3-D reconstruction from tomographic data using 2-D active contours.

Reconstructing three-dimensional (3-D) shapes of structures like internal organs from tomographic data is an important problem in medical imaging. Various forms of the deformable surface model have been proposed to tackle it, but they are either computationally expensive or limited to tubular shapes. In this paper a 3-D reconstruction mechanism that requires only 2-D deformations is proposed. Advantages of the proposed model include that it is conformable to any 3-D shape, efficient, and highly parallelizable. Most importantly, it requires from the user an initial 2-D contour on only one of the tomograph slices to start with. Experimental results are shown to illustrate the performance of the model.     

Acquiring 3-D models from sequences of contours

This paper explores shape from contour for acquiring 3-D graphics models. In this method, a continuous sequence of images is taken as an object rotates. A smooth convex shape can be estimated instantaneously from its contour and by the first derivative of contour movement (trace of contour, or contour distribution with time). We also analyze shapes that do not satisfy the conditions of smoothness and visibility, which are indispensable for modeling an object. A region that does not expose as contour yields a nonsmoothness in the tracked contour movement. We can thus detect such a region by contour distribution filtering and extract its accurate location by computing the left and right derivatives of the distribution. This has not been studied previously. These unknown regions are obtained for further investigation using other visual cues. A general approach for building a geometrical object model using contours is then described. The entire process from silhouettes to a 3-D model is based local computation; this is promising for producing shapes in real time. Our direct goal is to establish 3-D graphics models of human faces for the growing needs of visual communications. We have obtained some good results     

无二义性从轮廓线重建三维医学表面的新方法

设计了一种将轮廓线三维建模与多尺度二维图像处理技术相结合的新方法。该方法的核心是边缘距离图算法。该方法对于复杂环境下的重建结果优于传统方法,对于传统方法较难解决的复杂环境下轮廓线对应和分支问题,能较好地解决。并且,当原始切片纵向分辨率较低时,该方法有较高的抵抗插值噪声的能力。     

Perception of surfaces from line drawings

We test the perception of 3D surfaces that have been rendered by a set of lines drawn on the surface. Each surface is rendered as a family of curves which are in the simplest case the intersections with a family of parallel planes. On each trial, a surface or its “distorted” version is shown in this way, in an arbitrary orientation on an LCD screen or in a volumetric 3D display. The distortion is produced by stretching the surface in the z-direction by 30%. The subject’s task is to decide whether two sequentially presented surfaces are identical or not. The subject’s performance is measured by the discriminability d′, which is a conventional dependent variable in signal detection experiments. The work investigates the question whether a surface rendered with planar and geodesic curves is easier to recognize than one where the curves are not planar or not geodesic.     

Narrow band region-based active contours and surfaces for 2D and 3D segmentation

We describe a narrow band region approach for deformable curves and surfaces in the perspective of 2D and 3D image segmentation. Basically, we develop a region energy involving a fixed-width band around the curve or surface. Classical region-based methods, like the Chan–Vese model, often make strong assumptions on the intensity distributions of the searched object and background. In order to be less restrictive, our energy achieves a trade-off between local features of gradient-like terms and global region features. Relying on the theory of parallel curves and surfaces, we perform a mathematical derivation to express the region energy in a curvature-based form allowing efficient computation on explicit models. We introduce two different region terms, each one being dedicated to a particular configuration of the target object. Evolution of deformable models is performed by means of energy minimization using gradient descent. We provide both explicit and implicit implementations. The explicit models are a parametric snake in 2D and a triangular mesh in 3D, whereas the implicit models are based on the level set framework, regardless of the dimension. Experiments are carried out on MRI and CT medical images, in 2D and 3D, as well as 2D color photographs.     

Affine reconstruction of curved surfaces from uncalibrated views ofapparent contours

In this paper, we consider uncalibrated reconstruction of curved surfaces from apparent contours. Since apparent contours are not fixed features (viewpoint independent), we cannot directly apply the recent results of the uncalibrated reconstruction from fixed features. We show that, nonetheless, curved surfaces can be reconstructed up to an affine ambiguity from their apparent contours viewed from uncalibrated cameras with unknown linear translations. Furthermore, we show that, even if the reconstruction is nonmetric (non-Euclidean), we can still extract useful information for many computer vision applications just from the apparent contours. We first show that if the camera motion is linear translation (but arbitrary direction and magnitude), the epipolar geometry can be recovered from the apparent contours without using any optimization process. The extracted epipolar geometry is next used for reconstructing curved surfaces from the deformations of the apparent contours viewed from uncalibrated cameras. The result is applied to distinguishing curved surfaces from fixed features in images. It is also shown that the time-to-contact to the curved surfaces can be computed from simple measurements of the apparent contours     

Shape and orientation of revolution surfaces from contours and reflections

The reconstruction of shape and pose of a solid of revolution from a single image is addressed. When there is no cross section, whose contour can be extracted from the image, this problem is underdeterminate; therefore, a reflection from a point light source is used in addition to the contour information. Under the orthoperspective hypothesis, when axial-symmetric reflection model is applicable, the reflection appears along a meridian of the revolution surface. This fact is exploited in order to determine both the orientation of the revolution axis and the shape of the profile. Promising experimental results have been obtained.     

Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces

A new representation for parametric curves and surfaces is introduced here. It is in rational form and uses rational Gaussian bases. This representation allows design of 2-D and 3-D shapes, and makes recovery of shapes from noisy image data possible. The standard deviations of Gaussians in a curve or surface control the smoothness of a recovered shape. The control points of a surface in this representation are not required to form a regular grid and a scattered set of control points is sufficient to reconstruct a surface. Examples of shape design, shape recovery, and image segmentation using the proposed representation are given.     

Fast generation of 3-D deformable moving surfaces

Dynamic surface modeling is an important subject of geometric modeling due to their extensive applications in engineering design, entertainment and medical visualization. Many deformable objects in the real world are dynamic objects as their shapes change over time. Traditional geometric modeling methods are mainly concerned with static problems, therefore unsuitable for the representation of dynamic objects. Apart from the definition of a dynamic modeling problem, another key issue is how to solve the problem. Because of the complexity of the representations, currently the finite element method or finite difference method is usually used. Their major shortcoming is the excessive computational cost, hence not ideal for applications requiring real-time performance. We propose a representation of dynamic surface modeling with a set of fourth order dynamic partial differential equations (PDEs). To solve these dynamic PDEs accurately and efficiently, we also develop an effective resolution method. This method is further extended to achieve local deformation and produce n-sided patches. It is demonstrated that this new method is almost as fast and accurate as the analytical closed form resolution method and much more efficient and accurate than the numerical methods.     

Retrieving articulated 3-D models using medial surfaces

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. We demonstrate the use of this representation for 3-D object model retrieval. Our formulation uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. We present comparative retrieval results against the techniques of shape distributions (Osada et al.) and harmonic spheres (Kazhdan et al.) on 425 models from the McGill Shape Benchmark, representing 19 object classes. For objects with articulating parts, the precision vs recall curves using our method are consistently above and to the right of those of the other two techniques, demonstrating superior retrieval performance. For objects that are rigid, our method gives results that compare favorably with these methods. A preliminary version of this article was published in EMMCVPR 2005. In this extended version we have included results on the significantly larger McGill Shape Benchmark, making a stronger case for the advantages of our method for models with articulating parts. We have also included expanded introduction, medial surface computation, matching, indexing, experimental results, and discussion sections, along with several new figures.     

Object pose from 2-D to 3-D point and line correspondences

In this paper we present a method for optimally estimating the rotation and translation between a camera and a 3-D object from point and/or line correspondences. First we devise an error function and second we show how to minimize this error function. The quadratic nature of this function is made possible by representing rotation and translation with a dual number quaternion. We provide a detailed account of the computational aspects of a trust-region optimization method. This method compares favourably with Newton's method which has extensively been used to solve the problem at hand, with Faugeras-Toscani's linear method (Faugeras and Toscani 1986) for calibrating a camera, and with the Levenberg-Marquardt non-linear optimization method. Finally we present some experimental results which demonstrate the robustness of our method with respect to image noise and matching errors.This work has been supported by the Esprit programme through the SECOND project (Esprit-BRA No. 6769).     

Generating contours on FEM/BEM higher-order surfaces using Java 3D textures

An efficient technique to visualize primary and secondary results for combined finite element method/boundary element method models as contours is presented. The technique is based on dividing higher-order surfaces into triangles and on using texture interpolation to produce contour plots. Since results of high accuracy with significant gradients can be obtained using sparse meshes of boundary elements and finite elements, special attention is devoted to element face subdivision. Subdivision density is defined on the basis of both face edge curvature and ranges of result fields over element faces. Java 3D API is employed for code development.     

Determination of camera location from 2-D to 3-D line and pointcorrespondences

A method for the determination of camera location from two-dimensional (2-D) to three-dimensional (3-D) straight line or point correspondences is presented. With this method, the computations of the rotation matrix and the translation vector of the camera are separable. First, the rotation matrix is found by a linear algorithm using eight or more line correspondences, or by a nonlinear algorithm using three or more line correspondences, where the line correspondences are either given or derived from point correspondences. Then, the translation vector is obtained by solving a set of linear equations based on three or more line correspondences, or two or more point correspondences. Eight 2-D to 3-D line correspondences or six 2-D to 3-D point correspondences are needed for the linear approach; three 2-D to 3-D line or point correspondences for the nonlinear approach. Good results can be obtained in the presence of noise if more than the minimum required number of correspondences are used     

