Improved,feature-centric EMD for 3D surface modeling and processing

Since late 1990s, Empirical Mode Decomposition (EMD) starts to emerge as a powerful tool for processing non-linear and non-stationary signals. Nonetheless, the research on exploring EMD-relevant techniques in the domain of geometric modeling and processing is extremely rare. Directly applying EMD to coordinate functions of 3D shape geometry will not take advantage of the attractive EMD properties. To ameliorate, in this paper we articulate a novel 3D surface modeling and processing framework founded upon improved, feature-centric EMD, with a goal of realizing the full potential of EMD. Our strategy starts with a measure of mean curvature as a surface signal for EMD. Our newly-formulated measure of mean curvature is computed via the inner product of Laplacian vector and vertex normal. Such measure is both rotation-invariant and translation-invariant, facilitates the computation of different scale features for original surfaces, and avoids boundary shrinkage when processing open surfaces. Moreover, we modify the original EMD formulation by devising a feature-preserving multiscale decomposition algorithm for surface analysis and synthesis. The key idea is to explicitly formulate details as oscillation between local minima and maxima. Within our novel framework, we could accommodate many modeling and processing operations, such as filter design, detail transfer, and feature-preserving smoothing and denoising. Comprehensive experiments and quantitative evaluations/comparisons on popular models have demonstrated that our new surface processing methodology and algorithm based on the improved, feature-centric EMD are of great value in digital geometry processing, analysis, and synthesis.     

Multi-scale geometric detail enhancement for time-varying surfaces

This paper presents a new multi-scale geometric detail enhancement approach for time-varying surfaces. We first develop an adaptive spatio-temporal bilateral filter, which produces temporally-coherent and feature-preserving multi-scale representation for the time-varying surfaces. We then extract the geometric details from the time-varying surfaces, and enhance geometric details by exaggerating detail information at each scale across the time-varying surfaces. Our approach can process mesh sequences with consistent connections or point sequences with unconstructed point set. In addition, as applications, based on the developed multi-scale surface representation and detail enhancement operators, we present geometric detail transfer, space–time morphing, and local regions detail enhancement for the time-varying surface.     

Multi-scale anisotropic heat diffusion based on normal-driven shape representation

Multi-scale geometric processing has been a popular and powerful tool in graphics, which typically employs isotropic diffusion across scales. This paper proposes a novel method of multi-scale anisotropic heat diffusion on manifold, based on the new normal-driven shape representation and Edge-weighted Heat Kernels (EHK). The new shape representation, named as Normal-Controlled Coordinates (NCC), can encode local geometric details of a vertex along its normal direction and rapidly reconstruct surface geometry. Moreover, the inner product of NCC and its corresponding vertex normal, called Normal Signature (NS), defines a scalar/heat field over curved surface. The anisotropic heat diffusion is conducted using the weighted heat kernel convolution governed by local geometry. The convolution is computed iteratively based on the semigroup property of heat kernels toward accelerated performance. This diffusion is an efficient multi-scale procedure that rigorously conserves the total heat. We apply our new method to multi-scale feature detection, scalar field smoothing and mesh denoising, and hierarchical shape decomposition. We conduct various experiments to demonstrate the effectiveness of our method. Our method can be generalized to handle any scalar field defined over manifold.     

Detail-replicating shape stretching

Mesh deformation has become a powerful tool for creating shape variations. Existing deformation techniques work on preserving surface details under bending and twisting operations. Stretching different parts of a shape is also a useful operation for generating shape variations. However, under stretching, texture-like geometric details should not be preserved but rather replicated. We propose a simple and efficient method that helps create model variations by applying nonuniform stretching on 3D models with organic geometric details. The method replicates the geometric details and synthesizes extensions by adopting texture synthesis techniques on surface details. We work on analyzing and separating the stretching of surface details from the stretching of the base mesh resulting in the appearance of preserved details. The efficiency of our method is attributed to a local parameterization of the surface with the help of curve skeletons. We show a variety of experimental results that demonstrate the usefulness of this intuitive stretching tool in creating shape variations.     

