-Level Normal Reconstruction of Polished Surfaces

High-quality reconstruction of polished surfaces is a promising yet challenging task in the industrial field. Due to its extreme reflective properties, state-of-the-art methods have not achieved a satisfying trade-off between retaining texture and removing the effects of specular outliers. In this paper, we propose a learning based pixel-level photometric stereo method to estimate the surface normal. A feature fusion convolutional neural network is used to extract the features from the normal map solved by the least square method and from the original images respectively, and combine them to regress the normal map. The proposed network outperforms the state-of-the-art methods on the DiLiGenT benchmark dataset. Meanwhile, we use the polished rail welding surface to verify the generalization of our method. To fit the complex geometry of the rails, we design a flexible photometric stereo information collection hardware with multi-angle lights and multi-view cameras, which can collect the light and shade information of the rail surface for photometric stereo. The experimental results indicate that the proposed method is able to reconstruct the normal of the polished surface at the pixel level with abundant texture information.

High-Throughput Legume Seed Phenotyping Using a Handheld 3D Laser Scanner

High-throughput phenotyping involves many samples and diverse trait types. For the goal of automatic measurement and batch data processing, a novel method for high-throughput legume seed phenotyping is proposed. A pipeline of automatic data acquisition and processing, including point cloud acquisition, single-seed extraction, pose normalization, three-dimensional (3D) reconstruction, and trait estimation, is proposed. First, a handheld laser scanner is used to obtain the legume seed point clouds in batches. Second, a combined segmentation method using the RANSAC method, the Euclidean segmentation method, and the dimensionality of the features is proposed to conduct single-seed extraction. Third, a coordinate rotation method based on PCA and the table normal is proposed to conduct pose normalization. Fourth, a fast symmetry-based 3D reconstruction method is built to reconstruct a 3D model of the single seed, and the Poisson surface reconstruction method is used for surface reconstruction. Finally, 34 traits, including 11 morphological traits, 11 scale factors, and 12 shape factors, are automatically calculated. A total of 2500 samples of five kinds of legume seeds are measured. Experimental results show that the average accuracies of scanning and segmentation are 99.52% and 100%, respectively. The overall average reconstruction error is 0.014 mm. The average morphological trait measurement accuracy is submillimeter, and the average relative percentage error is within 3%. The proposed method provides a feasible method of batch data acquisition and processing, which will facilitate the automation in high-throughput legume seed phenotyping.