Representing Quadric Surfaces Using NURBS Surfaces

A method for representing quadrc surfaces using NURBS is presented.By means of the necessary and sufficient conditons for NURBS curves to precisely represent circular arcs and other conics,quadric surfaces can be represented by NURBS surfaces with fewer control vertices.The method can be used not only for NURBS surface representation of quadric surfaces,but also for rounding polyhedrons.Many examples are given in the paper.     

二次代数曲面拼接中的光顺处理

针对直接采用理想交理论得到的拼接曲面在实际中不一定连续的问题,研究如何通过改变拼接曲面的构造方程以得到连续的拼接曲面及其光顺处理。首先,分析了拼接曲面在实际应用不连续的原因,若过渡曲面中含某个变元的项在其他变元满足某个值时变为0,则其与该变元不再相关,在几何图形上会表现为断开;然后,给出了保证拼接曲面在实际应用中连续的方法;之后,讨论了0阶和任意阶拼接曲面的光顺处理方法。对于0阶光滑连续曲面,将辅助曲面作为因子乘以一次函数后补偿到构造方程中的主曲面部分,调节参数使得拼接曲面光顺;对于任意阶连续曲面,在主曲面过渡方程中直接增加补偿函数。该方法可使0阶光滑连续曲面在不提高次数的情况下做到光顺。     

全向立体成像系统场景深度估计

基于单相机双抛物面反射镜设计了一种共轴结构的折反射全向立体成像装置,给出了针对相应展开柱面全景立体图像对深度估计的应点匹配方法,最后通过3D Max构造相应虚拟装置和虚拟场景进行了仿真实验,初步证明了该结构设计和对应深度估计方法的有效性。     

Improved quadric surfaces recognition from scanned mechanical models

This paper presents a novel algorithm for identifying quadric surfaces from scanned mechanical models. We make several important improvements over the existing variational 3D shape segmentation framework, which utilizes Lloyd's iteration. First, instead of using randomized initialization(which likely falls into non-optimal minimum), the RANSAC-based initialization approach is adopted. Given a good initialization, our method converges quickly than previous approaches. Second, in order to enhance the stability and the robustness, we carefully modify the distortion-minimizing flooding algorithm by using seed regions instead of seed triangles. Third, the geometric constraints are introduced into the optimization framework. The segmentation quality is further improved. We validate the efficiency and the robustness of our proposed method on various datasets, and demonstrate that our method outperforms state-of-art approaches.     

A note on two-sided holes in implicit quadric spline surfaces

Some implicit spline surface schemes require filling two-sided holes [Dahmen 1989; Guo 1993] and a blending technique of Warren (1987) can be used to fill two-sided holes in quadric spline surfaces. This note shows that there are important cases where the blending technique does not apply. These cases are identified and an applicatble technique is proposed.     

A portable stereo vision system for whole body surface imaging

This paper presents a whole body surface imaging system based on stereo vision technology. We have adopted a compact and economical configuration which involves only four stereo units to image the frontal and rear sides of the body. The success of the system depends on a stereo matching process that can effectively segment the body from the background in addition to recovering sufficient geometric details. For this purpose, we have developed a novel sub-pixel, dense stereo matching algorithm which includes two major phases. In the first phase, the foreground is accurately segmented with the help of a predefined virtual interface in the disparity space image, and a coarse disparity map is generated with block matching. In the second phase, local least squares matching is performed in combination with global optimization within a regularization framework, so as to ensure both accuracy and reliability. Our experimental results show that the system can realistically capture smooth and complete whole body shapes with high accuracy.     

Interpolation on quadric surfaces with rational quadratic spline curves

Given a sequence of points {X_i}_i=1ⁿ on a regular quadric S: X^TAX = 0 ⊂ E^d, d ⩾ 3, we study the problem of constructing a G¹ rational quadratic spline curve lying on S that interpolates {X_i}_i=1ⁿ. It is shown that a necessary condition for the existence of a nontrivial interpolant is (X₁^TAX₂)(X_i^TAX_i+1) > 0, i = 1,2…,n − 1. Also considered is a Hermite interpolation problem on the quadric S: a biarc consisting of two conic arcs on S joined with G¹ continuity is used to interpolate two points on S and two associated tangent directions, a method similar to the biarc scheme in the plane (Bolton, 1975) or space (Sharrock, 1987). A necessary and sufficient condition is obtained on the existence of a biarc whose two arcs are not major elliptic arcs. In addition, it is shown that this condition is always fulfilled on a sphere for generic interpolation data.     