A Framework for Interactive Hypertexture Modelling

Hypertexturing can be a powerful way of adding rich geometric details to surfaces at low memory cost by using a procedural three‐dimensional (3D) space distortion. However, this special kind of texturing technique still raises a major problem: the efficient control of the visual result. In this paper, we introduce a framework for interactive hypertexture modelling. This framework is based on two contributions. First, we propose a reformulation of the density modulation function. Our density modulation is based on the notion of shape transfer function. This function, which can be easily edited by users, allows us to control in an intuitive way the visual appearance of the geometric details resulting from the space distortion. Second, we propose to use a hybrid surface and volume‐point‐based representation in order to be able to dynamically hypertexture arbitrary objects at interactive frame rates. The rendering consists in a combined splat‐ and raycasting‐based direct volume rendering technique. The splats are used to model the volumetric object while raycasting allows us to add the details. An experimental study on users shows that our approach improves the design of hypertextures and yet preserves their procedural nature.     

单幅植物叶片图像的3维重建

目的 植物叶片形态复杂,在虚拟场景中很难真实表现。为了从信息量有限的单幅图像中恢复植物叶片的3维形状,本文基于从明暗恢复形状（shape from shading,SFS）的方法,利用亮度统计规律和植物形态特征恢复叶片的3维形状。方法 在SFS的基础上,设计基于图像骨架的距离场偏置加强表面细节;针对SFS对恢复宏观几何形状的不足,提出根据图像亮度统计分布选取控制点控制表面宏观形状变化,并利用叶片中轴的距离场约束恢复宏观几何形状,每种方法对于表面宏观几何形状恢复的权重基于恢复的反射图和输入图像间的相似度设定;将表面细节添加到宏观几何形状上得到目标对象的3维形状。结果 选取植物叶片图像进行实验,并与其他方法进行比较,实验结果表明本文方法增强了表面细节显示,并有明显的宏观几何形状变化。同时为了验证本文方法对其他物体表面细节恢复的适用性,分别对硬币和恐龙恢复表面细节,实验结果表明提出的增强表面细节的方法同样适用于其他物体。结论 针对单幅植物叶片图像的3维重建,在SFS的基础上提出了根据骨架特征加强表面细节,根据图像亮度统计分布和叶片中轴距离场约束共同恢复表面宏观几何形状的算法,实验结果验证了本文方法的可行性。     

Feature sensitive deformation for triangular mesh models

Shape deformation is a useful tool for shape modeling and animation in computer graphics. In this paper, we propose a novel surface deformation method based on a feature sensitive (FS) metric. Firstly, taking unit normal vectors into account, we derive a FS Laplacian operator, which is more sensitive to featured regions of mesh models than existing operators. Secondly, we use the 1‐ring tetrahedron in the dual mesh, a volumetric structure, to encode geometric details. To preserve the shape of the tetrahedron, we introduce linear tetrahedron constraints minimizing both the distortion of the base triangle and the change of the corresponding height. These ensure that geometric details are accurately preserved during deformation. The time complexity of our new method is similar to that of existing linear Laplacian methods. Examples are included to show that our FS deformation method better preserves mesh details, especially features, than existing Laplacian methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Data Dependent Thin Plate Energy and its use in Interactive Surface Modeling

When modeling spline surfaces of complex shape, one has to deal with an overwhelming number of control points. Modeling by direct manipulation of the control points is a tedious task. In particular, it is very difficult to maintain a generally pleasant looking surface shape. It becomes therefore increasingly important to build tools that allow the designer to specify only a few geometric constraints while automatically determining the explicit representation of the surface. The basic concept of such a tool is simple. In a first step one has to somehow measure the “fairness” (=quality) of a surface. Once this is achieved, an optimization process selects the one surface with optimal fairness from all surfaces satisfying the user specified geometric constraints. To measure the fairness, thin plate energy functionals are a good choice. However, for interactive use these functionals are far too complex. W e will present appropriate approximations to these functionals that allow an optimization nearly in real time. Thefunctionals are obtained by introducing reference surfaces thus leading to data dependent, quadratic approximations to the exact thin plate energy functionals. We apply the method to interactive surface manipulations based on energy constraints.     

图像驱动的三维模型外观细节增强

随着计算机游戏与电影视觉特效的普及应用,仅通过纹理贴图已不能满足用户需求。然而,为三维模型制作视觉真实的表面外观,即在包含几何细节变化(如金属腐蚀、石料风化、木质裂纹等)同时辅之以与几何变化合理匹配的材质颜色却是一件困难且耗时的工作。文章提出了一种能够从单幅图像中提取物体的外观细节(材质与几何信息)并增强至三维模型表面的方法。该方法是一种新型的几何约束的非刚性2D-3D融合配准算法,可以通过将配准后的模型提供的几何信息作为先验知识实现更好的本征图像分解结果。利用图像中同步分解出的互相关的多尺度几何信息与材质纹理信息组成的非参数外观模型,文中提出了一种法向量约束的几何变形算法将外观纹理恢复到代理模型上。通过上述步骤,文章提出的方法能够帮助建模师制作具有多尺度外观细节的三维模型。     

HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid-based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques.     

