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The surface O or Zn vacancy of ZnO is extremely important, so in this paper we have studied the structural and electronic properties of the ZnOO-polar surface with O vacancy and Zn-polar surface with Zn vacancy comparatively using the first-principles calculations. For the former case, the topmost oxygen atoms relax outward and the angle between Zn–O–Zn bonds in the topmost double-layer decreases to 105.01° with respect to the unrelaxed surface. However, for the latter case, the topmost zinc atoms relax inward and the angle between O–Zn–O bonds in the topmost double-layer increases to 117.61° with respect to the unrelaxed surface. Both the two reconstructed surfaces become semiconducting property in contrast to the metallic property of the unreconstructed surface. The calculated surface vacancy formation energy indicates that the surface with O vacancy is slightly more easier to be formed compared to the surface with Zn vacancy. By employing the technique of ab initio atomistic thermodynamics, we calculated the surface Gibbs free energy to determine the lowest-energy structure, indicating that the surface with O vacancy is more stable than the surface with Zn vacancy under the oxygen poor condition.

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 $\sigma$, $d_{max}$, $d_{\mathrm{\text{mean}}}$, 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.

To discount effects of uneven illumination we have designed and tested a neural network that can adaptively control light sensitivity at the photosensor level. Our neural network architecture simulates the ON channel response of the visual system using multiple layers of hexagonally arranged nodes having partially overlapping receptive fields of different spatial frequencies. Feedforward connections are excitatory while feedback pathways subserve lateral inhibition. The outputs of these nodes are combined so as to maximize the signal to noise ratio while providing constant feedback that resets photosensor thresholds to maintain high sensitivity. A sparse primitive interpolation technique was applied to the ensemble output of the sensitivity control module to determine if it sufficiently encodes surface reflectance. The motivation is to determine to what extent the ratio principle, as captured by the sensitivity control system, explains the lightness constancy phenomenon and whether information contained within an ON channel response is adequate to reconstruct the surface lightness. Our connectionist architecture can account for many characteristics attributed to the lightness constancy phenomenon observed in biological systems. The results suggest that our module maintains high sensitivity across a large range of intensities without interfering with the transmission of visual information embedded in the spatial discontinuities of intensity. However, the amplitude of the luminance derivative as encoded in ON channel responses is not sufficient to approximate surface reflectance.

The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm¹ using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming that the sample was sufficiently dense. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the first such topological guarantee for this problem.

The algorithm of Edelsbrunner for surface reconstruction by "wrapping" a set of points in ℝ³ is described.

The distance function to surfaces in three dimensions plays a key role in many geometric modeling applications such as medial axis approximations, surface reconstructions, offset computations and feature extractions among others. In many cases, the distance function induced by the surface can be approximated by the distance function induced by a discrete sample of the surface. The critical points of the distance functions are known to be closely related to the topology of the sets inducing them. However, no earlier theoretical result has found a link between topological properties of a geometric object and critical points of the distance to a discrete sample of it. We provide this link by showing that the critical points of the distance function induced by a discrete sample of a surface fall into two disjoint classes: those that lie very close to the surface and those that are near its medial axis. This closeness is precisely quantified and is shown to depend on the sampling density. It turns out that critical points near the medial axis can be used to extract topological information about the sampled surface. Based on this, we provide a new flow-complex-based surface reconstruction algorithm that, given a tight ε-sample of a surface, approximates the surface geometrically, both in distance and normals, and captures its topology. Furthermore, we show that the same algorithm can be used for curve reconstruction.

Interpolating a piecewise-linear triangulated surface between two polygons lying in parallel planes has attracted a lot of attention in the literature over the past three decades. This problem is the simplest variant of interpolation between parallel slices, which may contain multiple polygons with unrestricted geometries and/or topologies. Its solution has important applications to medical imaging, digitization of objects, geographical information systems, and more. Practically all currently-known methods for surface reconstruction from parallel slices assume a priori the existence of a non-self-intersecting triangulated surface defined over the vertices of the two polygons, which connects them. Gitlin et al. were the first to specify a nonmatable pair of polygons. In this paper we provide proof of the nonmatability of a “simpler” pair of polygons, which is less complex than the example given by Gitlin et al. Furthermore, we provide a family of polygon pairs with unbounded complexity, which we believe to be nonmatable. We also give a few sufficient conditions for polygon matability.

