Geometry curves: A compact representation for 3D shapes

We propose a novel compact surface representation, namely geometry curves, which record the essence of shape geometry and topology. The geometry curves mainly contain two parts: the interior and boundary lines. The interior lines, which correspond to the feature lines, record the geometry information of the 3D shapes; the boundary lines, which correspond to the boundary or fundamental polygons, record the topology information of the 3D shapes. As a vector representation, geometry curves can depict highly complex geometry details. The concept of geometry curves can be utilized in many potential applications, e.g., mesh compression, shape modeling and editing, animation, and level of details. Furthermore, we develop a procedure for automatically constructing geometry curves which obtain an excellent approximation to the original mesh.     

Preserving detailed features in digital bas-relief making

This paper presents a novel algorithm for digitally making bas-reliefs. The problem requires visibly retaining fine details present in original 3D objects while greatly compressing their depths to produce an almost planar result. Our approach performs compression on the gradient domain; gradients are first estimated from a height field representing the input scene. A new compression function based on arctangent is introduced to preserve desired details of reliefs, allowing accurate height adjustment via a data-dependent threshold. We explicitly consider how to preserve fine details present in the original objects, which is crucial for producing high-quality bas-reliefs. Laplacian coordinates are used to store detailed features before depth compression and then restore them afterwards. Laplacian sharpening is also used to emphasize detailed features in the relief itself. Prior to depth compression, we process the input height field to reduce gaps in height, and detect the outer silhouette which allows to compute the output relief relative to a planar background or other surface, by solving a Poisson equation. This combination of techniques allows our method to produce bas-reliefs with well-preserved details.     

Parallel computation of spherical parameterizations for mesh analysis

Mesh parameterization is central to a broad spectrum of applications. In this paper, we present a novel approach to spherical mesh parameterization based on an iterative quadratic solver that is efficiently parallelizable on modern massively parallel architectures. We present an extensive analysis of performance results on both GPU and multicore architectures. We introduce a number of heuristics that exploit various system characteristics of the underlying architectures to speed up the parallel realization of our algorithms. Furthermore, we demonstrate the applicability of our approach to real-time feature detection, mesh decomposition and similarity-based 3D object retrieval. Finally, we offer visual results and a demonstration video.     

A quantitative assessment of approaches to mesh generation for surgical simulation

In surgical simulation, it is common practice to use tetrahedral meshes as models for anatomy. These meshes are versatile, and can be used with a number of different physically based modelling schemes. A variety of mesh generators are available that can automatically create tetrahedral meshes from segmented anatomical volumes. Each mesh generation scheme offers its own set of unique attributes. However, few are readily available. When choosing a mesh generator for simulation, it is critical for it to output good-quality, patient-specific meshes that provide a good approximation of the shape or volume to be modelled. To keep computation time within the bounds required for real-time interaction, there is also a limit imposed on the number of elements in the mesh generated. To the authors knowledge, there has been little work directly assessing the suitability of mesh generators for surgical simulation. This paper seeks to address this issue by assessing the use of six mesh generators in a surgical simulation scenario, and examining how they affect simulation precision. This paper aims to perform these comparisons against high-resolution reference meshes, where we examine the precision of meshes from the same mesh generator at different levels of complexity.

Filtered Quadrics for High‐Speed Geometry Smoothing and Clustering

Modern 3D capture pipelines produce dense surface meshes at high speed, which challenge geometric operators to process such massive data on‐the‐fly. In particular, aiming at instantaneous feature‐preserving smoothing and clustering disqualifies global variational optimizers and one usually relies on high‐performance parallel kernels based on simple measures performed on the positions and normal vectors associated with the surface vertices. Although these operators are effective on small supports, they fail at properly capturing larger scale surface structures. To cope with this problem, we propose to enrich the surface representation with filtered quadrics, a compact and discriminating range space to guide processing. Compared to normal‐based approaches, this additional vertex attribute significantly improves feature preservation for fast bilateral filtering and mode‐seeking clustering, while exhibiting a linear memory cost in the number of vertices and retaining the simplicity of convolutional filters. In particular, the overall performance of our approach stems from its natural compatibility with modern fine‐grained parallel computing architectures such as graphics processor units (GPU). As a result, filtered quadrics offer a superior ability to handle a broad spectrum of frequencies and preserve large salient structures, delivering meshes on‐the‐fly for interactive and streaming applications, as well as quickly processing large data collections, instrumental in learning‐based geometry analysis.     

