Shape optimization of quad mesh elements

We study the problem of optimizing the face elements of a quad mesh surface, that is, re-sampling a given quad mesh to make it possess, as much as possible, face elements of some desired aspect ratio and size. Unlike previous quad mesh optimization/improvement methods based on local operations on a small group of elements, we adopt a global approach that does not introduce extra singularities and therefore preserves the original quad structure of the input mesh. Starting from a collection of quad patches extracted from an input quad mesh, two global operations, i.e. re-sampling and re-distribution, are performed to optimize the number and spacings of grid lines in each patch. Both operations are formulated as simple optimization problems with linear constraints.     

Shape optimal design and free mesh generation

The concept of structural optimization was introduced in the early sixties. It was at that time that Professor Schmit, from Los Angeles, California University, suggested a combination of structural analysis by finite element and optimization methods (Schmit 1960).At present, the use of optimization methods is generally well understood. The capabilities (and limitations) of these methods are known and some industrial softwares exist. One of these is SAMCEF which can be applied to design of thin-walled structures or to shape optimization. The techniques used for the solution of large scale problems are presented in this paper. A summary of the main difficulties involved in shape optimization is also given. Several industrial problems are solved to illustrate the proposed concepts.     

Incremental reconstruction of sharp edges on mesh surfaces

Limited by the regular grids in computing, many modelling approaches (e.g. field-based methods) sample 3D shape insensitive to sharp features therefore exhibit aliasing errors, by which a lot of sharp edges and corners are lost on the reconstructed surface. An incremental approach for recovering sharp edges on an insensitive sampled triangular mesh is presented in this paper, so that shape approximation errors are greatly reduced. Either chamfered or blended sharp edges on an input triangular mesh could be successfully reconstructed by the signals inherent in the mesh. As a non-iterative method, our approach could be finished in a very short time comparing to those diffusion-based sharp-feature reproducers. The region embedding sharp features is first identified through normal variations. The positions of vertices in the sharp-feature embedded region are then predicted progressively from outer to the inner of sharp regions so that sharp edges could be recovered in the sense of region shrinking.     

基于隐函数的三维纹理网格重建

目前,面向实景图像的单图三维重建算法大多无法重建或者只能重建出已知拓扑结构类型的带纹理三维网格.文章结合目标检测网络,构建了基于隐函数的纹理推断网络"ColorNet",用于预测三维网格顶点的RGB值,并且为Pix3D数据集的三维模型添加UV纹理映射,并进行渲染、颜色采样.网络在经预处理后的数据集上训练并测试.实验表明,"ColorNet"可以预测出三维网格顶点的RGB值,并通过与三维重建网络"IM-RCNN"相结合,实现从单张实景图像中自动地重建接近真实纹理的三维模型.     

Optimized triangle mesh reconstruction from unstructured points

A variety of approaches have been proposed for polygon mesh reconstruction from a set of unstructured sample points. Suffering from severe aliases at sharp features and having a large number of unnecessary faces, most resulting meshes need to be optimized using input sample points in a postprocess. In this paper, we propose a fast algorithm to reconstruct high-quality meshes from sample data. The core of our proposed algorithm is a new mesh evaluation criterion which takes full advantage of the relation between the sample points and the reconstructed mesh. Based on our proposed evaluation criterion, we develop necessary operations to efficiently incorporate the functions of data preprocessing, isosurface polygonization, mesh optimization and mesh simplification into one simple algorithm, which can generate high-quality meshes from unstructured point clouds with time and space efficiency. Published online: 28 January 2003 Correspondence to: Y.-J. Liu     

A mesh reconstruction algorithm driven by an intrinsic property of a point cloud

This paper presents an algorithm for reconstructing a triangle mesh surface from a given point cloud. Starting with a seed triangle, the algorithm grows a partially reconstructed triangle mesh by selecting a new point based on an intrinsic property of the point cloud, namely, the sampling uniformity degree. The reconstructed mesh is essentially an approximate minimum-weight triangulation to the point cloud constrained to be on a two-dimensional manifold. Thus, the reconstructed surface has only small topological difference from the surface of the sampled object. Topological correct reconstruction can be guaranteed by adding a post-processing step.     