Many algorithms for applications such as pattern recognition, computer vision, and computer graphics seek to compute actual optimal paths in weighted directed graphs. The standard approach for reporting an actual optimal path is based on building a single-source optimal path tree. A technique by Chen et al.² was given for a class of problems such that a single actual optimal path can be reported without maintaining any single-source optimal path tree, thus significantly reducing the space bound of those problems with no or little increase in their running time. In this paper, we extend the technique by Chen et al.² to the generalized problem of reporting many actual optimal paths with different starting and ending vertices in certain directed graphs, and show how this new technique yields improved results on several application problems, such as reconstructing a 3-D surface band bounded by two simple closed curves, finding various constrained segmentation of 2-D medical images, and circular string-to-string correction. We also correct an error in the time/space complexity for the well-cited circular string-to-string correction algorithm¹² and give an improved result for this problem. Although the generalized many-path problem seems more difficult than the single-path cases, our algorithms have nearly the same space and time bounds as those of the single-path cases. Our technique is likely to help improve many other optimal paths or dynamic programming algorithms.

This paper presents a new method for reconstructing piecewise linear surfaces from planar polygonal contours that branch. For non-branching contours, experience has shown that the piecewise linear surface of minimum surface area which connects a pair of contours often provides a good solution. The current algorithm extends this idea by searching for the surface of minimal area which connects two contours comprised of more than one polygon. Several examples that justify this heuristic are provided.

Transient CO₂ formation has been studied under "quasi-steady-state" measuring conditions by means of surface titrations. By this method the reactivity of the surface could be sampled as a function of time, thereby following the formation of the surface reconstruction induced by oxygen. The reactivity of the surface towards CO oxidation was reduced in the course of the developing surface reconstruction. A possible influence of subsurface oxygen on the CO₂ formation rates can be excluded.

Based on the Density Functional Theory (DFT) with noncollinear-magnetism formulations, we have calculated the magnetism of single 3d transition-metal atoms and the magnetic anisotropies of supported Ni chains on the Au(110)-(1 × 2) surface. Our results for single absorbed 3d transition-metal atoms show that the surface relaxations enhance the orbital moments of left-end elements (Ti, V) and quenches the orbital moments of right-end elements (Fe, Co, Ni) on the Au(110)-(1 × 2) surface. The magnetic anisotropies of Ni atomic chains on the surface are closely related to orbital quenching. The easy magnetized axes change from the direction parallel to the chains to the direction perpendicular to the Ni chains when they absorb on the surface.

This paper describes a new and fast method for reconstructing a 3D computerized model from a cloud of points sampled from the object's surface. The proposed method aggregates very large scale 3D scanning data into a Hierarchical Space Decomposition Model (HSDM), realized by the Octree data structure. This model can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the boundary reconstruction process becomes more robust and stable with respect to sampling noise. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving critical geometrical features and object topology. As a result of data reduction, the execution time of the reconstruction process is significantly reduced. Moreover, the proposed model naturally allows multiresolution boundary extraction, represented by a mesh with regular properties.

The proposed surface reconstruction approach is based on Connectivity Graph extraction from HSDM, and facet reconstruction. This method's feasibility will be presented on a number of complex objects.

The topic of interpolation between slices has been an intriguing problem for many years, as it offers means to visualize and investigate a three-dimensional object given only by its level sets. A slice consists of multiple non-intersecting simple contours, each defined by a cyclic list of vertices. An interpolation solution matches between a number of such slices (two or more at a time), providing means to create a closed surface connecting these slices, or the equivalent morph from one slice to another.

We offer a method to incorporate the influence of more than two slices at each point in the reconstructed surface. We investigate the flow of the surface from one slice to the next by matching vertices and extracting differential geometric quantities from that matching. Interpolating these quantities with surface patches then allows a nonlinear reconstruction which produces a free-form, non-intersecting surface. No assumptions are made about the input, such as on the number of contours in each slice, their geometric similarity, their nesting hierarchy, etc., and the proposed algorithm handles automatically all branching and hierarchical structures. The resulting surface is smooth and does not require further subdivision measures.

In a research context in which multiple and well-behaved Surface Reconstruction algorithms already exist, the main goal is not to implement a visualization toolkit able render complex object, but the implementation of methods which can improve our knowledge on the observed world. This work presents a general Surface Reconstruction framework which encapsulates the uncertainty of the sampled data, making no assumption on the shape of the surface to be reconstructed. Starting from the input points (either points clouds or multiple range images), an Estimated Existence Function (EEF) is built which models the space in which the desired surface could exist and, by the extraction of EEF critical points, the surface is reconstructed. The final goal is the development of a generic framework that is able to adapt the result to different kinds of additional information coming that is from multiple sensors.

