基于变分水平集的三维模型复杂孔洞修复*

针对三维模型重建后存在大量复杂孔洞的问题,提出一种孔洞修补算法。首先构造符号距离函数,孔洞所在曲面用静态符号距离函数的零水平集表达,另一动态符号距离函数表示初始曲面;借助隐式曲面上的变分水平集,引入全局凸优化能量模型,通过对其极小化诱导,从而将提取孔洞边缘的问题转化为维体上隐式曲面的演化过程;最后以提取到的孔洞边缘曲面作为初始观察面,通过卷积和合成两个交替的步骤进行体素扩散完成孔洞修补。实验表明该算法能够有效恢复复杂孔洞区域的显著几何特征,且适用于含有网格较多的模型的孔洞修复。     

GEncode: Geometry-driven compression for General Meshes

Performances of actual mesh compression algorithms vary significantly depending on the type of model it encodes. These methods rely on prior assumptions on the mesh to be efficient, such as regular connectivity, simple topology and similarity between its elements. However, these priors are implicit in usual schemes, harming their suitability for specific models. In particular, connectivity‐driven schemes are difficult to generalize to higher dimensions and to handle topological singularities. GEncode is a new single‐rate, geometry‐driven compression scheme where prior knowledge of the mesh is plugged into the coder in an explicit manner. It encodes meshes of arbitrary dimension without topological restrictions, but can incorporate topological properties, such as manifoldness, to improve the compression ratio. Prior knowledge of the geometry is taken as an input of the algorithm, represented by a function of the local geometry. This suits particularly well for scanned and remeshed models, where exact geometric priors are available. Compression results surfaces and volumes are competitive with existing schemes.     

On the Characterization of Absentee-Voxels in a Spherical Surface and Volume of Revolution in $${\mathbb Z}^3$$

We show that the construction of a digital sphere by circularly sweeping a digital semi-circle (generatrix) around its diameter results in the appearance of some holes (absentee-voxels) in its spherical surface of revolution. This incompleteness calls for a proper characterization of the absentee-voxels whose restoration in the surface of revolution can ensure the required completeness. In this paper, we present a characterization of the absentee-voxels using certain techniques of digital geometry and show that their count varies quadratically with the radius of the semi-circular generatrix. Next, we design an algorithm to fill up the absentee-voxels so as to generate a spherical surface of revolution, which is complete and realistic from the viewpoint of visual perception. We also show how the proposed technique for absentee-filling can be used to generate a variety of digital surfaces of revolution by choosing an arbitrary curve as the generatrix. We further show that covering a solid sphere by a set of complete spheres also results to an asymptotically larger count of absentees, which is cubic in the radius of the sphere. A complete characterization of the absentee-voxels that aids the subsequent generation of a solid digital sphere is also presented. Test results have been furnished to substantiate our theoretical findings.     

基于球面参数化的点模型渐变

为了获得光滑自然的点模型渐变效果,基于球面参数化,提出了一种鲁棒的渐变算法。该算法首先对源和目标模型进行球面参数化,使得参数化后的模型嵌入到单位球面上;然后在球面上自适应地对齐模型间的相应特征点,并将球面映射到矩形参数域上,基于该域建立模型间各采样点的对应关系;接着在渐变过程中,采用拉普拉斯算子计算出中间点模型的几何位置,以保持模型的细节;最后利用移动最小二乘曲面进行动态上采样,以消除中间模型的裂缝。实验结果表明,该算法具有良好匹配的采样点对应和光滑的渐变过程。     