Shape recovery from turntable sequence using rim reconstruction

This paper makes use of both feature points and silhouettes to deliver fast 3D shape recovery. The algorithm exploits object silhouettes in two views to establish a 3D rim curve, which is defined with respect to the two frontier points arising from two views. The images of this 3D rim curve in the two views are matched using cross-correlation technique. A 3D planar rim curve is then reconstructed using point-based reconstruction method. A set of 3D rim curves enclosing the object can be obtained from an image sequence captured under circular motion. Silhouettes are further utilized to check for mismatched rim points. The proposed method solves the problem of reconstruction of concave object surface, which is usually left unresolved in general silhouette-based reconstruction methods. In addition, the property of the reconstructed 3D rim curves allows fast surface extraction. Experimental results with real data are presented.     

Textured mesh surface reconstruction of large buildings with multi-view stereo

There are three main approaches for reconstructing 3D models of buildings. Laser scanning is accurate but expensive and limited by the laser’s range. Structure-from-motion (SfM) and multi-view stereo (MVS) recover 3D point clouds from multiple views of a building. MVS methods, especially patch-based MVS, can achieve higher density than do SfM methods. Sophisticated algorithms need to be applied to the point clouds to construct mesh surfaces. The recovered point clouds can be sparse in areas that lack features for accurate reconstruction, making recovery of complete surfaces difficult. Moreover, segmentation of the building’s surfaces from surrounding surfaces almost always requires some form of manual inputs, diminishing the ease of practical application of automatic 3D reconstruction algorithms. This paper presents an alternative approach for reconstructing textured mesh surfaces from point cloud recovered by patch-based MVS method. To a good first approximation, a building’s surfaces can be modeled by planes or curve surfaces which are fitted to the point cloud. 3D points are resampled on the fitted surfaces in an orderly pattern, whose colors are obtained from the input images. This approach is simple, inexpensive, and effective for reconstructing textured mesh surfaces of large buildings. Test results show that the reconstructed 3D models are sufficiently accurate and realistic for 3D visualization in various applications.     

Transitive mesh space of a progressive mesh

The paper investigates the set of all selectively refined meshes that can be obtained from a progressive mesh. We call the set the transitive mesh space of a progressive mesh and present a theoretical analysis of the space. We define selective edge collapse and vertex split transformations, which we use to traverse all selectively refined meshes in the transitive mesh space. We propose a complete selective refinement scheme for a progressive mesh based on the transformations and compare the scheme with previous selective refinement schemes in both theoretical and experimental ways. In our comparison, we show that the complete scheme always generates selectively refined meshes with smaller numbers of vertices and faces than previous schemes for a given refinement criterion. The concept of dual pieces of the vertices in the vertex hierarchy plays a central role in the analysis of the transitive mesh space and the design of selective edge collapse and vertex split transformations.     

3D reconstruction of cultural heritages: Challenges and advances on precise mesh integration

Several methods perform the integration of multiple range scans of an object aiming the generation of a reconstructed triangle mesh; however, achieving high fidelity digital reconstructions is still a challenge. That is mostly due to the existence of outliers in the acquired range data, and their harmful effects on the integration algorithms. In this work, we first discuss artifacts usually found on real range data captured with 3D scanners based on laser triangulation. Following that there is the assessment of two widely used volumetric integration techniques (VRIP and Consensus Surface) and our suggested improvements. We also present a novel, hybrid approach that combines strengths from both VRIP and Consensus Surface, named IMAGO Volumetric Integration Algorithm (IVIA). Our novel algorithm adds new ideas while improving the detection and elimination of artifacts. Further, IVIA works in close cooperation with the subsequent hole filling process, which greatly improves the overall quality of the generated 3D models. Our technique leads to better results when assessed in different situations, when compared to VRIP, Consensus Surface, and also to a well known state-of-the-art surface-based method, Poisson Surface Reconstruction.     