A spatial warping method for freeform modeling based on a level-set method

Providing an intuitive and effective tool for freeform geometric modeling is important for product design. We introduce in this paper a level-set based spatial warping method for freeform modeling, allowing shape deformation to be initialed by rigid body transformations of volumetric tools. Intuitive user operations including imprinting, deformation and smoothing are developed to shield the user from the underlying geometric complexity. Unlike mesh-based spatial warping methods, the developed method represents a digital model by implicit distance field data and describes its change of geometry by the level-set method. This guarantees the generation of topologically correct triangular mesh models and circumvents the error-prone remeshing and mesh-repairing processes, thus preventing topological errors such as self-intersections. We present this method with algorithm details, numerical experiments and modeling examples.     

Snake pedals: compact and versatile geometric models withphysics-based control

We introduce a geometric shape modeling scheme which allows for representation of global and local shape characteristics of an object. Geometric models are well-suited for representing global shapes without local detail, but we propose a scheme which represents global shapes with local detail and permits model shaping as well as topological changes via physics-based control. The scheme represents shapes by pedal curves and surfaces, i.e. the loci of the foot of perpendiculars to the tangents of a fixed curve/surface from a fixed point called the pedal point. By varying the location of the pedal point, one can synthesize a large class of shapes which exhibit both local and global deformations. We introduce physics-based control for shaping these geometric models by letting the pedal point vary and use a snake to represent the position of this varying point. The model, a “snake pedal”, allows for interactive manipulation via forces applied to the snake. We develop a fast numerical iterative algorithm for shape recovery from image data using this scheme. The algorithm involves the Levenberg-Marquardt (LM) method in the outer loop for solving the global parameters and the alternating direction implicit (ADI) method in the inner loop for solving the local parameters of the model. The combination of the global and local scheme leads to an efficient numerical solution to the model fitting problem. We demonstrate the applicability of this modeling scheme via examples of shape synthesis and shape estimation from real image data     

Interactive Image‐Guided Modeling of Extruded Shapes

A recent trend in interactive modeling of 3D shapes from a single image is designing minimal interfaces, and accompanying algorithms, for modeling a specific class of objects. Expanding upon the range of shapes that existing minimal interfaces can model, we present an interactive image‐guided tool for modeling shapes made up of extruded parts. An extruded part is represented by extruding a closed planar curve, called base, in the direction orthogonal to the base. To model each extruded part, the user only needs to sketch the projected base shape in the image. The main technical contribution is a novel optimization‐based approach for recovering the 3D normal of the base of an extruded object by exploring both geometric regularity of the sketched curve and image contents. We developed a convenient interface for modeling multi‐part shapes and a method for optimizing the relative placement of the parts. Our tool is validated using synthetic data and tested on real‐world images.     

Optimizing Structure Preserving Embedded Deformation for Resizing Images and Vector Art

Smart deformation and warping tools play an important part in modern day geometric modeling systems. They allow existing content to be stretched or scaled while preserving visually salient information. To date, these techniques have primarily focused on preserving local shape details, not taking into account important global structures such as symmetry and line features. In this work we present a novel framework that can be used to preserve the global structure in images and vector art. Such structures include symmetries and the spatial relations in shapes and line features in an image. Central to our method is a new formulation of preserving structure as an optimization problem. We use novel optimization strategies to achieve the interactive performance required by modern day modeling applications. We demonstrate the effectiveness of our framework by performing structure preservation deformation of images and complex vector art at interactive rates.     

Skeleton-guided 3D shape distance field metamorphosis

We introduce an automatic 3D shape morphing method without the need of manually placing anchor correspondence points. Given a source and a target shape, we extract their skeletons and automatically estimate the meaningful anchor points based on their skeleton node correspondences. Based on the anchors, dense correspondences between the interior of source and target shape can be established using earth mover’s distance (EMD) optimization. Skeleton node correspondence, estimated with a voting-based method, leads to part correspondence which can be used to confine the dense correspondence within matched part pairs. This produces smooth and plausible morphing sequence based on distance field interpolation (DFI). We demonstrate the effectiveness of our algorithm over shapes with large geometric variation and structural difference.     

