Shape Reconstruction of 3D Bilaterally Symmetric Surfaces

The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoint and the illumination are not necessarily frontal. Furthermore, no correspondence between symmetric points is required.The basic idea is that an image taken from a general, non frontal viewpoint, under non-frontal illumination can be regarded as a pair of images. Each image of the pair is one half of the object, taken from different viewing positions and with different lighting directions. Thus, one-image-variants of geometric stereo and of photometric stereo can be used. Unlike the separate invocation of these approaches, which require point correspondence between the two images, we show that integrating the photometric and geometric information suffice to yield a dense correspondence between pairs of symmetric points, and as a result, a dense shape recovery of the object. Furthermore, the unknown lighting and viewing parameters, are also recovered in this process.Unknown distant point light source, Lambertian surfaces, unknown constant albedo, and weak perspective projection are assumed. The method has been implemented and tested experimentally on simulated and real data.     

物体三维形状恢复的遗传算法方法

提出了一种新的物体三维形状恢复的遗传算法方法。用固定位置的摄像机在不同位置的球扩展光源下获取图象序列,并用遗传算法对物体表面每一点的法线矢量进行快速搜索。实验结果表明,此方法能有效地恢复扩展光源下物体的三维形状。不仅放宽了对光源和物体表面的限制,而且精度及鲁棒性均有很大提高。     

3D Structure Recovery and Unwarping of Surfaces Applicable to Planes

The deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry (lengths and areas are conserved) and vanishing Gaussian curvature. We show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape. We show that these partial differential equations can be reduced to the Hopf equation that arises in non-linear wave propagation, and deformations of the paper can be interpreted in terms of the characteristics of this equation. A new exact integration of these equations is developed that relates the 3-D structure of the applicable surface to an image. The solution is tested by comparison with particular exact solutions. We present results for both the forward and the inverse 3D structure recovery problem.     

Estimation of 3D Surface Shape and Smooth Radiance from 2D Images: A Level Set Approach

We cast the problem of shape reconstruction of a scene as the global region segmentation of a collection of calibrated images. We assume that the scene is composed of a number of smooth surfaces and a background, both of which support smooth Lambertian radiance functions. We formulate the problem in a variational framework, where the solution (both the shape and radiance of the scene) is a minimizer of a global cost functional which combines a geometric prior on shape, a smoothness prior on radiance and a data fitness score. We estimate the shape and radiance via an alternating minimization: The radiance is computed as the solutions of partial differential equations defined on the surface and the background. The shape is estimated using a gradient descent flow, which is implemented using the level set method. Our algorithm works for scenes with smooth radiances as well as fine homogeneous textures, which are known challenges to traditional stereo algorithms based on local correspondence.     

基于粗糙表面模型的三维形貌恢复研究

文中提出了一种针对粗糙物体的表面反射模型,即用Oren-Nayar模型代替通用的朗伯体表面反射模型(Lamber-tian surface reflection model),并基于透视投影从明暗恢复形状(shape from shading),对图像进行三维重建,此三维重建具有很高的现实意义.实验用该模型对两幅较粗糙的真实图像进行重建并与在朗伯体模型下得到的结果进行比较,实验结果表明对于粗糙物体文中方法能得到较好的恢复效果,说明本SFS方法是有效且收敛的.     

Deformable Pedal Curves and Surfaces: Hybrid Geometric Active Models for Shape Recovery

In this paper, we propose significant extensions to the snake pedal model, a powerful geometric shape modeling scheme introduced in (Vemuri and Guo, 1998). The extension allows the model to automatically cope with topological changes and for the first time, introduces the concept of a compact global shape into geometric active models. The ability to characterize global shape of an object using very few parameters facilitates shape learning and recognition. In this new modeling scheme, object shapes are represented using a parameterized function—called the generator—which accounts for the global shape of an object and the pedal curve (surface) of this global shape with respect to a geometric snake to represent any local detail. Traditionally, pedal curves (surfaces) are defined as the loci of the feet of perpendiculars to the tangents of the generator from a fixed point called the pedal point. Local shape control is achieved by introducing a set of pedal points—lying on a snake—for each point on the generator. The model dubbed as a snake pedal allows for interactive manipulation via forces applied to the snake. In this work, we replace the snake by a geometric snake and derive all the necessary mathematics for evolving the geometric snake when the snake pedal is assumed to evolve as a function of its curvature. Automatic topological changes of the model may be achieved by implementing the geometric snake in a level-set framework. We demonstrate the applicability of this modeling scheme via examples of shape recovery from a variety of 2D and 3D image data.     

