Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity

Multiresolution shape representation is a very effective way to decompose surface geometry into several levels of detail. Geometric modeling with such representations enables flexible modifications of the global shape while preserving the detail information. Many schemes for modeling with multiresolution decompositions based on splines, polygonal meshes and subdivision surfaces have been proposed recently. In this paper we modify the classical concept of multiresolution representation by no longer requiring a global hierarchical structure that links the different levels of detail. Instead we represent the detail information implicitly by the geometric difference between independent meshes. The detail function is evaluated by shooting rays in normal direction from one surface to the other without assuming a consistent tesselation. In the context of multiresolution shape deformation, we propose a dynamic mesh representation which adapts the connectivity during the modification in order to maintain a prescribed mesh quality. Combining the two techniques leads to an efficient mechanism which enables extreme deformations of the global shape while preventing the mesh from degenerating. During the deformation, the detail is reconstructed in a natural and robust way. The key to the intuitive detail preservation is a transformation map which associates points on the original and the modified geometry with minimum distortion. We show several examples which demonstrate the effectiveness and robustness of our approach including the editing of multiresolution models and models with texture.     

织物模拟中的自适应网格剖分研究

本文提出一种在织物模拟中的动态网格剖分方法，针对传统模拟算法中因网格剖分固定和曲面整体网格均匀剖分造成模拟误差与计算耗费，分别从织物物理和几何角度出发，提出在动态模拟过程中的自适应的网格剖分方法。利用模拟过程中曲面片局部形变信息，对网格进行动态剖分与合并，有效提高了模拟效率。经实际应用表明：该算法具有模拟效率高、易于计算机实现等优点，特别在对非均匀形变物体模拟中，该算法从模拟效率和精度均得到满意结果。     

Multi-view Performance Capture of Surface Details

This paper presents a novel approach to recover true fine surface detail of deforming meshes reconstructed from multi-view video. Template-based methods for performance capture usually produce a coarse-to-medium scale detail 4D surface reconstruction which does not contain the real high-frequency geometric detail present in the original video footage. Fine scale deformation is often incorporated in a second pass by using stereo constraints, features, or shading-based refinement. In this paper, we propose an alternative solution to this second stage by formulating dense dynamic surface reconstruction as a global optimization problem of the densely deforming surface. Our main contribution is an implicit representation of a deformable mesh that uses a set of Gaussian functions on the surface to represent the initial coarse mesh, and a set of Gaussians for the images to represent the original captured multi-view images. We effectively find the fine scale deformations for all mesh vertices, which maximize photo-temporal-consistency, by densely optimizing our model-to-image consistency energy on all vertex positions. Our formulation yields a smooth closed form energy with implicit occlusion handling and analytic derivatives. Furthermore, it does not require error-prone correspondence finding or discrete sampling of surface displacement values. We demonstrate our approach on a variety of datasets of human subjects wearing loose clothing and performing different motions. We qualitatively and quantitatively demonstrate that our technique successfully reproduces finer detail than the input baseline geometry.     

Non-rigid 3D shape tracking from multiview video

We present a fast and efficient non-rigid shape tracking method for modeling dynamic 3D objects from multiview video. Starting from an initial mesh representation, the shape of a dynamic object is tracked over time, both in geometry and topology, based on multiview silhouette and 3D scene flow information. The mesh representation of each frame is obtained by deforming the mesh representation of the previous frame towards the optimal surface defined by the time-varying multiview silhouette information with the aid of 3D scene flow vectors. The whole time-varying shape is then represented as a mesh sequence which can efficiently be encoded in terms of restructuring and topological operations, and small-scale vertex displacements along with the initial model. The proposed method has the ability to deal with dynamic objects that may undergo non-rigid transformations and topological changes. The time-varying mesh representations of such non-rigid shapes, which are not necessarily of fixed connectivity, can successfully be tracked thanks to restructuring and topological operations employed in our deformation scheme. We demonstrate the performance of the proposed method both on real and synthetic sequences.     