Coarse-to-fine surface reconstruction from silhouettes and range data using mesh deformation

We present a coarse-to-fine surface reconstruction method based on mesh deformation to build watertight surface models of complex objects from their silhouettes and range data. The deformable mesh, which initially represents the object visual hull, is iteratively displaced towards the triangulated range surface using the line-of-sight information. Each iteration of the deformation algorithm involves smoothing and restructuring operations to regularize the surface evolution process. We define a non-shrinking and easy-to-compute smoothing operator that fairs the surface separately along its tangential and normal directions. The mesh restructuring operator, which is based on edge split, collapse and flip operations, enables the deformable mesh to adapt its shape to the object geometry without suffering from any geometrical distortions. By imposing appropriate minimum and maximum edge length constraints, the deformable mesh, hence the object surface, can be represented at increasing levels of detail. This coarse-to-fine strategy, that allows high resolution reconstructions even with deficient and irregularly sampled range data, not only provides robustness, but also significantly improves the computational efficiency of the deformation process. We demonstrate the performance of the proposed method on several real objects.     

3D face reconstruction using images from cameras with varying parameters

In this paper, we present a new technique of 3D face reconstruction from a sequence of images taken with cameras having varying parameters without the need to grid. This method is based on the estimation of the projection matrices of the cameras from a symmetry property which characterizes the face, these projections matrices are used with points matching in each pair of images to determine the 3D points cloud, subsequently, 3D mesh of the face is constructed with 3D Crust algorithm. Lastly, the 2D image is projected on the 3D model to generate the texture mapping. The strong point of the proposed approach is to minimize the constraints of the calibration system: we calibrated the cameras from a symmetry property which characterizes the face, this property gives us the opportunity to know some points of 3D face in a specific well-chosen global reference, to formulate a system of linear and nonlinear equations according to these 3D points, their projection in the image plan and the elements of the projections matrix. Then to solve these equations, we use a genetic algorithm which consists of finding the global optimum without the need of the initial estimation and allows to avoid the local minima of the formulated cost function. Our study is conducted on real data to demonstrate the validity and the performance of the proposed approach in terms of robustness, simplicity, stability and convergence.     

Example-based photometric stereo: shape reconstruction with general, varying BRDFs

This paper presents a technique for computing the geometry of objects with general reflectance properties from images. For surfaces with varying material properties, a full segmentation into different material types is also computed. It is assumed that the camera viewpoint is fixed, but the illumination varies over the input sequence. It is also assumed that one or more example objects with similar materials and known geometry are imaged under the same illumination conditions. Unlike most previous work in shape reconstruction, this technique can handle objects with arbitrary and spatially-varying BRDFs. Furthermore, the approach works for arbitrary distant and unknown lighting environments. Finally, almost no calibration is needed, making the approach exceptionally simple to apply.     

Combinatorial manifold mesh reconstruction and optimization from unorganized points with arbitrary topology

In this paper, a novel approach is proposed to reliably reconstruct the geometric shape of a physically existing object based on unorganized point cloud sampled from its boundary surface. The proposed approach is composed of two steps. In the first step, triangle mesh structure is reconstructed as a continuous manifold surface by imposing explicit relationship among the discrete data points. For efficient reconstruction, a growing procedure is employed to build the 2-manifold directly without intermediate 3D representation. Local and global topological operations with ensured completeness and soundness are defined to incrementally construct the 2-manifold with arbitrary topology. In addition, a novel criterion is proposed to control the growing process for ensured geometric integrity and automatic boundary detection with a non-metric threshold. The reconstructed manifold surface captures the object topology with the built-in combinatorial structure and approximates the object geometry to the first order. In the second step, new methods are proposed to efficiently obtain reliable curvature estimation for both the object surface and the reconstructed mesh surface. The combinatorial structure of the triangle mesh is then optimized by changing its local topology to minimize the curvature difference between the two surfaces. The optimized triangle mesh achieves second order approximation to the object geometry and can serve as a basis for many applications including virtual reality, computer vision, and reverse engineering.     

Topological numbering of features on a mesh

Assume we are given ann ×n binary image containing horizontally convex features; i.e., for each feature, each of its row's pixels form an interval on that row. In this paper we consider the problem of assigning topological numbers to such features, i.e., assign a number to every featuref so that all features to the left off in the image have a smaller number assigned to them. This problem arises in solutions to the stereo matching problem. We present a parallel algorithm to solve the topological numbering problem inO(n) time on ann ×n mesh of processors. The key idea of our solution is to create a tree from which the topological numbers can be obtained even though the tree does not uniquely represent the to the left of relationship of the features.The work of M. J. Atallah was supported by the Office of Naval Research under Grants N00014-84-K-0502 and N00014-86-K-0689, and the National Science Foundation under Grant DCR-8451393, with matching funds from AT&T. Part of this work was done while he was a Visiting Scientist at the Center for Advanced Architectures project of the Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, CA 94035, USA. S. E. Hambrusch's work was supported by the Office of Naval Research under Contracts N00014-84-K-0502 and N00014-86K-0689, and by the National Science Foundation under Grant MIP-87-15652. Part of this work was done while she was visiting the International Computer Science Institute, Berkeley, CA 94704, USA. The work of L. E. TeWinkel was supported by the Office of Naval Research under Contract N00014-86K-0689.     

