Anisotropic nonlinear diffusion in flow visualization

In this paper, we present a new greedy algorithm for surface reconstruction from unorganized point sets. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first and in such a way as to prevent the appearance of topological singularities. The output is thus guaranteed to be a piecewise linear orientable manifold, possibly with boundary. Experiments show that this method is very fast and achieves topologically correct reconstruction in most cases. Moreover, it can handle surfaces with complex topology, boundaries, and nonuniform sampling.

Reconstructing an unknown curve or surface from sample points is an important task in geometric modeling applications. Sample points obtained from real applications are usually noisy. For example, when data sets are obtained by scanning images in the plane or images in three dimensions. In computer graphics, many curve and surface reconstruction algorithms have been developed. However, their common drawback is the lack of theoretical guarantees on the quality of the reconstruction. This motivates computational geometers to propose algorithms that return provably faithful reconstructions. Algorithms of this type are known when there is no noise in the input. This leaves the problem of noise handling open. We propose a probabilistic noise model for the curve reconstruction problem. Based on this model, we design a curve reconstruction algorithm for noisy input points. The reconstruction is faithful with probability approaching 1 as the sampling density increases. Then we extend our approach to surface reconstruction from noisy input points. Not only do we improve the algorithm to make it run faster, we also make the noise model deterministic which extends its applicability and simplifies the analysis of the algorithm. We show that the surface reconstructed is faithful if the input points satisfy the deterministic noise model.

The existing surface reconstruction algorithms currently reconstruct large amounts of mesh data. Consequently, many of these algorithms cannot meet the efficiency requirements of real-time data transmission in a web environment. This paper proposes a lightweight surface reconstruction method for online 3D scanned point cloud data oriented toward 3D printing. The proposed online lightweight surface reconstruction algorithm is composed of a point cloud update algorithm (PCU), a rapid iterative closest point algorithm (RICP), and an improved Poisson surface reconstruction algorithm (IPSR). The generated lightweight point cloud data are pretreated using an updating and rapid registration method. The Poisson surface reconstruction is also accomplished by a pretreatment to recompute the point cloud normal vectors; this approach is based on a least squares method, and the postprocessing of the PDE patch generation was based on biharmonic-like fourth-order PDEs, which effectively reduces the amount of reconstructed mesh data and improves the efficiency of the algorithm. This method was verified using an online personalized customization system that was developed with WebGL and oriented toward 3D printing. The experimental results indicate that this method can generate a lightweight 3D scanning mesh rapidly and efficiently in a web environment.

On the basis of the analysis of the existing reconstruction methods' limitations,a fast neural network based algorithm for 3D surface reconstruction from cloud data was presented.Firstly,a unitary processing for the cloud data was made.And then the contour lines were extracted and the surface based contour lines were segmented.The method can directly from the neural network value matrix get the right curve control points or surface control mesh,and through neural network values restriction achieve the right curve or patch of smooth connection.Experimental results show that this method can quickly obtain good shape Mesh.

Bitmask drawing is still the established standard for manual annotation of brain structures by experts. To alleviate problems such as bitmask inconsistencies between slices that lead to jagged contours in corresponding orthogonal cross-sections, we propose a 2-D spline-based contour editing tool in combination with a new algorithm for surface reconstruction from 3-D point clouds. This approach uses a new implicit surface formulation that adapts to the local density of points. We show that manual segmentation of the brainstem, cerebellum, corpus callosum, caudate, putamen, hippocampus and thalamus can be performed with high reproducibility in Magnetic Resonance (MR) data and sufficient accuracy to analyze volume changes for mild Traumatic Brain Injury (TBI) patients. In addition, we show that the new surface reconstruction method allows to reconstruct the shape of brain structures such as the brainstem better than other established surface reconstruction approaches. Our tool can, therefore, not only be used for volume measurements, but may also be used to assess local shape changes of brain structures going along with the progression of neuro-degenerative diseases such as TBI.Keywordsneuro segmentationmanual tracingsurface recovery

With the continuous improvement of living standards in modern society, the demand for refined 3D object representation models has grown considerably.Concurrently, the diversification of methods for acquiring 3D point clouds has significantly enhanced our ability to digitally express the surrounding environment.Consequently, the efficient and straightforward generation of high-precision 3D mesh models from point clouds has become particularly vital.As a typical production method for 3D mesh models, point cloud surface reconstruction technology has gained widespread application across various industries owing to its convenience and efficiency.Therefore, in this paper, we propose a distance-constrained scale-space surface reconstruction algorithm, which utilizes the neighborhood distances of point clouds to constrain the anomalous triangular mesh generated by the scale-space reconstruction algorithm, thereby enabling the more precise and efficient surface reconstruction of point clouds.Initially, the raw point set obtained from 3D laser scanning undergoes preprocessing, followed by point cloud reconstruction and mesh construction using the distance-constrained scale-space algorithm.Finally, the constructed mesh is back-projected onto the original point set, resulting in a more refined 3D model.Experiments conducted on the urban underground tunnel dataset successfully reconstructed the surface model of the tunnels, validating the effectiveness of the proposed method and enhancing the visual quality of the model.