Geometric texturing using level sets

We present techniques for warping and blending (or subtracting) geometric textures onto surfaces represented by high resolution level sets. The geometric texture itself can be represented either explicitly as a polygonal mesh or implicitly as a level set. Unlike previous approaches, we can produce topologically connected surfaces with smooth blending and low distortion. Specifically, we offer two different solutions to the problem of adding fine-scale geometric detail to surfaces. Both solutions assume a level set representation of the base surface which is easily achieved by means of a mesh-to-level-set scan conversion. To facilitate our mapping, we parameterize the embedding space of the base level set surface using fast particle advection. We can then warp explicit texture meshes onto this surface at nearly interactive speeds or blend level set representations of the texture to produce high-quality surfaces with smooth transitions.     

Direct Reconstruction of a Displaced Subdivision Surface from Unorganized Points

In this paper we describe the generation of a displaced subdivision surface directly from a set of unorganized points. The displaced subdivision surface is an efficient mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface and has many benefits including compression, rendering, and animation, which overcome limitations of an irregular mesh produced by an ordinary mesh reconstruction scheme. Unlike previous displaced subdivision surface reconstruction methods, our method does not rely on a highly detailed reconstructed mesh. Instead, we efficiently create a coarse base mesh, which is used to sample displacements directly from unorganized points, and this results in a simple process and fast calculation. We suggest a shrink-wrapping-like shape approximation and a point-based mesh simplification method that uses the distance between a set of points and a mesh as an error metric to generate a domain surface that optimally approximates the given points. We avoid time-consuming energy minimization by employing a local subdivision surface fitting scheme. Finally, we show several reconstruction results that demonstrate the usability of our algorithm.     

A Semi‐Lagrangian Closest Point Method for Deforming Surfaces

We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.     

Accurate and scalable surface representation and reconstruction from images

We introduce a new surface representation method, called patchwork, to extend three-dimensional surface reconstruction capabilities from multiple images. A patchwork is the combination of several patches that are built one by one. This design potentially allows for the reconstruction of an object with arbitrarily large dimensions while preserving a fine level of detail. We formally demonstrate that this strategy leads to a spatial complexity independent of the dimensions of the reconstructed object and to a time complexity that is linear with respect to the object area. The former property ensures that we never run out of storage and the latter means that reconstructing an object can be done in a reasonable amount of time. In addition, we show that the patchwork representation handles equivalently open and closed surfaces, whereas most of the existing approaches are limited to a specific scenario, an open or closed surface, but not both. The patchwork concept is orthogonal to the method chosen for surface optimization. Most of the existing optimization techniques can be cast into this framework. To illustrate the possibilities offered by this approach, we propose two applications that demonstrate how our method dramatically extends a recent accurate graph technique based on minimal cuts. We first revisit the popular carving techniques. This results in a well-posed reconstruction problem that still enjoys the tractability of voxel space. We also show how we can advantageously combine several image-driven criteria to achieve a finely detailed geometry by surface propagation. These two examples demonstrate the versatility and flexibility of patchwork reconstruction. They underscore other properties inherited from patchwork representation: Although some min-cut methods have difficulty in handling complex shapes (e.g., with complex topologies), they can naturally manipulate any geometry through the patchwork representation while preserving their intrinsic qualities. The above properties of patchwork representation and reconstruction are demonstrated with real image sequences.     

Stable Real-Time Surgical Cutting Simulation of Deformable Objects Embedded with Arbitrary Triangular Meshes

Surgical simulators need to simulate deformation and cutting of deformable objects. Adaptive octree mesh based cutting methods embed the deformable objects into octree meshes that are recursively refined near the cutting tool trajectory. Deformation is only applied to the octree meshes; thus the deformation instability problem caused by degenerated elements is avoided. Biological tissues and organs usually contain complex internal structures that are ignored by previous work. In this paper the deformable objects are modeled as voxels connected by links and embedded inside adaptive octree meshes. Links swept by the cutting tool are disconnected and object surface meshes are reconstructed from disconnected links. Two novel methods for embedding triangular meshes as internal structures are proposed. The surface mesh embedding method is applicable to arbitrary triangular meshes, but these meshes have no physical properties. The material sub-region embedding method associates the interiors enclosed by the triangular meshes with physical properties, but requires that these meshes are watertight, and have no self-intersections, and their smallest features are larger than a voxel. Some local features are constructed in a pre-calculation stage to increase simulation performance. Simulation tests show that our methods can cut embedded structures in a way consistent with the cutting of the deformable objects. Cut fragments can also deform correctly along with the deformable objects.     

