一种新的几何约束结构及其射影不变量

几何不变量,特别是射影不变量,是基于单视点灰度图像识别三维物体的一条有效途径．但理论研究表明,只有特定的几何约束结构,才具有射影不变量．所以,研究并发现这种几何约束结构就具有十分重要的意义．该文提出了一种新的由相邻3平面上5条直线组成的几何约束结构及其所具有的射影不变量．该结构较Sugimoto提出的几何约束结构简单,可从结构同样复杂的物体中获得更多的几何不变量,有利于提高物体识别的稳定性;同时,由于该结构大量存在于由多面体组合而构成的人造物体及地面建筑物中,因此它非常适合这类物体的识别．实验验证了文中提出的几何约束结构具有不随物体成像视点改变的射影不变量．     

Cooperative Stereo–Motion: Matching and Reconstruction

One of the most interesting goals of computer vision is the 3D structure recovery of scenes. Traditionally, two cues are used: structure from motion and structure from stereo, two subfields with complementary sets of assumptions and techniques. This paper introduces a new general framework of cooperation between stereo and motion. This framework combines the advantages of both cues: (i) easy correspondence from motion and (ii) accurate 3D reconstruction from stereo. First, we show how the stereo matching can be recovered from motion correspondences using only geometric constraints. Second, we propose a method of 3D reconstruction of both binocular and monocular features using all stereo pairs in the case of a calibrated stereo rig. Third, we perform an analysis of the performance of the proposed framework as well as a comparison with an affine method. Experiments involving real and synthetic stereo pairs indicate that rich and reliable information can be derived from the proposed framework. They also indicate that robust 3D reconstruction can be obtained even with short image sequences.     

Motion Analysis by Random Sampling and Voting Process

In computer vision, motion analysis is a fundamental problem. Applying the concepts of congruence checking in computational geometry and geometric hashing, which is a technique used for the recognition of partially occluded objects from noisy data, we present a new random sampling approach for the estimation of the motion parameters in two- and three-dimensional Euclidean spaces of both a completely measured rigid object and a partially occluded rigid object. We assume that the two- and three-dimensional positions of the vertices of the object in each image frame are determined using appropriate methods such as a range sensor or stereo techniques. We also analyze the relationships between the quantization errors and the errors in the estimation of the motion parameters by random sampling, and we show that the solutions obtained using our algorithm converge to the true solutions if the resolution of the digitalization is increased.     

3D Articulated Models and Multiview Tracking with Physical Forces

We present a method for automatically estimating the motion of an articulated object filmed by two or more fixed cameras. We focus our work on the case where the quality of the images is poor, and where only an approximation of a geometric model of the tracked object is available. Our technique uses physical forces applied to each rigid part of a kinematic 3D model of the object we are tracking. These forces guide the minimization of the differences between the pose of the 3D model and the pose of the real object in the video images. We use a fast recursive algorithm to solve the dynamical equations of motion of any 3D articulated model. We explain the key parts of our algorithms: how relevant information is extracted from the images, how the forces are created, and how the dynamical equations of motion are solved. A study of what kind of information should be extracted in the images and of when our algorithms fail is also presented. Finally we present some results about the tracking of a person. We also show the application of our method to the tracking of a hand in sequences of images, showing that the kind of information to extract from the images depends on their quality and of the configuration of the cameras.     

共面多边形不变量计算方法研究

不变量的场景理解和目标识别是计算机视觉研究的一个重要领域,以往有关不 变量研究主要集中在点、直线、二次曲线等几何元素之间。在二维平面点的射影变换的基础 上,利用平面三角形面积不变量构造了三角形、四边形、五边形、六边形等共面多边形的不 变量,并提出了具体的计算方法。在此基础上通过举例分析和实验验证,证明文中所给公式 的正确性。     

Building Detection from Multiple Aerial Images in Dense Urban Areas

In this paper we present a novel approach for building detection from multiple aerial images in dense urban areas. The approach is based on accurate surface reconstruction, followed by extraction of building façades that are used as a main cue for building detection. For the façade detection, a simple but nevertheless flexible and robust algorithm is proposed. It is based on the observation that building façades correspond to the accumulation of 3D data, available from different views, in object space. Knowledge-driven thresholding of 3D data accumulators followed by Hough transform-based segment detection results in the extraction of façade positions. Three-dimensional planar regions resulting from surface reconstruction procedure and bounded by the extracted façades are detected as building hypotheses through testing a set of spatial criteria. Then, a set of verification criteria is proposed for the hypothesis confirmation.     