A Multi-Channel Salience Based Detail Exaggeration Technique for 3D Relief Surfaces

Visual saliency can always persuade the viewer’s visual attention to fine-scale mesostructure of 3D complex shapes.Owing to the multi-channel salience measure and salience-domain shape modeling technique,a novel visual saliency based shape depiction scheme is presented to exaggerate salient geometric details of the underlying relief surface.Our multi-channel salience measure is calculated by combining three feature maps,i.e.,the 0-order feature map of local height distribution,the 1-order feature map of normal difference,and the 2-order feature map of mean curvature variation.The original relief surface is firstly manipulated by a salience-domain enhancement function,and the detail exaggeration surface can then be obtained by adjusting the surface normals of the original surface as the corresponding final normals of the manipulated surface.The advantage of our detail exaggeration technique is that it can adaptively alter the shading of the original shape to reveal visually salient features whilst keeping the desired appearance unimpaired.The experimental results demonstrate that our non-photorealistic shading scheme can enhance the surface mesostructure effectively and thus improving the shape depiction of the relief surfaces.     

A simple method for interpolating meshes of arbitrary topology by Catmull–Clark surfaces

Interpolating an arbitrary topology mesh by a smooth surface plays important role in geometric modeling and computer graphics. In this paper we present an efficient new algorithm for constructing Catmull–Clark surface that interpolates a given mesh. The control mesh of the interpolating surface is obtained by one Catmull–Clark subdivision of the given mesh with modified geometric rule. Two methods—push-back operation based method and normal-based method—are presented for the new geometric rule. The interpolation method has the following features: (1) Efficiency: we obtain a generalized cubic B-spline surface to interpolate any given mesh in a robust and simple manner. (2) Simplicity: we use only simple geometric rule to construct control mesh for the interpolating subdivision surface. (3) Locality: the perturbation of a given vertex only influences the surface shape near this vertex. (4) Freedom: for each edge and face, there is one degree of freedom to adjust the shape of the limit surface. These features make interpolation using Catmull–Clark surfaces very simple and thus make the method itself suitable for interactive free-form shape design.     

一种针对复杂曲面的快速自由交互拾取算法

三维模型的交互拾取作为最直观的人机交互方式,在各个领域都有广泛地应用,如几何建模、 3D 游戏和有限元分析等。针对目前含有复杂曲面模型的拾取效率和拾取自由度低等问题,提出了一种对复杂 曲面的快速自由交互拾取算法。首先采用一种类似画刷的工具,对画刷在屏幕中移动的路径进行离散,接着对 每一个离散点应用基于 BVH 结构的单点拾取法来拾取复杂曲面,然后用 2 个哈希结构降低算法的响应时间, 最后对该算法进行了验证。     

Detailed 3D reconstruction of large-scale heritage sites with integrated techniques

Many cultural heritage applications require 3D reconstruction of real-world objects and scenes. Over the past few years, it has become increasingly common to use 3D digitization and modeling for this purpose. This is mainly due to advances in laser-scanning techniques, 3D modeling software, image-based modeling techniques, computer power, and virtual reality. Our approach integrates several technologies based on our experience over more than a decade of trying to accurately and completely model large-scale heritage monuments and sites. Using both interactive and automatic techniques, we can model a highly detailed structure or site at various levels of detail. We use image-based modeling for basic shape and structural elements, and laser scanning for fine details and sculpted surfaces. To present the site in its proper context, we use image-based rendering for landscapes and surroundings. To apply this approach, we created hundreds of models from sites all over the world for documentation, walk-through movies, and interactive visualization. The results were compelling and encouraging.     

Globally optimal surface mapping for surfaces with arbitrary topology

Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in computer graphics and such a method provides us a ubiquitous tool for geometric modeling and data visualization. Its vast variety of applications includes shape registration/matching, shape blending, material/data transfer, data fusion, information reuse, etc. The mapping quality is typically measured in terms of angular distortions among different shapes. This paper proposes and develops a novel quasi-conformal surface mapping framework to globally minimize the stretching energy inevitably introduced between two different shapes. The existing state-of-the-art inter-surface mapping techniques only afford local optimization either on surface patches via boundary cutting or on the simplified base domain, lacking rigorous mathematical foundation and analysis. We design and articulate an automatic variational algorithm that can reach the global distortion minimum for surface mapping between shapes of arbitrary topology, and our algorithm is sorely founded upon the intrinsic geometry structure of surfaces. To our best knowledge, this is the first attempt towards numerically computing globally optimal maps. Consequently, our mapping framework offers a powerful computational tool for graphics and visualization tasks such as data and texture transfer, shape morphing, and shape matching.