一种基于物理的实时细节保持变形算法

实时变形是计算机图形学研究的热点问题之一,复杂物体的实时变形至今仍未得到很好的解决.从物理变形方法和多分辨率网格编辑技术的优点出发,提出了一种适合于复杂弹性物体的实时变形算法.在预处理阶段,将原始精细网格模型进行简化以建立其基网格表示,基于基网格对模型的局部细节特征进行编码;在实时绘制阶段,在基网格上进行物理变形操作,并通过变形后的基网格和细节编码重构出变形后的精细网格.以上过程充分利用图形硬件的并行处理能力,利用像素处理器进行大部分计算操作.实验结果表明,该算法在变形过程中较好地保持了物体的局部特征,适合于表面细节复杂物体的实时变形应用.     

Automatic Conversion of Mesh Animations into Skeleton-based Animations

Recently, it has become increasingly popular to represent animations not by means of a classical skeleton‐based model, but in the form of deforming mesh sequences. The reason for this new trend is that novel mesh deformation methods as well as new surface based scene capture techniques offer a great level of flexibility during animation creation. Unfortunately, the resulting scene representation is less compact than skeletal ones and there is not yet a rich toolbox available which enables easy post‐processing and modification of mesh animations. To bridge this gap between the mesh‐based and the skeletal paradigm, we propose a new method that automatically extracts a plausible kinematic skeleton, skeletal motion parameters, as well as surface skinning weights from arbitrary mesh animations. By this means, deforming mesh sequences can be fully‐automatically transformed into fullyrigged virtual subjects. The original input can then be quickly rendered based on the new compact bone and skin representation, and it can be easily modified using the full repertoire of already existing animation tools.     

Locally Injective Mappings

Mappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that modifies any deformation energy to guarantee a locally injective mapping, i.e., without inverted elements. Our formulation can be used to compute continuous planar or volumetric piecewise‐linear maps and it uses a barrier term to prevent inverted elements. Differently from previous methods, we carefully design both the barrier term and the associated numerical techniques to be able to provide immediate feedback to the user, enabling interactive manipulation of inversion‐free mappings. Stress tests show that our method robustly handles extreme deformations where previous techniques converge very slowly or even fail. We demonstrate that enforcing local injectivity increases fidelity of the results in applications such as shape deformation and parameterization.     

Rigidity controllable as-rigid-as-possible shape deformation

Shape deformation is one of the fundamental techniques in geometric processing. One principle of deformation is to preserve the geometric details while distributing the necessary distortions uniformly. To achieve this, state-of-the-art techniques deform shapes in a locally as-rigid-as-possible (ARAP) manner. Existing ARAP deformation methods optimize rigid transformations in the 1-ring neighborhoods and maintain the consistency between adjacent pairs of rigid transformations by single overlapping edges. In this paper, we make one step further and propose to use larger local neighborhoods to enhance the consistency of adjacent rigid transformations. This is helpful to keep the geometric details better and distribute the distortions more uniformly. Moreover, the size of the expanded local neighborhoods provides an intuitive parameter to adjust physical stiffness. The larger the neighborhood is, the more rigid the material is. Based on these, we propose a novel rigidity controllable mesh deformation method where shape rigidity can be flexibly adjusted. The size of the local neighborhoods can be learned from datasets of deforming objects automatically or specified by the user, and may vary over the surface to simulate shapes composed of mixed materials. Various examples are provided to demonstrate the effectiveness of our method.     