Perceptual Organization Based Computational Model for Robust Segmentation of Moving Objects

The role of perceptual organization in motion analysis has heretofore been minimal. In this work we present a simple but powerful computational model and associated algorithms based on the use of perceptual organizational principles, such as temporal coherence (or common fate) and spatial proximity, for motion segmentation. The computational model does not use the traditional frame by frame motion analysis; rather it treats an image sequence as a single 3D spatio-temporal volume. It endeavors to find organizations in this volume of data over three levels—signal, primitive, and structural. The signal level is concerned with detecting individual image pixels that are probably part of a moving object. The primitive level groups these individual pixels into planar patches, which we call the temporal envelopes. Compositions of these temporal envelopes describe the spatio-temporal surfaces that result from object motion. At the structural level, we detect these compositions of temporal envelopes by utilizing the structure and organization among them. The algorithms employed to realize the computational model include 3D edge detection, Hough transformation, and graph based methods to group the temporal envelopes based on Gestalt principles. The significance of the Gestalt relationships between any two temporal envelopes is expressed in probabilistic terms. One of the attractive features of the adopted algorithm is that it does not require the detection of special 2D features or the tracking of these features across frames. We demonstrate that even with simple grouping strategies, we can easily handle drastic illumination changes, occlusion events, and multiple moving objects, without the use of training and specific object or illumination models. We present results on a large variety of motion sequences to demonstrate this robustness.     

Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done essentially using incremental algorithms. Incremental algorithms have the reputation of being efficient but they lack an important property: robustness. The voxelized representation should envelop its continuous model. However, without robust methods this cannot be guaranteed. This article describes novel techniques of robust voxelization and visualization of implicit surfaces. First of all our recursive subdivision voxelization algorithm is reviewed. This algorithm was initially inspired by Duff's image space subdivision method. Then, we explain the algorithm to voxelize implicit surfaces defined in spherical or cylindrical coordinates. Next, we show a new technique to produce infinite replications of implicit objects and their voxelization method. Afterward, we comment on the parallelization of our voxelization procedure. Finally we present our voxel visualization algorithm based on point display. Our voxelization algorithms can be used with any data structure, thanks to the fact that a voxel is only stored once the last subdivision level is reached. We emphasize the use of the octree, though, because it is a convenient way to store the discrete model hierarchically. In a hierarchy the discrete model refinement is simple and possible from any previous voxelized scene thanks to the fact that the voxelization algorithms are robust.     

Range Flow Estimation

We discuss the computation of the instantaneous 3D displacement vector fields of deformable surfaces from sequences of range data. We give a novel version of the basic motion constraint equation that can be evaluated directly on the sensor grid. The various forms of the aperture problem encountered are investigated and the derived constraint solutions are solved in a total least squares (TLS) framework. We propose a regularization scheme to compute dense full flow fields from the sparse TLS solutions. The performance of the algorithm is analyzed quantitatively for both synthetic and real data. Finally we apply the method to compute the 3D motion field of living plant leaves.     

Solution of the Simultaneous Pose and Correspondence Problem Using Gaussian Error Model

The use of hypothesis verification is recurrent in the model-based recognition literature. Verification consists in measuring how many model features transformed by a pose coincide with some image features. When data involved in the computation of the pose are noisy, the pose is inaccurate and difficult to verify, especially when the objects are partially occluded. To address this problem, the noise in image features is modeled by a Gaussian distribution. A probabilistic framework allows the evaluation of the probability of a matching, knowing that the pose belongs to a rectangular volume of the pose space. It involves quadratic programming, if the transformation is affine. This matching probability is used in an algorithm computing the best pose. It consists in a recursive multiresolution exploration of the pose space, discarding outliers in the match data while the search is progressing. Numerous experimental results are described. They consist of 2D and 3D recognition experiments using the proposed algorithm.     