利用序列ISAR图像获取空间目标3-D信息的方法

如何从空间目标序列性二维(2-D,Two-Dimentional)逆合成孔径雷达(ISAR,Inverse Synthetic Aperture Radar)成像获取目标的三维(3-D)信息,是目标特征自动识别(ATR,Automatic Target Recognition)技术的重要研究课题。利用双向射线跟踪(BART,Bidirectional Analytic Ray Tracing)方法,计算连续多角度观测条件下空间目标的电磁散射数据,并由此获取空间目标的ISAR序列2-D图像。再利用KLT(Kanade-Lucas-Tomasi)特征跟踪算法,跟踪提取2\|D序列ISAR图像中的特征点(强散射点),获得其2-D坐标。然后,基于正交因式分解法(OFM,Orthographic Factorization Method),计算强散射点的3\|D坐标,获取空间目标的3-D信息。通过简单六棱柱模型,验证重构算法的精度;并以ENVISAT卫星模型为例,给出强散射点的3-D重构结果。结果表明,本文对空间目标3\|D信息获取方法能有效地从ISAR序列2-D图像中重构目标的三维信息。     

Matching 3-D anatomical surfaces with non-rigid deformations using octree-splines

This paper presents a new method for determining the minimal non-rigid deformation between two 3-D surfaces, such as those which describe anatomical structures in 3-D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3-D surfaces.     

Matching 3-D Models to 2-D Images

We consider the problem of analytically characterizing the set of all 2-D images that a group of 3-D features may produce, and demonstrate that this is a useful thing to do. Our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3-D to 2-D affine transformation. We show how to represent the set of images that a group of 3-D points produces with two lines (1-D subspaces), one in each of two orthogonal, high-dimensional spaces, where a single image group corresponds to one point in each space. The images of groups of oriented point features can be represented by a 2-D hyperbolic surface in a single high-dimensional space. The problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures. Moreover, we show that these are the simplest and lowest dimensional representations possible for these cases.We demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems. In particular, we use this result to build a space-efficient indexing system that performs 3-D to 2-D matching by table lookup. This system is analytically built and accessed, accounts for the effects of sensing error, and is tested on real images. We also derive new results concerning the existence of invariants and non-accidental properties in this domain. Finally, we show that oriented points present unexpected difficulties: indexing requires fundamentally more space with oriented than with simple points, we must use more images in a motion sequence to determine the affine structure of oriented points, and the linear combinations result does not hold for oriented points.     

Building 3-D Visual Perception of a Mobile Robot Employing Extended Kalman Filter

The paper aims at designing a novel scheme for sensory data fusion by a mobile robot for reconstructing its 3-D world from their multiple gray images. Extended Kalman filter has been employed for determining the coordinates of the 3-D vertices and equation of the planes of the obstacles in the robot's workspace from their multiple images. The geometric relations among these 3-D planes are then determined by using a logic program for recognizing the obstacles. The time required for recognition of a typical planer obstacle such as a box on a Pentium-III client with 64 MB RAM and a Pioneer-2 type robot server including the time involvement for the motion of the robot around the obstacle is approximately 18 seconds.     

A particular class of spline in reconstruction of revolution surfaces from 3-D data measured by CMM

In this paper, we tackle the problem of revolution surface reconstruction starting from a cloud of points measured by a coordinate-measuring machine. The proposed method is a mix of two mathematical techniques: approximation by λ integral quasi-interpolating spline and linear algebraic transformation. It takes into account that a surface of revolution can be described by rotating a single cross-section around a symmetric axis and the measured points are affected by manufacturing inaccuracy and measurement uncertainty. An experimental example shows that this approach gives more accurate results with respect to B-spline approximation.     

A Galerkin Method for the Simulation of the Transient 2-D/2-D and 3-D/3-D Linear Boltzmann Equation

Many production steps used in the manufacturing of integrated circuits involve the deposition of material from the gas phase onto wafers. Models for these processes should account for gaseous transport in a range of flow regimes, from continuum flow to free molecular or Knudsen flow, and for chemical reactions at the wafer surface. We develop a kinetic transport and reaction model whose mathematical representation is a system of transient linear Boltzmann equations. In addition to time, a deterministic numerical solution of this system of kinetic equations requires the discretization of both position and velocity spaces, each two-dimensional for 2-D/2-D or each three-dimensional for 3-D/3-D simulations. Discretizing the velocity space by a spectral Galerkin method approximates each Boltzmann equation by a system of transient linear hyperbolic conservation laws. The classical choice of basis functions based on Hermite polynomials leads to dense coefficient matrices in this system. We use a collocation basis instead that directly yields diagonal coefficient matrices, allowing for more convenient simulations in higher dimensions. The systems of conservation laws are solved using the discontinuous Galerkin finite element method. First, we simulate chemical vapor deposition in both two and three dimensions in typical micron scale features as application example. Second, stability and convergence of the numerical method are demonstrated numerically in two and three dimensions. Third, we present parallel performance results which indicate that the implementation of the method possesses very good scalability on a distributed-memory cluster with a high-performance Myrinet interconnect.