Interactive modeling of complex geometric details based on empirical mode decomposition for multi-scale 3D shapes

In this paper we develop an interactive modeling system for complex geometric details transformation based on empirical mode decomposition (EMD) on multi-scale 3D shapes. Given two models, we aim to transfer geometric details from one model to another one in an interactive manner. Taking full advantages of the multi-scale representation computed via EMD, different-scale geometric details can be transferred individually or in a concerted way, which makes our algorithm much more flexible than cut-and-paste and cloning based methods in transferring geometry details. In this process, the target surface with new transferred details could be generated by a mesh reconstruction method widely used in Laplacian surface editing. With the original positions of target surface serving as the soft constraints, the overall shape of the target model will be fully preserved. Our method can also support real-time continuous details transfer. Compared with state-of-the-art algorithms, our method provides an easier-to-use modeling tool and produces varied modeling results. We demonstrate the effectiveness of our modeling tool with various applications, such as detail transfer and enrichment, model reuse and recreation, and detail recovery for shape completion.     

Generation of accurate integral surfaces in time-dependent vector fields

We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces.     

基于模版的三角网格拓扑压缩

提出一种基于面的高效三角网格拓扑压缩算法.该算法是单分辨率无损压缩算法,是对Edgebreaker算法的改进:在网格遍历部分,通过自适应网格遍历方法使非常影响压缩比的分割图形操作尽可能少;在熵编码部分,为网格遍历后得到的每个操作符各设计一个模版,根据模版确定该操作符的二进制表示,然后采用自适应算术编码方法压缩该二进制表示得到最后的压缩结果.与网格拓扑压缩领域中基于面的最好的算法得到的压缩比相比较,该算法得到的压缩比有很大提高.     

The 3D Model Acquisition Pipeline

Three-dimensional (3D) image acquisition systems are rapidly becoming more affordable, especially systems based on commodity electronic cameras. At the same time, personal computers with graphics hardware capable of displaying complex 3D models are also becoming inexpensive enough to be available to a large population. As a result, there is potentially an opportunity to consider new virtual reality applications as diverse as cultural heritage and retail sales that will allow people to view realistic 3D objects on home computers.
Although there are many physical techniques for acquiring 3D data—including laser scanners, structured light and time-of-flight—there is a basic pipeline of operations for taking the acquired data and producing a usable numerical model. We look at the fundamental problems of range image registration, line-of-sight errors, mesh integration, surface detail and color, and texture mapping. In the area of registration we consider both the problems of finding an initial global alignment using manual and automatic means, and refining this alignment with variations of the Iterative Closest Point methods. To account for scanner line-of-sight errors we compare several averaging approaches. In the area of mesh integration, that is finding a single mesh joining the data from all scans, we compare various methods for computing interpolating and approximating surfaces. We then look at various ways in which surface properties such as color (more properly, spectral reflectance) can be extracted from acquired imagery. Finally, we examine techniques for producing a final model representation that can be efficiently rendered using graphics hardware.     

Robust mesh editing using Laplacian coordinates

Shape deformation and editing are important for animation and game design. Laplacian surface based methods have been widely investigated and used in many works. In this paper we propose a robust mesh editing framework which improves traditional Laplacian surface editing. It consists of two procedures: skeleton based as-rigid-as-possible (ARAP) shape modeling and detail-preserving mesh optimization. Traditional ARAP shape modeling relies on the mesh quality. Degenerated mesh may adversely affect the deformation performance. A preprocessing step of mesh optimization can alleviate this problem. However, skinny triangles can still be generated during deformation, which adversely affect the editing performance. Thus our method performs Laplacian mesh deformation and optimization alternately in each iteration, which ensures mesh quality without noticeably increasing computational complexity or changing the shape details. This approach is more robust than those solely using Laplacian mesh deformation. An additional benefit is that the skeleton-based ARAP modeling can approximately preserve the volume of an object with large-scale deformations. The volume is roughly kept by leveraging the skeleton information and employing a carefully designed energy function to preserve the edge length. This method does not break the manifoldness of traditional ARAP methods or sacrifice speed. In our experiments, we show that (1) our method is robust even for degenerated meshes, (2) the deformation is natural in terms of recovering rotations, and (3) volumes are roughly kept even under large-scale deformations. The system achieves real time performance for surface meshes with 7k vertices.