Direct Differential Photometric Stereo Shape Recovery of Diffuse and Specular Surfaces

Recovering the 3D shape of an object from shading is a challenging problem due to the complexity of modeling light propagation and surface reflections. Photometric Stereo (PS) is broadly considered a suitable approach for high-resolution shape recovery, but its functionality is restricted to a limited set of object surfaces and controlled lighting setup. In particular, PS models generally consider reflection from objects as purely diffuse, with specularities being regarded as a nuisance that breaks down shape reconstruction. This is a serious drawback for implementing PS approaches, since most common materials have prominent specular components. In this paper, we propose a PS model that solves the problem for both diffuse and specular components aimed at shape recovery of generic objects with the approach being independent of the albedo values thanks to the image ratio formulation used. Notably, we show that by including specularities, it is possible to solve the PS problem for a minimal number of three images using a setup with three calibrated lights and a standard industrial camera. Even if an initial separation of diffuse and specular components is still required for each input image, experimental results on synthetic and real objects demonstrate the feasibility of our approach for shape reconstruction of complex geometries.     

基于形变模型由立体序列图象恢复物体的3D形状

结合立体视觉和形变模型提出了一种新的物体3D形状的恢复方法。采用立体视觉方法导出物体表面的3D坐标;利用光流模型估计物体的3D运动,根据此运动移动形变模型,使其对准物体的表面块;由形变模型将由各幅图象得到的离散的3D点融为一起,得到物体的表面形状。实验结果表明该方法能用于形状复杂的物体恢复。     

3D-FUTURE: 3D Furniture Shape with TextURE

International Journal of Computer Vision - The 3D CAD shapes in current 3D benchmarks are mostly collected from online model repositories. Thus, they typically have insufficient geometric details...     

Efficient 2D Simulation on Moving 3D Surfaces

We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation on this base animation. In general, we solve a partial differential equation (PDE) on a level set surface obtained from the animated input surface. The properties of the input surface are transferred to a sparse volume data structure that is then used for the simulation. We introduce one-way coupling strategies from input properties to our simulation and we add conservation of mass and momentum to existing methods that solve a PDE in a narrow-band using the Closest Point Method. In this way, we efficiently compute high-resolution 2D simulations on coarse input surfaces. Our approach helps visual effects creators easily integrate a workflow to simulate material flow on evolving surfaces into their existing production pipeline.     

边界对齐的平滑三维对称标架场

为了把广泛应用于网格四边形化和纹理合成的二维表面标架场拓展到三维,提出一种生成三维对称标架场的方法.不同于表面对称标架场(四对称方向场),二维标架场的对称性能用一个切平面的旋转角度来表示,而三维对称标架场的对称性却不能这样简单地表示.为了解决这个问题,利用球面函数来获得一个对称性表述,该表述对于绕任意一个轴的π/2旋转以及它们的复合是不变的.基于球面函数的表示可以获得一个有效的标架场光顺程度的度量,并以球面调和分析进行加速计算;基于一组边界约束,可以通过极小化这个度量函数来获得一个光顺的标架场,该标架场在表面上能很好地对齐法线.最后通过表面投影、流线追踪和奇异点来可视化这个标架场,并将这个光顺的标架场用于六面体网格生成,且讨论了它在生成高质量纯六面体网格方面的潜力,其与表面标架场在生成四边形网格方面的潜力是一致的.     

基于图像辅助的三维模型形状检索

随着3D建模技术的快速发展,互联网上可用的3D模型库出现了爆炸式增长,越来越多的3D模型可以方便地通过网络下载使用.这直接促使了3D形状检索技术的发展,即给出特定的搜索信息,要求系统搜索出符合要求的、相似的3D模型.文章提出了一种新的3D形状检索方法,以3D模型作为输入,系统将会从模型数据库中自动检索出与输入形状最相似的模型.对于给定的输入模型以及数据库中的每一个模型,首先由计算机生成多幅在不同视角下的2D草图;然后,应用Gabor滤波器对每一幅2D草图提取图像上的局部特征,并对特征进行量化,从而得到代表该图像特征的直方图,这样对于每一个3D模型将得到多个代表该模型的直方图;最终,通过对比两个模型之间直方图的相似性,可以得到它们的相似性值,从而检索出与输入模型最相似的模型.文章所提出的方法通过采取2D图像分析方法提取能反映3D模型的特征并计算出模型之间的相似性值.经过测试,在一些公开的数据集上得到了较好的效果.     