Face Relighting from a Single Image under Arbitrary Unknown Lighting Conditions

In this paper, we present a new method to modify the appearance of a face image by manipulating the illumination condition, when the face geometry and albedo information is unknown. This problem is particularly difficult when there is only a single image of the subject available. Recent research demonstrates that the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace using a spherical harmonic representation. Moreover, morphable models are statistical ensembles of facial properties such as shape and texture. In this paper, we integrate spherical harmonics into the morphable model framework by proposing a 3D spherical harmonic basis morphable model (SHBMM). The proposed method can represent a face under arbitrary unknown lighting and pose simply by three low-dimensional vectors, i.e., shape parameters, spherical harmonic basis parameters, and illumination coefficients, which are called the SHBMM parameters. However, when the image was taken under an extreme lighting condition, the approximation error can be large, thus making it difficult to recover albedo information. In order to address this problem, we propose a subregion-based framework that uses a Markov random field to model the statistical distribution and spatial coherence of face texture, which makes our approach not only robust to extreme lighting conditions, but also insensitive to partial occlusions. The performance of our framework is demonstrated through various experimental results, including the improved rates for face recognition under extreme lighting conditions.     

Comprehensive Halftoning of 3D Scenes

The display of images on binary output hardware requires a halftoning step. Conventional halftoning algorithms approximate image values independently from the image content and often introduce artificial texture that obscures fine details. The objective of this research is to adapt a halftoning technique to 3D scene information and thus to enhance the display of computer generated 3D scenes. Our approach is based on the control of halftoning texture by the combination of ordered dithering and error diffusion techniques. We extend our previous work and enable a user to specify the shape, scale, direction, and contrast of the halftoning texture using an external buffer. We control texture shape by constructing a dither matrix from an arbitrary image or a procedural texture. Texture direction and scale are adapted to the external information by the mapping function. Texture contrast and the accuracy of tone reproduction are varied across the image using the error diffusion process. We halftone images of 3D scenes by using the geometry, position, and illumination information to control the halftoning texture. Thus, the texture provides visual cues and can be used to enhance the viewer's comprehension of the display.     

Local Shape from Mirror Reflections

We study the problem of recovering the 3D shape of an unknown smooth specular surface from a single image. The surface reflects a calibrated pattern onto the image plane of a calibrated camera. The pattern is such that points are available in the image where position, orientations, and local scale may be measured (e.g. checkerboard). We first explore the differential relationship between the local geometry of the surface around the point of reflection and the local geometry in the image.We then study the inverse problem and give necessary and sufficient conditions for recovering surface position and shape.We prove that surface position and shape up to third order can be derived as a function of local position, orientation and local scale measurements in the image when two orientations are available at the same point (e.g. a corner). Information equivalent to scale and orientation measurements can be also extracted from the reflection of a planar scene patch of arbitrary geometry, provided that the reflections of (at least) 3 distinctive points may be identified.We validate our theoretical results with both numerical simulations and experiments with real surfaces.     

Stereo‐Consistent Contours in Object Space

Notebook scribbles, art or technical illustrations—line drawings are a simplistic method to visually communicate information. Automated line drawings often originate from virtual 3D models, but one cannot trivially experience their three‐dimensionality. This paper introduces a novel concept to produce stereo‐consistent line drawings of virtual 3D objects. Some contour lines do not only depend on an objects geometry, but also on the position of the observer. To accomplish consistency between multiple view positions, our approach exploits geometrical characteristics of 3D surfaces in object space. Established techniques for stereo‐consistent line drawings operate on rendered pixel images. In contrast, our pipeline operates in object space using vector geometry, which yields many advantages: The position of the final viewpoint(s) is flexible within a certain window even after the contour generation, e.g. a stereoscopic image pair is only one possible application. Such windows can be concatenated to simulate contours observed from an arbitrary camera path. Various types of popular contour generators can be handled equivalently, occlusions are natively supported and stylization based on geometry characteristics is also easily possible.     

