Point-sampled Surface Research Articles

Generative 3D Cardiac Shape Modelling for in-silico Trials.

We propose a deep learning method to model and generate synthetic aortic shapes based on representing shapes as the zero-level set of a neural signed distance field, conditioned by a family of trainable embedding vectors with encode the geometric features of each shape. The network is trained on a dataset of aortic root meshes reconstructed from CT images by making the neural field vanish on sampled surface points and enforcing its spatial gradient to have unit norm. Empirical results show that our model can represent aortic shapes with high fidelity. Moreover, by sampling from the learned embedding vectors, we can generate novel shapes that resemble real patient anatomies, which can be used for in-silico trials.

Exploring differential geometry in neural implicits

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions.To train a neural implicit function, we propose a loss functional that approximates a signed distance function, and allows terms with high-order derivatives, such as the alignment between the principal directions of curvature, to learn more geometric details. During training, we consider a non-uniform sampling strategy based on the curvatures of the point-sampled surface to prioritize points with more geometric details. This sampling implies faster learning while preserving geometric accuracy when compared with previous approaches.We also use the analytical derivatives of a neural implicit function to estimate the differential measures of the underlying point-sampled surface.

Nanoscale morphology and fractal analysis of TiO2 coatings on ITO substrate by electrodeposition.

In this paper, we introduced an advanced discussion of the 3D morphology of TiO2 coatings deposited on ITO substrate by electrodeposition under different deposition times. Atomic force microscopy was applied for obtaining topographic images of the samples. The images were processed using the MountainsMap 8.0 commercial software according to ISO 25178-2:2012. Moreover, fractal theory was applied to study the surface microtexture of coatings. The morphology was affected by the deposition time, where the grain size decreased with the increase of the time, making film's surfaces smoother. In addition, the surface roughness exhibited a random behaviour, but does not presented significant difference between samples. The fractal dimension showed similar values for all coatings. In contrast, surface texture isotropy also exhibited random behaviour. However, advanced fractal parameters revealed that when the deposition time increased, the coatings microtexture has become uniform and less porous. Furthermore, all coatings presented high topographic uniformity, regardless of deposition time. These results revealed that the morphology and microtexture of TiO2 -based coatings can be controlled by the deposition time. LAY DESCRIPTION: An advanced characterization on the micromorphology of 3D morphology, using AFM images, of Titanium dioxide (TiO2 ) coatings deposited on ITO substrate by electrodeposition under different deposition times. TiO2 is one of the most studied semiconductors to make photovoltaic devices. The versatility of this semiconductor is associated with low toxicity, high photochemical stability, abundance, and the facility to obtain by conventional synthesis routes. The obtention of a homogeneous and stable layer in the semiconductor TiO2 film deposition is a crucial stage in the assembly of sensitized photovoltaic devices. Atomic Force Microscopy (AFM) is a technique which can magnify up to a billion times and it uses a tip or probe which touches the sample surface point by point. The tip deflection is interpreted as the surface topography by the software, producing 2D or 3D images that generate several tribological parameters such as roughness in respect to a scanned area, has been a technique widely reported in the morphological characterization, determination of thickness, roughness, and particle size in thin films. Therefore, in this paper, the morphology was studied by atomic force microscopy using MountainsMap commercial software. The main goal was to study the influence of the deposition time on the morphology and microtexture of the material. New parameters such as surface entropy, fractal succolarity and fractal lacunarity were obtained for studying coatings microtexture's complexity.

Computational fluid dynamics on 3D point set surfaces

Computational fluid dynamics (CFD) in many cases requires designing 3D models manually, which is a tedious task that requires specific skills. In this paper, we present a novel method for performing CFD directly on scanned 3D point clouds. The proposed method builds an anisotropic volumetric tetrahedral mesh adapted around a point-sampled surface, without an explicit surface reconstruction step. The surface is represented by a new extended implicit moving least squares (EIMLS) scalar representation that extends the definition of the function to the entire computational domain, which makes it possible for use in immersed boundary flow simulations. The workflow we present allows us to compute flows around point-sampled geometries automatically. It also gives a better control of the precision around the surface with a limited number of computational nodes, which is a critical issue in CFD.

Selective propagation and beam splitting of surface plasmons on metallic nanodisk chains.