We have studied the correlation between film structures and the azimuthal dependence of the magnetization reversal in (001) and (111) Ni films grown on MgO substrates using molecular beam epitaxy (MBE). For as-grown (001) Ni films, the coercive field exhibits four-fold azimuthal symmetry while in-situ annealed films exhibit additional uniaxial anisotropy. In-situ STM images show surface stripe nanopatterning on the annealed films, which is absent in the as-grown ones. Cross sectional TEM seems to indicate the presence of a highly ordered interfacial layer that we postulate may be fccNiO. Tetragonal distortion of this layer upon annealing may have induced the uniaxial anisotropy observed in the magnetic properties. Polarized neutron reflectivity measurements performed on some of the films are correlated with the interfacial surface structure and the magnetic anisotropy.

Many living organisms grow crystalline inorganic components (usually to add mechanical strength, but also for sensing and other applications). These organisms exert a high degree of control not just over the crystal orientation but also over the structure and composition of the crystals. They do this in wet environments, without the use of ultrahigh vacuum. There have been efforts to mimic this process in the laboratory by growing minerals under floating (Langmuir) monolayers, which serve as ordered organic templates. We have studied such processes using grazing-incidence X-ray diffraction to determine the structure of both organic and inorganic films during deposition. These studies illustrate that some of the same phenomena familiar to surface scientists working in UHV occur also in "real world" environments.

This paper improves the algorithm of point cloud filtering and registration in 3D modeling, aiming for smaller sampling error and shorter processing time of point cloud data. Based on collaborative sampling among several Kinect devices, we analyze the deficiency of current filtering algorithm, and use a novel method of point cloud filtering. Meanwhile, we use Fast Point Feature Histogram (FPFH) algorithm for feature extraction and point cloud registration. Compared with the aligning process using Point Feature Histograms (PFH), it only takes 9min when the number of points is about 500,000, shortening the aligning time by 47.1%. To measure the accuracy of the registration, we propose an algorithm which calculates the average distance of the corresponding coincident parts of two point clouds, and we improve the accuracy to an average distance of 0.7mm. In the surface reconstruction section, we adopt Ball Pivoting algorithm for surface reconstruction, obtaining image with higher accuracy in a shorter time.

In this paper, we propose a new approach for learning shape implicit neural representations (INRs) from point cloud data that do not require normal vectors as input. We show that our method, which uses a soft constraint on the divergence of the distance function to the shape’s surface, can produce smooth solutions that accurately orient gradients to match the unknown normal at each point, even outperforming methods that use normal vectors directly. This work extends the latest work on divergence-guided sinusoidal activation INRs [Y. Ben-Shabat, C. H. Koneputugodage and S. Gould, Proc IEEE/CVF Conf Computer Vision and Pattern Recognition, 2022, pp. 19323–19332], to Gaussian activation INRs and provides extended theoretical analysis and results. We evaluate our approach on tasks related to surface reconstruction and shape space learning.

To discount effects of uneven illumination we have designed and tested a neural network that can adaptively control light sensitivity at the photosensor level. Our neural network architecture simulates the ON channel response of the visual system using multiple layers of hexagonally arranged nodes having partially overlapping receptive fields of different spatial frequencies. Feedforward connections are excitatory while feedback pathways subserve lateral inhibition. The outputs of these nodes are combined so as to maximize the signal to noise ratio while providing constant feedback that resets photosensor thresholds to maintain high sensitivity. A sparse primitive interpolation technique was applied to the ensemble output of the sensitivity control module to determine if it sufficiently encodes surface reflectance. The motivation is to determine to what extent the ratio principle, as captured by the sensitivity control system, explains the lightness constancy phenomenon and whether information contained within an ON channel response is adequate to reconstruct the surface lightness. Our connectionist architecture can account for many characteristics attributed to the lightness constancy phenomenon observed in biological systems. The results suggest that our module maintains high sensitivity across a large range of intensities without interfering with the transmission of visual information embedded in the spatial discontinuities of intensity. However, the amplitude of the luminance derivative as encoded in ON channel responses is not sufficient to approximate surface reflectance.

Texture parameters computation on freeform surfaces is becoming an important topic in surface characterization. Triangular meshes are used to describe a measured freeform surface. This reconstruction method linearly interpolates three points, to better approximate the surface triangular Bézier patches are used. A method to compute areal texture parameters is proposed. Based on numerical experiments the degree of the function approximating the surface and the number of quadrature points required to compute parameters values are investigated.