A Comprehensive and Versatile Camera Model for Cameras with Tilt Lenses

We propose camera models for cameras that are equipped with lenses that can be tilted in an arbitrary direction (often called Scheimpflug optics). The proposed models are comprehensive: they can handle all tilt lens types that are in common use for machine vision and consumer cameras and correctly describe the imaging geometry of lenses for which the ray angles in object and image space differ, which is true for many lenses. Furthermore, they are versatile since they can also be used to describe the rectification geometry of a stereo image pair in which one camera is perspective and the other camera is telecentric. We also examine the degeneracies of the models and propose methods to handle the degeneracies. Furthermore, we examine the relation of the proposed camera models to different classes of projective camera matrices and show that all classes of projective cameras can be interpreted as cameras with tilt lenses in a natural manner. In addition, we propose an algorithm that can calibrate an arbitrary combination of perspective and telecentric cameras (no matter whether they are tilted or untilted). The calibration algorithm uses a planar calibration object with circular control points. It is well known that circular control points may lead to biased calibration results. We propose two efficient algorithms to remove the bias and thus obtain accurate calibration results. Finally, we perform an extensive evaluation of the proposed camera models and calibration algorithms that establishes the validity and accuracy of the proposed models.     

Hybrid Geometric — Image Based Rendering

We present a Hybrid Geometric‐Image Based Rendering (HGIBR) system for displaying very complex geometrical models at interactive frame rates. Our approach replaces distant geometry with a combination of image‐based representations and geometry, while rendering nearby objects from geometry. Reference images are computed on demand, which means that no pre‐processing, or additional storage are necessary. We present results for a massive model of a whole offshore gas platform, to demonstrate that interactive frame rates can be maintained using the HGIBR approach. Our implementation runs on a pair of PCs, using commodity graphics hardware for fast 3D warping.     

Model-driven active visual tracking

We have previously demonstrated that the performance of tracking algorithms can be improved by integrating information from multiple cues in a model-driven Bayesian reasoning framework. Here we extend our work to active vision tracking, with variable camera geometry. Many existent active tracking algorithms avoid the problem of variable camera geometry by tracking view independent features, such as corners and lines. However, the performance of algorithms based on those single features will greatly deteriorate in the presence of specularities and dense clutter. We show, by integrating multiple cues and updating the camera geometry on-line, that it is possible to track a complicated object moving arbitrarily in three-dimensional (3D) space.We use a four degree-of-freedom (4-DoF) binocular camera rig to track three focus features of an industrial object, whose complete model is known. The camera geometry is updated by using the rig control commands and kinematic model of the stereo head. The extrinsic parameters are further refined by interpolation from a previously sampled calibration of the head work space.The 2D target position estimates are obtained by a combination of blob detection, edge searching and gray-level matching, with the aid of model geometrical structure projection using current estimates of camera geometry. The information is represented in the form of a probability density distribution, and propagated in a Bayes Net. The Bayesian reasoning that is performed in the 2D image is coupled by the rigid model geometry constraint in 3D space.An αβ filter is used to smooth the tracking pursuit and to predict the position of the object in the next iteration of data acquisition. The solution of the inverse kinematic problem at the predicted position is used to control the position of the stereo head.Finally, experiments show that the target undertaking arbitrarily 3D motion can be successfully tracked in the presence of specularities and dense clutter.     

统一的数字几何处理框架

随着三维几何模型在工业界的广泛应用，处理几信号的算法变得越来越重要。尽管近几年数字几何处理研究有了很大的进展，仍然缺乏一个类似于数字图像处理的统一解决方案。该文提出了任意网格的数字信号处理框架，很好地满足了这一需求。该框架的核心思想是通过为任意网格模型构造一个全局球面（或平面）参数化，把模型的所有属性转化为定义在球面（或平面）上的信号，然后采用球面（或平面）正交分析工具对这些信号做分析处理。在这两个框架下，所有的数字图像处理技术都可以被扩展到网格模型。该文还给出了包括滤波、多分辨率编辑和压缩在内的几种典型应用的实现方法和试验结果。     

The Geometry of Visual Space: About the Incompatibility between Science and Mathematics

We address the problem of a geometrical model of vision. This problem is interesting for at least two reasons. First, any theory of vision (human or computer) must decide which geometry should be used to represent perceived objects (e.g., Euclidean vs projective). We believe that this representation should be compatible with geometrical properties of the imaging device (eye or camera). Second, the analysis of geometrical properties of vision will examine the usefulness of standard geometries and can lead to progress in mathematics itself. We analyze the geometry of image formation and show that human vision appears to involve a new branch of geometry whose properties are quite different from the properties of traditional geometries. We formulate these properties and use them to derive models of shape perception. Finally, we provide perceptual interpretations for our theoretical analyses.     