Manipulating the propagation of surface plasmons (SPs) on a nanoscale is a fundamental issue of nanophotonics. By using focused electron beam, SPs can be excited with high spatial accuracy. Here we report on the propagation of SPs on a chain of gold nanodisks with cathodoluminescence (CL) spectroscopy. Experimental evidence for the propagation of SPs excited by the focused electron beam is demonstrated. The wavelength of the transmitted SPs depends on the geometrical parameters of the nanodisk chain. Furthermore, we design and fabricate a beam splitter, which selectively transmits SPs of certain wavelengths to a specific direction. By scanning the sample surface point by point and collecting the CL spectra, we obtain the spectral mapping and identify that the chain of the smaller nanodisks can efficiently transport SPs at shorter wavelengths. This Letter provides a unique approach to manipulate in-plane propagation of SPs.

Adaptive Bilateral Smoothing For a Point-Sampled Blade Surface

Optical inspection of blades is important in computer vision and manufacturing automation. One problem commonly encountered is that the scanned point cloud may be polluted by noise, mainly from the scanning equipment. How to smooth the blade surface while preserving the thin-walled feature of leading/trailing edges is a challenging task. In this paper, we propose an adaptive bilateral method for the smoothing of a point-sampled surface. This paper is motivated by a bilateral filtering technique of a two-dimensional image. The basis of the method is the application of information entropy to distinguish density difference of point cloud. By minimizing defined smoothing density entropy and preserving density entropy, the optimal surface-smoothing factor and feature-preserving factor are calculated at each vertex. Applying the obtained factors, the objective of smoothing surface while preserving thin-walled feature is achieved, which overcomes the feature shrinking/shriveling problem. Our method does not require surface triangulation or curvature computation, and is very suitable for the object of a point-sampled surface with high-curvature feature or sharp features. Its robustness and efficiency are confirmed by experiments.

A method for generating large datasets of organ geometries for radiotherapy treatment planning studies.

BackgroundWith the rapidly increasing application of adaptive radiotherapy, large datasets of organ geometries based on the patient’s anatomy are desired to support clinical application or research work, such as image segmentation, re-planning, and organ deformation analysis. Sometimes only limited datasets are available in clinical practice. In this study, we propose a new method to generate large datasets of organ geometries to be utilized in adaptive radiotherapy.MethodsGiven a training dataset of organ shapes derived from daily cone-beam CT, we align them into a common coordinate frame and select one of the training surfaces as reference surface. A statistical shape model of organs was constructed, based on the establishment of point correspondence between surfaces and non-uniform rational B-spline (NURBS) representation. A principal component analysis is performed on the sampled surface points to capture the major variation modes of each organ.ResultsA set of principal components and their respective coefficients, which represent organ surface deformation, were obtained, and a statistical analysis of the coefficients was performed. New sets of statistically equivalent coefficients can be constructed and assigned to the principal components, resulting in a larger geometry dataset for the patient’s organs.ConclusionsThese generated organ geometries are realistic and statistically representative.

A case study of blade inspection based on optical scanning method

Blades play an important role in aviation engine, gas turbine and jet engine. Inspecting the blade by optical method is a meaningful work in manufacturing industry. During optical inspecting process, one common problem encountered is that the scanned point cloud is large scale and noisy. In this paper, we present a systematic introduction of simplification, smoothing and parameter extraction with respect to point-sampled blades. First, the moving least square surface is applied to create a geometric deviation, which is used to subdivide and cluster the point cloud. Then, the information entropy in k-neighbourhood is defined to smooth point-sampled surface, meanwhile preserving high curvature feature. Furthermore, the computation method of single/multi section parameters is presented, and test experiments are performed in iCloud3D Blade V1.0. Experimental results demonstrate the feasibility and effectiveness of the proposed method.

Point-Based Manifold Harmonics

This paper proposes an algorithm to build a set of orthogonal Point-Based Manifold Harmonic Bases (PB-MHB) for spectral analysis over point-sampled manifold surfaces. To ensure that PB-MHB are orthogonal to each other, it is necessary to have symmetrizable discrete Laplace-Beltrami Operator (LBO) over the surfaces. Existing converging discrete LBO for point clouds, as proposed by Belkin et al., is not guaranteed to be symmetrizable. We build a new point-wisely discrete LBO over the point-sampled surface that is guaranteed to be symmetrizable, and prove its convergence. By solving the eigen problem related to the new operator, we define a set of orthogonal bases over the point cloud. Experiments show that the new operator is converging better than other symmetrizable discrete Laplacian operators (such as graph Laplacian) defined on point-sampled surfaces, and can provide orthogonal bases for further spectral geometric analysis and processing tasks.