Polygonal space carving with geometric anti-aliasing

This paper proposes an algorithm that solves the shape recovery problem from N arbitrary images. By introducing a polygonal carving technique, the proposed algorithm can reconstruct the image-consistent polygonal shape that is patched by input images. This algorithm eliminates the invalid vertices and polygons from the initial polygonal grid space according to the color variance that represents their image consistency. The carved shape is refined by moving the outlier vertices on the boundary of each image. The final reconstructed shape faithfully accounts for the input images, and its textured appearance reflects the similar color property of the target object.     

基于细分曲面的泊松网格编辑

针对具有丰富几何细节的三维网格模型,基于直接坐标操纵的传统编辑算法在编辑过程中不可避免地存在细节特征无法得到有效保持的问题.综合基于细分曲面的空间变形方法以及微分域网格编辑二者优势,提出一种基于细分曲面的泊松网格编辑方法.首先建立待变形网格模型的包围网格,以包围网格所决定的细分曲面构造变形控制曲面;然后根据用户变形意图操纵包围网格,将对应细分曲面变化信息转化为对网格模型泊松梯度场的改变;最后根据变化后的梯度场重建网格模型.文中方法交互简单、直观,具有多分辨率编辑的优势,可以有效地保持网格模型的细节特征.丰富的变形实例证明了该方法的有效性和可行性.     

Integration of CAD and boundary element analysis through subdivision methods

Subdivision methods have been mainly used in computer graphics. This paper extends their applications to mechanical design and boundary element analysis (BEA), and fulfills the seamless integration of CAD and BEA in the model and representation.Traditionally, geometric design and BEA are treated as separate modules requiring different representations and models, which include continuous parametric models and discrete models. Due to the incompatibility of the involved representations and models, the post-processing in geometric design or the pre-processing in BEA is essential. The transition from geometric design to BEA requires substantial effort and errors are inevitably introduced during the transition. In this paper, a framework of realizing the integration of CAD and BEA was first presented based on subdivision methods. A common model or a unified representation for geometric design and BEA was created with subdivision surfaces. For general 3D structures, automatic mesh generation for geometric design and BEA was fulfilled through subdivision methods. The seamless integration improves the accuracy of numerical analysis and shortens the cycle of geometric design and BEA.     

基于切平面中值坐标的Laplacian网格变形算法

网格模型变形往往需要保持局部几何细节,Laplacian网格变形算法能够较好地保持局部几何细节特征,但细节特征描述子-Laplacian坐标的计算欠缺精确性.从平面多边形中值坐标的角度出发,对Laplacian坐标进行重新定义,将顶点的一阶邻域投影到顶点处切平面上,根据顶点相对投影点的中值坐标构建的Laplacian坐标能够精确地描述模型的局部几何细节特征,实验验证能够获得较好的编辑效果.     

High-order curvilinear meshing using a thermo-elastic analogy

With high-order methods becoming increasingly popular in both academia and industry, generating curvilinear meshes that align with the boundaries of complex geometries continues to present a significant challenge. Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added naively, cause the element to self-intersect. Over the last few years, several curvilinear mesh generation techniques have been designed to tackle this issue, utilizing mesh deformation to move the interior nodes of the mesh in order to accommodate curvature at the boundary. Many of these are based on elastic models, where the mesh is treated as a solid body and deformed according to a linear or non-linear stress tensor. However, such methods typically have no explicit control over the validity of the elements in the resulting mesh. In this article, we present an extension of this elastic formulation, whereby a thermal stress term is introduced to ‘heat’ or ‘cool’ elements as they deform. We outline a proof-of-concept implementation and show that the adoption of a thermo-elastic analogy leads to an additional degree of robustness, by considering examples in both two and three dimensions.     

Constructing 3D human model from front and side images

Constructing 3D human model from 2D images provides a cost-effective approach to visualize digital human in virtual environment. This paper presents a systematic approach for constructing 3D human model using the front and side images of a person. The silhouettes of human body are first detected and the feature points on the silhouettes are subsequently identified. The feature points are further used to obtain the body dimensions that are necessary for identifying a template 3D human model. The shape of the template human model can be modified by the free-form deformation method. Moreover, the proposed approach has been applied for constructing the 3D human models of 30 subjects. The comparisons between the constructed 3D models and the 3D scanning models of the 30 subjects indicate that the proposed system is very effective and robust.     

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current hole-filling algorithms and the resolution of the image irradiance equations are overcome.     