CFD mesh generation for biological flows: Geometry reconstruction using diagnostic images

A new thrust in the use of CFD techniques for simulation of biological flows has necessitated the demand for robust grid generation techniques to characterize the complex geometries. While the techniques of image manipulation required are simple, most researchers in this field use proprietary 3rd party software for image manipulation and grid generation. In the current study, we propose a simple MATLAB based grid generation techniques suitable for CFD studies of external and internal biological flows such as blood flow and respiration and flows around the human body. As an example, the flow inside two specific intracranial aneurysms is modeled by generating CFD grids from 3D rotational angiography images. Specific issues of modeling, such as boundary conditions and location of flow inlets and outlets, in relation to the reconstructed geometry are discussed. The reconstructed arterial geometry including the aneurysm matches the visual representation generated by the angiogram software (Leonardo software). The calculated CFD flow patterns also show a good correlation to the flow visualization presented by the Leonardo software. Areas of high pressure and wall shear stress are identified. The same technique is also used to generate the CFD grid of a human trachea to study the particle dispersion patterns during a human cough cycle. The fluid is modeled using an actual human cough signal with the particles simulating the influenza virus. The flow pattern out of the mouth along with the dispersion pattern of the particles is validated against similar human experimental studies to track the spread of the disease through cough. Work is also currently underway to use the present grid generation program to construct a superficial mesh of the human body from MRI/CAT scan images of cadavers. The goal is to build an accurate and scalable model of the human body surface with articulate joints which can be posed in any environment to model the air flow patterns around the body.     

Topological numbering of features on a mesh

Assume we are given ann ×n binary image containing horizontally convex features; i.e., for each feature, each of its row's pixels form an interval on that row. In this paper we consider the problem of assigning topological numbers to such features, i.e., assign a number to every featuref so that all features to the left off in the image have a smaller number assigned to them. This problem arises in solutions to the stereo matching problem. We present a parallel algorithm to solve the topological numbering problem inO(n) time on ann ×n mesh of processors. The key idea of our solution is to create a tree from which the topological numbers can be obtained even though the tree does not uniquely represent the “to the left of” relationship of the features.     

Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants

In this paper we deal with the problem of reconstructing surfaces from unorganized sets of points, while capturing the significant geometry details of the modelled surface, such as edges, flat regions, and corners. This is obtained by exploiting the good approximation capabilities of the radial basis functions (RBF), the local nature of the method proposed in [1], and introducing information on shape features and data anisotropies detected from the given surface points.The result is a shape-preserving reconstruction, given by a weighted combination of locally aniso tropic interpolants. For each local interpolant the anisotropy is obtained by replacing the Euclidean norm with a suitable metric which takes into account the local distribution of the points. Thus hyperellipsoid basis functions, named anisotropic RBFs, are defined. Results from the application of the method to the reconstruction of object surfaces in ℝ³ are presented, confirming the effectiveness of the approach.     

Generating a nice triangular mesh on a regular parametric surface

In this paper, we present an iterative algorithm to generate a nice triangular curvilinear mesh on a regular parametric surface. The main idea is to obtain a reparametrization of the surface that behaves approximately like a conformal map in a finite number of points. These points are the vertices of a planar triangulation T ^op in the parameter space, which we would like to lift on the surface. The image of T ^op by means of the reparametrization provides us a triangular curvilinear mesh on the surface which reflects the properties of T ^op .     

Interpolation by bivariate quadratic splines on a four-directional mesh

We give sufficient conditions which guarantee that a set of points admits unique Lagrange interpolation by quadratic splines on a four-directional mesh. The poisedness of these sets will be proved by reducing one bivariate problem to a finite sequence of univariate problems.