Surface reconstruction is a foundational topic in computer graphics and has gained substantial research interest in recent years. With the emergence of advanced neural radiance fields (NeRFs) and 3D Gaussian splatting (3D GS), numerous innovative many novel algorithms for 3D model surface reconstruction have been developed. The rapid expansion of this field presents challenges in tracking ongoing advancements. This survey aims to present core methodologies for the surface reconstruction of 3D models and establish a structured roadmap that encompasses 3D representations, reconstruction methods, datasets, and related applications. Specifically, we introduce 3D representations using 3D Gaussians as the central framework. Additionally, we provide a comprehensive overview of the rapidly evolving surface reconstruction methods based on 3D Gaussian splatting. We categorize the primary phases of surface reconstruction algorithms for 3D models into scene representation, Gaussian optimization, and surface structure extraction. Finally, we review the available datasets, applications, and challenges and suggest potential future research directions in this domain. Through this survey, we aim to provide valuable resources that support and inspire researchers in the field, fostering advancements in 3D reconstruction technologies.

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

This work introduces a new algorithm for surface reconstruction in ℝ3 from spatially arranged one-dimensional cross sections embedded in ℝ3. This is generally the case with acoustic signals that pierce an object non-destructively. Continuous deformations (homotopies) that smoothly reconstruct information between any pair of successive cross sections are derived. The zero level set of the resulting homotopy field generates the desired surface. Four types of homotopies are suggested that are well suited to generate a smooth surface. We also provide derivation of necessary higher order homotopies that can generate a C 2 surface. An algorithm to generate surface from acoustic sonar signals is presented with results. Reconstruction accuracies of the homotopies are compared by means of simulations performed on basic geometric primitives.

In this paper, a simple method for direct acquisition of a cloud of points from an object surface is presented together with a novel surface reconstruction algorithm used to obtain an explicit 3D model for the measured object. This technique is aimed at relatively accurate but simple and reliable 3D reconstruction of anatomical parts for biomedical applications. The whole system is based on acquisition of unorganized range data by laser scanning and successive image processing, by expanding and fitting a regular geometrical model within the range data, for surface reconstruction. The prototype system proved to be working finely, with an estimated resolution <10 mum, a repeatability <50mum, an acquisition noise of ~17 mum (rms value), and accuracy of ~80 mum

This paper proposes a general framework for overfitting control in surface reconstruction from noisy point data. The problem we deal with is how to create a model that will capture as much detail as possible and simultaneously avoid reproducing the noise of the input points. The proposed framework is based on extra-sample validation. It is fully automatic and can work in conjunction with any surface reconstruction algorithm. We test the framework with a Radial Basis Function algorithm, Multi-level Partition of Unity implicits, and the Power Crust algorithm.

The paper proposes a robust fully-automatic segmentation scheme based on a modified edge-following technique. First, an image frame is partitioned into many B/spl times/B-pixel blocks. In each block, the pixel point having the maximum gray-level difference from its neighboring point can be selected as the initial point. Additionally, the threshold can be determined automatically according to the histogram of gray-level difference values of initial points with their neighboring points. By using this threshold value, the edge points are determined from the initial points. Based on edge points, the modified edge-following technique with multiple direction detections is performed to find the closed-loop contours. The whole process is fully automatic, so that the disadvantages of both snake and live wire on the fly (LWOF) schemes on manually selecting the initial contours and points, and of the watershed on manually setting the threshold value can be dramatically improved at the same time. Owing to the rapid and fully-automatic segmented results, the proposed scheme is more robust and applicable on various image and video applications than conventional segmentation schemes.

3D surface modeling from curves

3D surface modeling from curves

The development of a reliable algorithm for 3D reconstruction of jewel surfaces and the relative accuracy evaluation, are the main issues of this paper. They rely on the estimation of the depth and 3D shape of an object from a sequence of images taken at different focus settings (shape from focus). Assuming the focal plane be identified by the best local sharpness, it turns out that the criterion for sharpness evaluation is crucial for obtaining an accurate 3D reconstruction. We present for the first time a novel algorithm for sharpness evaluation, which is based on a particular combination of sum of square differences (SSD). The images processed with SSD have been captured using a novel homemade microscope prototype. The implementation of this technique allows computing the best-focus map (and, consequently, image) from the whole set of images. The assessment of the 3D reconstruction quality has been carried out by considering the structural similarity index (SSIM), since thanks to its effectiveness in measuring the quality of natural images distorted by a large variety of biases. Hence, the novel algorithm has been applied to study micro-morphological features of a modern replica of an Etruscan gold jewel. The granulation ornament on the jewel has been characterized through a geometrical model which can be introduced to illustrate the grains solder quality. The developed geometrical model has been used to analyze also the granulation on an original Etruscan bauletto earring.