Hierarchical aggregation for efficient shape extraction

This paper presents an efficient framework which supports both automatic and interactive shape extraction from surfaces. Unlike most of the existing hierarchical shape extraction methods, which are based on computationally expensive top-down algorithms, our framework employs a fast bottom-up hierarchical method with multiscale aggregation. We introduce a geometric similarity measure, which operates at multiple scales and guarantees that a hierarchy of high-level features are automatically found through local adaptive aggregation. We also show that the aggregation process allows easy incorporation of user-specified constraints, enabling users to interactively extract features of interest. Both our automatic and the interactive shape extraction methods do not require explicit connectivity information, and thus are applicable to unorganized point sets. Additionally, with the hierarchical feature representation, we design a simple and effective method to perform partial shape matching, allowing efficient search of self-similar features across the entire surface. Experiments show that our methods robustly extract visually meaningful features and are significantly faster than related methods.     

Parallel adaptive mesh generation and decomposition

An important class of methodologies for the parallel processing of computational models defined on some discrete geometric data structures (i.e. meshes, grids) is the so calledgeometry decomposition or splitting approach. Compared to the sequential processing of such models, the geometry splitting parallel methodology requires an additional computational phase. It consists of the decomposition of the associated geometric data structure into a number of balancedsubdomains that satisfy a number of conditions that ensure the load balancing and minimum communication requirement of the underlying computations on a parallel hardware platform. It is well known that the implementation of the mesh decomposition phase requires the solution of a computationally intensive problem. For this reason several fast heuristics have been proposed. In this paper we explore a decomposition approach which is part of a parallel adaptive finite element mesh procedure. The proposed integrated approach consists of five steps. It starts with a coarse background mesh that isoptimally decomposed by applying well known heuristics. Then, the initial mesh is refined in each subdomain after linking the new boundaries introduced by its decomposition. Finally, the decomposition of the new refined mesh is improved so that it satisfies the objectives and conditions of the mesh decomposition problem. Extensive experimentation indicates the effectiveness and efficiency of the proposed parallel mesh and decomposition approach.     

Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm

This paper describes mesh correction techniques necessary for meshing an arbitrary volume with a completely hexahedral mesh. Specifically, it describes seams and wedges, mechanisms that overcome major hurdles encountered in the preliminary work on the plastering algorithm. The plastering algorithm iteratively projects layers of elements inward from a quadrilateral discretization of the volume's bounding faces. Seams and wedges resolve incompatibilities in the mesh and in the progressing boundary, thus ensuring the correct formation of a hexahedral mesh from the plastering algorithm.     

Punctuated simplification of man-made objects

We present a simplification algorithm for manifold polygonal meshes of plane-dominant models. Models of this type are likely to appear in man-made environments. While traditional simplification algorithms focus on generality and smooth meshes, the approach presented here considers a specific class of man-made models. By detecting and classifying edge loops on the mesh and providing a guided series of binary mesh partitions, our approach generates a series of simplified models, each of which better respects the semantics of these kinds of models than conventional approaches do. A guiding principle is to eliminate simplifications that do not make sense in constructed environments. This, coupled with the concept of “punctuated simplification”, leads to an approach that is both efficient and delivers high visual quality. Comparative results are given.     

Multi-operator image retargeting with automatic integration of direct and indirect seam carving

Multi-operator image resizing can preserve important objects and structure in an image by combining multiple image resizing operators. However, traditional multi-operator methods do not take both horizontal and vertical content-aware resizing potential into consideration, which essentially leads to squeeze/stretch effect in the resultant images. In this paper, we propose a new multi-operator scheme that addresses aforementioned issue by integrating direct and indirect seam carving. Compared with previous methods, the proposed scheme remarkably reduces the cost of deciding when to change operators, by employing a newly defined image artifact measure. Furthermore, we propose a novel seam carving enhancement, named ACcumulated Energy Seam Carving (ACESC), as a basic operator to improve global structure preservation. By combining horizontal and vertical seam carving, our scheme preserves the shapes of important objects well. We present typical results to demonstrate the effectiveness of our method. User study shows that our method has high user preference.     

微分几何编码识别物体的形状

为更好地识别目标形状,编码方法需要对目标的刚体变换具有不变性,同时最大限度保持目标的原有信息。鉴于刚体平面曲线作变换时其曲率的不变性,提出了基于轮廓曲率提取的目标边界编码方法,并对此方法实施了离散化处理。提出了基于改进的KMP算法（D.K.Knuth,V.R.Pratt和J．H．Morris）的曲线匹配方法,并对目标轮廓的重建作了描述。实验证明,利用微分几何的思想描述目标边界,提取方法简单,存储量小,其编码针对目标刚体变换具有不变性,为识别提供了较大的方便。