Perception of 3-D surfaces from 2-D contours

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. The authors survey classes of techniques proposed in the past and provide a critical analysis. They show that two kinds of symmetries in figures, which are known as parallel and skew symmetries, give significant information about surface shape for a variety of objects. They derive the constraints imposed by these symmetries and show how to use them to infer 3-D shape. They also discuss the zero Gaussian curvature (ZGC) surfaces in depth and show results on the recovery of surface orientation for various ZGC surfaces     

Fast generation of spherical slicing surfaces for irregular volume rendering

An efficient algorithm for generating a set of concentric spherical slicing surfaces for volume rendering of irregular volume datasets is presented. Our original algorithm, which approximates volume rendering by accumulating concentric spherical slicing surfaces from back to front, generates these surfaces by means of a conventional isosurface generation algorithm. However, this causes a performance bottleneck. To solve the problem, we propose a proliferous generation of slicing surfaces from seed cells, which are automatically determined according to the extremum points of the values of distances from a viewing point. A benchmark test shows that this approach can improve the performance significantly. In addition, we compare this algorithm with a raycasting algorithm that we proposed previously, and discuss a criterion for selecting which one to use for maximizing the performance     

Interpolation techniques for 3-D object generation

The technique of interpolation (or blending) and its generalization is considered in this paper. A unifying model for generating 3-D objects using this technique is presented. Various factors which affect the shape of generated objects are identified. Several illustrative examples of 3-D objects generated by this technique, using linear as well as non-linear interpolation, are presented. Although many of the objects have complex shapes, they are represented by simple closed form mathematical equations.     

Fast algorithm for 3-D vascular tree modeling

In this short paper, accelerated three-dimensional computer simulations of vascular trees development, preserving physiological and haemodynamic features, are reported. The new computation schemes deal: (i). with the geometrical optimization of each newly created bifurcation; and (ii). with the recalculation of blood pressures and radii of vessels in the whole tree. A significant decrease of the computation time is obtained by replacing the global optimization by the fast updating algorithm allowing more complex structure to be simulated. A comparison between the new algorithms and the previous one is illustrated through the hepatic arterial tree.     

Modeling deformable surfaces with level sets

This article describes how to use level sets to represent and compute deformable surfaces. A deformable surface is a sequence of surface models obtained by taking an initial model and incrementally modifying its shape. Typically, we can parameterize the deformation over time, and thus we can imagine that a surface moves or flows under the influence of a vector field. The surface flow, v, can be determined as a function of spatial position (and time), or it can depend on the shape of the surface itself. The latter is called a geometric flow. Deformable surfaces have been used to solve a variety of problems in image processing, computer vision, visualization, and graphics. In graphics, for instance, deformable surface models have been used to form sequences of shapes that animate the morphing of one object into another. They have also been used to denoise or smooth surface models derived from a set of noisy 3D measurements.     

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.     

Touch-enabled haptic modeling of deformable multi-resolution surfaces

Currently, interactive data exploration in virtual environments is mainly focused on vision-based and non-contact sensory channels such as visual/auditory displays. The lack of tactile sensation in virtual environments removes an important source of information to be delivered to the users. In this paper, we propose the touch-enabled haptic modeling of deformable multi-resolution surfaces in real time. The 6-DOF haptic manipulation is based on a dynamic model of Loop surfaces, where the dynamic parameters are computed easily without subdividing the control mesh recursively. A local deforming scheme is developed to approximate the solution of the dynamics equations, thus the order of the linear equations is reduced greatly. During each of the haptic interaction loop, the contact point is traced and reflected to the rendering of updated graphics and haptics. The sense of touch against the deforming surface is calculated according to the surface properties and the damping-spring force profile. Our haptic system supports the dynamic modeling of deformable Loop surfaces intuitively through the touch-enabled interactive manipulation.     