Segmenting point-sampled surfaces

Extracting features from point-based representations of geometric surface models is becoming increasingly important for purposes such as model classification, matching, and exploration. In an earlier paper, we proposed a multiphase segmentation process to identify elongated features in point-sampled surface models without the explicit construction of a mesh or other surface representation. The preliminary results demonstrated the strength and potential of the segmentation process, but the resulting segmentations were still of low quality, and the segmentation process could be slow. In this paper, we describe several algorithmic improvements to overcome the shortcomings of the segmentation process. To demonstrate the improved quality of the segmentation and the superior time efficiency of the new segmentation process, we present segmentation results obtained for various point-sampled surface models. We also discuss an application of our segmentation process to extract ridge-separated features in point-sampled surfaces of CAD models.

Self-similarity based compression of point set surfaces with application to ray tracing

Many real-world, scanned surfaces contain repetitive structures, like bumps, ridges, creases, and so on. We present a compression technique that exploits self-similarity within a point-sampled surface. Our method replaces similar surface patches with an instance of a representative patch. We use a concise shape descriptor to identify and cluster similar patches. Decoding is achieved through simple instancing of the representative patches. Encoding is efficient, and can be applied to large data sets consisting of millions of points. Moreover, our technique offers random access to the compressed data, making it applicable to ray tracing, and easily allows for storing additional point attributes, like normals.

Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces

Efficient parameterization of point-sampled surfaces is a fundamental problem in the field of digital geometry processing. In order to parameterize a given point-sampled surface for minimal distance distortion, a differentials-based segmentation and parameterization approach is proposed in this paper. Our approach partitions the point-sampled geometry based on two criteria: variation of Euclidean distance between sample points, and angular difference between surface differential directions. According to the analysis of normal curvatures for some specified directions, a new projection approach is adopted to estimate the local surface differentials. Then a k-means clustering (k-MC) algorithm is used for partitioning the model into a set of charts based on the estimated local surface attributes. Finally, each chart is parameterized with a statistical method -- multidimensional scaling (MDS) approach, and the parameterization results of all charts form an atlas for compact storage.

A quasi-Monte Carlo method for computing areas of point-sampled surfaces

A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy–Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.

Feature-based decomposition of trimmed surface

A trimmed surface is usually represented by a parametric surface and a set of trimming curves. Because of the complexity in manipulating trimmed surfaces, many CAD processes and algorithms cannot be applied to trimmed surfaces directly. It is thus desirable to represent a trimmed surface by a group of regular surfaces. In this paper, an algorithm for decomposing a trimmed surface is presented. First, bisectors of the Voronoï diagram developed in the parametric space are used to define an isolated region for every trimming curve. Feature points on the trimming curves are extracted by considering curvatures of the curves. Correspondence between feature points and vertices on the bisectors are established by considering the similarity between the trimming curves and the bisectors. Regions of parametric patches are then identified. Finally, a group of regular surfaces are constructed by interpolating a set of sampled surface points on each of the identified regions.

EWA splatting

We present a framework for high quality splatting based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter, combining a reconstruction kernel with a low-pass filter. Because of the similarity to Heckbert's (1989) EWA (elliptical weighted average) filter for texture mapping, we call our technique EWA splatting. Our framework allows us to derive EWA splat primitives for volume data and for point-sampled surface data. It provides high image quality without aliasing artifacts or excessive blurring for volume data and, additionally, features anisotropic texture filtering for point-sampled surfaces. It also handles nonspherical volume kernels efficiently; hence, it is suitable for regular, rectilinear, and irregular volume datasets. Moreover, our framework introduces a novel approach to compute the footprint function, facilitating efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in rendering surface and volume data.

Effects of data point distribution and mathematical model on finding the best-fit sphere to data

Probe calibration on a coordinate measuring machine is dependent on the accuracy with which the center of a reference sphere can be located. In this article, a theoretical model for sphere is fitted to a set of sampled surface points using the least-squares criterion. An analysis is conducted of various errors involved during the steps leading to the identification of the sphere and location of its center. The errors include those associated with surface accessibility for sampling, points sampling strategies, optimization algorithm, and probe diameter versus reference sphere diameter. Inferences are drawn regarding the relative influence of these errors, and a calibration strategy is proposed as a function of sampled points, optimization algorithm, and the geometric surface involved.

On gray scale image measurements: II. Surface area and volume

We introduce methods for approximating area of a surface and volume of a region whose boundary is a closed surface where the data are taken from a 3-dimensional lattice of gray scale values. The methods require construction of unit normal vectors for the sampled surface points. The volume can be approximated by using these normal vectors in the divergence theorem from calculus. Two major advantages for this new method are that no geometric ordering of data points is required and that the algorithms are easily implemented. We compare the method to standard algorithms for measuring surface area and volume, using both artificially created data and actual data obtained from a computed tomography scanner.