Image‐to‐Geometry Registration: a Mutual Information Method exploiting Illumination‐related Geometric Properties

This work concerns a novel study in the field of image‐to‐geometry registration. Our approach takes inspiration from medical imaging, in particular from multi‐modal image registration. Most of the algorithms developed in this domain, where the images to register come from different sensors (CT, X‐ray, PET), are based on Mutual Information, a statistical measure of non‐linear correlation between two data sources. The main idea is to use mutual information as a similarity measure between the image to be registered and renderings of the model geometry, in order to drive the registration in an iterative optimization framework. We demonstrate that some illumination‐related geometric properties, such as surface normals, ambient occlusion and reflection directions can be used for this purpose. After a comprehensive analysis of such properties we propose a way to combine these sources of information in order to improve the performance of our automatic registration algorithm. The proposed approach can robustly cover a wide range of real cases and can be easily extended.     

Implementation of 3D mesh streaming and compression techniques in NVEs

In this paper, we present a framework that integrates three‐dimensional (3D) mesh streaming and compression techniques and algorithms into our EVE‐II networked virtual environments (NVEs) platform, in order to offer support for large‐scale environments as well as highly complex world geometry. This framework allows the partial and progressive transmission of 3D worlds as well as of separate meshes, achieving reduced waiting times for the end‐user and improved network utilization. We also present a 3D mesh compression method focused on network communication, which is designed to support progressive mesh transmission, offering a fast and effective means of reducing the storage and transmission needs for geometrical data. This method is integrated in the above framework and utilizes prediction to achieve efficient lossy compression of 3D geometry. Copyright © 2006 John Wiley & Sons, Ltd.     

Spherical surface parameterization for perspective shape from shading

We propose a new mathematical formulation for perspective shape from shading (PSFS) problems. Our approach is based on representing the unknown surface as a spherical surface, expressed by Euclidean distance to the optical centre, as opposed to the traditional representation by distance from the image plane. We show that our parameterization is better suited for perspective camera models and results in simpler models and equations for classical PSFS problems with a light source in the optical centre. The unknown distance field satisfies a simple isotropic Eikonal equation on the unit sphere in the case of a Lambertian surface reflection model. This is in contrast to previous methods with depth field parameterization, which result in anisotropic equations. Adding light attenuation to the model, we show that the distance field satisfies an Eikonal type of equation with a zero order term. We show how both Eikonal equations can be approximated by very efficient Fast Marching methods. A number of numerical tests and examples are provided to demonstrate our approach, and to compare with previous work. Our results indicate competitive accuracy and computational time that are several orders of magnitude faster than state-of-the-art iterative algorithms. A preliminary investigation indicates that our method could be used in more general PSFS problems.     

Subdivision connectivity remeshing and its applications

This paper presents a subdivision connectivity remeshing approach for closed genus 0 meshes. It is based on spherical parameterization and umbrella‐operator smoothing. Our main contribution lies in adopting a low‐distortion spherical parameterization approach to generate high‐quality subdivision connectivity meshes. Besides, a simple and efficient point location method on the sphere based on the uniform partition of the rectangle is presented, which is used to find the containing triangle in the spherical mesh for each point on the sphere rapidly. Our method can generate high‐quality subdivision connectivity meshes fast, which can be applied to level of detail and progressive transmission. All the application examples demonstrate that our remeshing procedure is robust and efficient. Copyright © 2011 John Wiley & Sons, Ltd.