Animation of deformable models using implicit surfaces

The paper presents a general approach for designing and animating complex deformable models with implicit surfaces. Implicit surfaces are introduced as an extra layer coating any kind of structure that moves and deforms over time. Offering a compact definition of a smooth surface around an object, they provide an efficient collision detection mechanism. The implicit layer deforms in order to generate exact contact surfaces between colliding bodies. A simple physically based model approximating elastic behavior is then used for computing collision response. The implicit formulation also eases the control of the object's volume with a new method based on local controllers. We present two different applications that illustrate the benefits of these techniques. First, the animation of simple characters made of articulated skeletons coated with implicit flesh exploits the compactness and enhanced control of the model. The second builds on the specific properties of implicit surfaces for modeling soft inelastic substances capable of separation and fusion that maintain a constant volume when animated     

Monocular 3D tracking of deformable surfaces using sequential second order cone programming

Reconstructing structures of deformable objects from monocular image sequences is important for applications like visual servoing and augmented reality. In this paper, we propose a method to recover 3D shapes of deformable surfaces using sequential second order cone programming (SOCP). The key of our approach is to represent the surface as a triangulated mesh and introduce two sets of constraints, one for model-to-image keypoint correspondences which are SOCP constraints, another for retaining the original lengths of the mesh edges which are non-convex constraints. In the process of tracking, the surface structure is iteratively updated by solving sequential SOCP feasibility problems in which the non-convex constraints are replaced by a set of convex constraints over a local convex region. The shape constraints used in our approach is more generic than previous methods, that enables us to reliably recover surface shapes with smooth, sharp and other complex deformations. The capability and efficiency of our approach are evaluated quantitatively with synthetic image sequences and qualitatively with real image sequences.     

基于Harris的快速3-D特征点检测算子

图像匹配是数字摄影测量和计算机视觉领域中的关键技术.目前,基于特征点的匹配广泛应用于图像匹配中,至关重要的是如何定位特征点,高精度的特征点产生高精度的匹配结果.本文提出了3-D Harris特征点检测算子,分两个步骤实现:采用高斯算子平滑灰度突变点和利用Harris算子提出视频中的像素角点.实验结果表明了3-D Harris算子的高效性和精确性.     

基于FDK法的三维CT快速计算方法

在三维CT的图像重建过程中,单圆轨迹锥形束扫描是一种常用的方法,其算法普遍采用滤波反投影的形式(FBP)实现。由于滤波可以用FFT快速实现,因此反投影部分占据了计算的主要时间。论文提出同时从四个视角计算插值并作反投影累加,利用三角函数的周期性,减少传统算法中反投影阶段的乘法和正、余弦的计算次数,从而加快计算速度。分析和实验结果表明该方法对减少反投影计算所需的时间是行之有效的。     

超宽带穿墙雷达三维快速成像算法

超宽带穿墙雷达是一种能够隔墙探测和定位的新型实时成像雷达系统,在城区巷战,反恐斗争和人质救援中应用非常广泛.穿墙雷达对成像的实时性要求非常高,传统的成像算法已不能满足计算时间上的要求.本文将基于逆边界散射变换的快速成像算法应用到穿墙雷达系统中,利用FDTD数值仿真验证了对隐藏在墙后目标的三维成像结果,并分析了墙壁对目标定位误差的影响.研究表明,与传统的后向投影成像算法相比,基于逆边界散射变换的成像算法计算效率高,实时性好,且能对目标边界形状清晰成像.     

一种快速三维散乱点云的三角剖分算法

改进了一种三维散乱点云三角剖分算法。三角剖分是点云数据曲面重构的主要算法之一,但针对三维散乱点云的三角剖分存在剖分效率不高,剖分得到的三角曲面形状无法控制,细节特征表现不足的问题。提出了基于空间栅格划分的三角剖分算法,并提出了一个新的评价函数,以控制三角网格曲面的生长。实验证明,改进后的算法极大的提高了剖分效率,而且能保证最终生成的三角网格曲面平滑而保有丰富的细节特征,适用于在虚拟现实、曲面重构等领域推广使用。     

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.     