BOXTREE: A Hierarchical Representation for Surfaces in 3D

We introduce the boxtree, a versatile data structure for representing triangulated or meshed surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient ray tracing and collision detection. It is simple and robust, and requires minimal space. In situations where storage is at a premium, boxtrees are effective alternatives to octrees and BSP trees. They are also more flexible and efficient than R-trees, and nearly as simple to implement.     

Smooth Stream Surfaces of Fourth Order Precision

We introduce a novel technique for the construction of smooth stream surfaces of 4th order precision. While common stream surface techniques use linear interpolation for generating seed points for new streamlines in the refinement phase, we use Hermite interpolation. The derivatives needed for Hermite interpolation are obtained by integration along the streamlines. This yields stream surfaces of4th order precision. Additionally, we analyse the accuracy ofthe well known Hultquist approach and our new algorithm and proof that Hultquist's method is exact for linear vector fields. We compare both methods using the well known distance based and a novel error based refinement strategy. Our resulting surface is C¹ -continuous, enabling improved rendering among other benefits.     

The Alignment of Objects with Smooth Surfaces

This paper examines the recognition of rigid objects bounded by smooth surfaces, using an alignment approach. The projected image of such an object changes during rotation in a manner that is generally difficult to predict. An approach to this problem is suggested, using the 3D surface curvature at the points along the silhouette. The curvature information requires a single number for each point along the object′s silhouette, the radial curvature at the point. We have implemented this method and tested it on images of complex 3D objects. Models of the viewed objects were acquired using three images of each object. The implemented scheme was found to give accurate predictions of the objects′ appearances for large transformations. Using this method, a small number of (viewer-centered) models can be used to predict the new appearance of an object from any given viewpoint.     

塑造n边形曲面的外形

提出了一种高效基于物理性质的算法来动态的塑造n边形曲面的外形.这种算法是基于曲面的物理性质.通过极小化一个能量泛函,用户能够直接使用不同形式的外力作为虚拟的塑造工具来改变n边形曲面的外形.用户也能够定义必要的几何约束来进一步控制曲面外形.与通常移动控制点的方法比较,这种基于物理性质的方法更直观和有效.     

Hierarchical Quad Meshing of 3D Scanned Surfaces

In this paper we present a novel method to reconstruct watertight quad meshes on scanned 3D geometry. There exist many different approaches to acquire 3D information from real world objects and sceneries. Resulting point clouds depict scanned surfaces as sparse sets of positional information. A common downside is the lack of normals, connectivity or topological adjacency data which makes it difficult to actually recover a meaningful surface. The concept described in this paper is designed to reconstruct a surface mesh despite all this missing information. Even when facing varying sample density, our algorithm is still guaranteed to produce watertight manifold meshes featuring quad faces only. The topology can be set‐up to follow superimposed regular structures or align naturally to the point cloud's shape. Our proposed approach is based on an initial divide and conquer subsampling procedure: Surface samples are clustered in meaningful neighborhoods as leafs of a kd‐tree. A representative sample of the surface neighborhood is determined for each leaf using a spherical surface approximation. The hierarchical structure of the binary tree is utilized to construct a basic set of loose tiles and to interconnect them. As a final step, missing parts of the now coherent tile structure are filled up with an incremental algorithm for locally optimal gap closure. Disfigured or concave faces in the resulting mesh can be removed with a constrained smoothing operator.     

3D点云形状补全GAN

在真实的扫描环境中,由于视线遮挡或技术人员操作不当,实际采集到的点云模型会存在形状不完整的问题.点云模型的不完整性会对后续应用产生严重的影响,因此提出3D点云形状补全GAN用于完成点云模型的形状补全.该网络的点云重建部分由PointNet中用于数据对齐的T-Net结构与3D点云AutoEncoder网络相结合,来完成预...