3-D shape reconstruction in an active stereo vision system using genetic algorithms

The recovery of 3-D shape information (depth) using stereo vision analysis is one of the major areas in computer vision and has given rise to a great deal of literature in the recent past. The widely known stereo vision methods are the passive stereo vision approaches that use two cameras. Obtaining 3-D information involves the identification of the corresponding 2-D points between left and right images. Most existing methods tackle this matching task from singular points, i.e. finding points in both image planes with more or less the same neighborhood characteristics. One key problem we have to solve is that we are on the first instance unable to know a priori whether a point in the first image has a correspondence or not due to surface occlusion or simply because it has been projected out of the scope of the second camera. This makes the matching process very difficult and imposes a need of an a posteriori stage to remove false matching.In this paper we are concerned with the active stereo vision systems which offer an alternative to the passive stereo vision systems. In our system, a light projector that illuminates objects to be analyzed by a pyramid-shaped laser beam replaces one of the two cameras. The projections of laser rays on the objects are detected as spots in the image. In this particular case, only one image needs to be treated, and the stereo matching problem boils down to associating the laser rays and their corresponding real spots in the 2-D image. We have expressed this problem as a minimization of a global function that we propose to perform using Genetic Algorithms (GAs). We have implemented two different algorithms: in the first, GAs are performed after a deterministic search. In the second, data is partitioned into clusters and GAs are independently applied in each cluster. In our second contribution in this paper, we have described an efficient system calibration method. Experimental results are presented to illustrate the feasibility of our approach. The proposed method yields high accuracy 3-D reconstruction even for complex objects. We conclude that GAs can effectively be applied to this matching problem.     

Omnistereo: panoramic stereo imaging

An omnistereo panorama consists of a pair of panoramic images, where one panorama is for the left eye and another panorama is for the right eye. The panoramic stereo pair provides a stereo sensation up to a full 360 degrees. Omnistereo panoramas can be constructed by mosaicing images from a single rotating camera. This approach also enables the control of stereo disparity, giving larger baselines for faraway scenes, and a smaller baseline for closer scenes. Capturing panoramic omnistereo images with a rotating camera makes it impossible to capture dynamic scenes at video rates and limits omnistereo imaging to stationary scenes. We present two possibilities for capturing omnistereo panoramas using optics without any moving parts. A special mirror is introduced such that viewing the scene through this mirror creates the same rays as those used with the rotating cameras. The lens used for omnistereo panorama is also introduced, together with the design of the mirror. Omnistereo panoramas can also be rendered by computer graphics methods to represent virtual environments     

Correspondenceless stereo and motion: planar surfaces

It is shown that a binocular observer can recover the depth and three-dimensional motion of a rigid planar patch without using any correspondences between the left and right image frames (static) or between the successive dynamic frames (dynamic). Uniqueness and robustness issues are studied with respect to this problem and experimental results are given from the application of the theory to real images     

Solid reconstruction using recognition of quadric surfaces from orthographic views

The reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided.     

A setup for panoramic stereo imaging

In this paper, based on the proposed basic implementation of circular projection, a multi-camera setup which can be used for panoramic stereo imaging is presented. Firstly, we get multiple stereo pairs instantly by fixing multiple cameras on the proposed setup, which is an approximate implementation of circular projection. We then prove that the influence on the resultant stereo pairs generated by this approximate setup is slight based on similar triangles and structural similarity (SSIM). With these stereo pairs, the automatic panoramic image stitching algorithm is applied to generate panoramas for both eyes. In addition, with reasonable distance between cameras and the scene, physical dimensions of this setup are given. Finally, experimental results demonstrate that our scheme can be used to generate cylindrical stereo panoramic image with proper scene depth, which can provide viewers with distinguishing stereoscopic experience. The device can be installed on the mobile equipment and captures panoramic stereo image in a moment without stopping. In the future, the proposed setup can be used in the field of network navigation, video monitor and virtual reality.     