Dynamic interaction between deformable surfaces and nonsmooth objects

In this paper, we introduce new techniques that enhance the computational performance for the interactions between sharp objects and deformable surfaces. The new formulation is based on a time-domain predictor-corrector model. For this purpose, we define a new kind of (/spl pi/, /spl beta/, I)-surface. The partitioning of a deformable surface into a finite set of (/spl pi/, /spl beta/, I)-surfaces allows us to prune a large number of noncolliding feature pairs. This leads to a significant performance improvement in the collision detection process. The intrinsic collision detection is performed in the time domain. Although it is more expensive compared to the static interference test, it avoids portions of the surfaces passing through each other in a single time step. In order to resolve all the possible collision events at a given time, a penetration-free motion space is constructed for each colliding particle. By keeping the velocity of each particle inside the motion space, we guarantee that the current colliding feature pairs will not penetrate each other in the subsequent motion. A static analysis approach is adopted to handle friction by considering the forces acting on the particles and their velocities. In our formulation, we further reduce the computational complexity by eliminating the need to compute repulsive forces.     

Fast dimensional inspection of deformable parts from partial views

One of the conventional ways to inspect deformable parts is to compare a data model against its nominal CAD model. This process assumes that the data model includes most of the visible surface including regions around fixation points where the part will be attached to others. This paper proposes a method to inspect deformable part by acquiring only regions that need to be inspected and then by applying to the CAD model a non-linear deformation using FEM modeling to minimize the differences with the partial views. The process first starts with a rigid alignment followed by an iterative process where the part's deformation is iteratively matched to the partial views. In this scheme, fixation points are not digitized and the non-linear part deformation calculations are estimated by interpolation. Test results performed on real parts compares favorably to deformation calculations using complete data model from the point-of-view of speed and accuracy.     

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.     

三维Delaunay三角剖分快速点定位算法研究

提高点定位的速度是提高Delaunay三角剖分运行效率的关键。本文对四面体定位算法进行了研究,结合有向查找定位的技术,建立合理的数据结构,通过对每个搜索四面体只需计算三个面的法向量,优化了基于法向定位的算法,从减少算法中运算量的角度提高运行效率。该算法定位路径唯一,效率更高,而且具有较好的效果。     

Fast display of well-tesselated surfaces

Well-tesselated surfaces are piecewise planar functions on the sphere. Their planar faces are triangles which must meet a local geometric constraint. The faces may have arbitrary properties of transparency or reflectivity. These surfaces admit of simple hidden-line and -surface algorithms. In a raster graphics environment, the algorithms yield a priority ordering for painting entire faces. This order depends only upon the 3-D directions of face vertices as seen from the origin, and is independent of the radial position of vertices. Hence the order is independent of the actual function realized by the surface. Since perspective distortion and an approximate version of object rotation may both be accomplished by changing only radial vertex positions, these useful transformations may be visualized without resorting.Specific methods for creating well-tesselated surfaces are given, and general constraints defining them are stated. An efficient hidden surface/line algorithm is presented, with a simpler method for the case of opaque faced polyhedra. Proofs of correctness are provided.     

Fast template matching based on deformable best-buddies similarity measure

Accuracy and speed are the essential metrics for the template matching algorithms in solving object tracking problems. Since the method based on Best Buddies Similarity (BBS) has achieved the state-of-the-art performance in terms of accuracy, matching speed becomes the shortest piece of wood of the bucket. In this paper, we propose a fast template matching method based on our deformable BBS measure. The deformable BBS measure enables matching to be performed between the patches in varying sizes, and hence leads to even higher accuracy than the original BBS-based methods. More important, we develop a fast potential-area discovery algorithm based on proposal generation and selection. It significantly reduces the numbers of useless attempts on calculating and comparing similarities of impossible image patches. The experimental results show that, with the deformable BBS measure and the fast potential-area discovery, our template matching method outperforms the state-of-the-art methods in terms of accuracy, speed and robustness.