Epipolar geometry of opti-acoustic stereo imaging

Optical and acoustic cameras are suitable imaging systems to inspect underwater structures, both in regular maintenance and security operations. Despite high resolution, optical systems have limited visibility range when deployed in turbid waters. In contrast, the new generation of high-frequency (MHz) acoustic cameras can provide images with enhanced target details in highly turbid waters, though their range is reduced by one to two orders of magnitude compared to traditional low-/midfrequency (10s-100s KHz) sonar systems. It is conceivable that an effective inspection strategy is the deployment of both optical and acoustic cameras on a submersible platform, to enable target imaging in a range of turbidity conditions. Under this scenario and where visibility allows, registration of the images from both cameras arranged in binocular stereo configuration provides valuable scene information that cannot be readily recovered from each sensor alone. We explore and derive the constraint equations for the epipolar geometry and stereo triangulation in utilizing these two sensing modalities with different projection models. Theoretical results supported by computer simulations show that an opti-acoustic stereo imaging system outperforms a traditional binocular vision with optical cameras, particularly for increasing target distance and (or) turbidity.     

Model-based interpretation of stereo imagery of textured surfaces

We present a scheme for reliable and accurate surface reconstruction from stereoscopic images containing only fine texture and no stable high-level features. Partial shape information is used to improve surface computation: first by fitting an approximate, global, parametric model, and then by refining this model via local correspondence processes. This scheme eliminates the window size selection problem in existing area-based stereo correspondence schemes. These ideas are integrated in a practical vision system that is being used by environmental scientists to study wind erosion of bulk material such as coal ore being transported in open rail cars. Received: 14 August 1995 / Accepted: 27 May 1997     

Robust active stereo vision using Kullback-Leibler divergence

Active stereo vision is a method of 3D surface scanning involving the projecting and capturing of a series of light patterns where depth is derived from correspondences between the observed and projected patterns. In contrast, passive stereo vision reveals depth through correspondences between textured images from two or more cameras. By employing a projector, active stereo vision systems find correspondences between two or more cameras, without ambiguity, independent of object texture. In this paper, we present a hybrid 3D reconstruction framework that supplements projected pattern correspondence matching with texture information. The proposed scheme consists of using projected pattern data to derive initial correspondences across cameras and then using texture data to eliminate ambiguities. Pattern modulation data are then used to estimate error models from which Kullback-Leibler divergence refinement is applied to reduce misregistration errors. Using only a small number of patterns, the presented approach reduces measurement errors versus traditional structured light and phase matching methodologies while being insensitive to gamma distortion, projector flickering, and secondary reflections. Experimental results demonstrate these advantages in terms of enhanced 3D reconstruction performance in the presence of noise, deterministic distortions, and conditions of texture and depth contrast.     

A mathematical framework for rigid contact detection between quadric and superquadric surfaces

The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C² continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton–Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C² continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super) ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.     

Fast panoramic stereo matching using cylindrical maximum surfaces.

This paper presents a fast panoramic stereo matching algorithm using a cylindrical maximum surface technique. The disparity for a pair of panoramic images is found in a cylindrical shaped correlation coefficient volume by obtaining the maximum surface rather than simply choosing a position that gives the maximum correlation coefficient value. The use of our cylindrical maximum surface technique ensures that the disparities obtained at the left and the right columns of the panoramic stereo images are properly constrained. Typical running time for a pair of 1324 x 120 images is about 0.33 s on a 1.7-GHz PC. A variety of real images have been tested, and good results have been obtained.     

一种主动式全景立体视觉传感器设计

现有的三维激光扫描仪无法实时、全自动地计算空间三维信息,需要对获得的点云数据进行配准.为解决这些问题,研制了一种新型主动式全景立体视觉传感器( ASODVS),并且从影响ASODVS测距精度的各个因素进行了分析.实验结果表明:设计的ASODVS能自动、实时地进行空间物点深度测量,并得到相应的点云数据.