Fuzzy Distance Transform: Theory, Algorithms, and Applications

This paper describes the theory and algorithms of distance transform for fuzzy subsets, called fuzzy distance transform (FDT). The notion of fuzzy distance is formulated by first defining the length of a path on a fuzzy subset and then finding the infimum of the lengths of all paths between two points. The length of a path π in a fuzzy subset of the n-dimensional continuous space ⁿ is defined as the integral of fuzzy membership values along π. Generally, there are infinitely many paths between any two points in a fuzzy subset and it is shown that the shortest one may not exist. The fuzzy distance between two points is defined as the infimum of the lengths of all paths between them. It is demonstrated that, unlike in hard convex sets, the shortest path (when it exists) between two points in a fuzzy convex subset is not necessarily a straight line segment. For any positive number θ≤1, the θ-support of a fuzzy subset is the set of all points in ⁿ with membership values greater than or equal to θ. It is shown that, for any fuzzy subset, for any nonzero θ≤1, fuzzy distance is a metric for the interior of its θ-support. It is also shown that, for any smooth fuzzy subset, fuzzy distance is a metric for the interior of its 0-support (referred to as support). FDT is defined as a process on a fuzzy subset that assigns to a point its fuzzy distance from the complement of the support. The theoretical framework of FDT in continuous space is extended to digital cubic spaces and it is shown that for any fuzzy digital object, fuzzy distance is a metric for the support of the object. A dynamic programming-based algorithm is presented for computing FDT of a fuzzy digital object. It is shown that the algorithm terminates in a finite number of steps and when it does so, it correctly computes FDT. Several potential applications of fuzzy distance transform in medical imaging are presented. Among these are the quantification of blood vessels and trabecular bone thickness in the regime of limited special resolution where these objects become fuzzy.     

Solving the recognition problem for six lines using the Dixon resultant

The “Six-line Problem” arises in computer vision and in the automated analysis of images. Given a three-dimensional (3D) object, one extracts geometric features (for example six lines) and then, via techniques from algebraic geometry and geometric invariant theory, produces a set of 3D invariants that represents that feature set. Suppose that later an object is encountered in an image (for example, a photograph taken by a camera modeled by standard perspective projection, i.e. a “pinhole” camera), and suppose further that six lines are extracted from the object appearing in the image. The problem is to decide if the object in the image is the original 3D object. To answer this question two-dimensional (2D) invariants are computed from the lines in the image. One can show that conditions for geometric consistency between the 3D object features and the 2D image features can be expressed as a set of polynomial equations in the combined set of two- and three-dimensional invariants. The object in the image is geometrically consistent with the original object if the set of equations has a solution. One well known method to attack such sets of equations is with resultants. Unfortunately, the size and complexity of this problem made it appear overwhelming until recently. This paper will describe a solution obtained using our own variant of the Cayley–Dixon–Kapur–Saxena–Yang resultant. There is reason to believe that the resultant technique we employ here may solve other complex polynomial systems.     

Tracking of Human Limbs by Multiocular Vision

This article proposes a method for the tracking of human limbs from multiocular sequences of perspective images. These limbs and the associated articulations must first be modelled. During the learning stage, we model the texture linked to the limbs. The lack of characteristic points on the skin is compensated by the wearing of nonrepetitive texture tights. The principle of the method is based on the interpretation of image textured patterns as the 3D perspective projections of points of the textured articulated model. An iterative Levenberg–Marquardt process is used to compute the model pose in accordance with the analyzed image. The calculated attitude is filtered (Kalman filter) to predict the model pose in the following image of the sequence. The image patterns are extracted locally according to the textured articulated model in the predicted attitude. Tracking experiments, illustrated in this paper by cycling sequences, demonstrate the validity of the approach.     

Reconstruction and Simplification of Surfaces from Contours

In this paper we consider the problem of reconstructing triangular surfaces from given contours. An algorithm solving this problem must decide which contours of two successive slices should be connected by the surface (branching problem) and, given that, which vertices of the assigned contours should be connected for the triangular mesh (correspondence problem). We present a new approach that solves both tasks in an elegant way. The main idea is to employ discrete distance fields enhanced with correspondence information. This allows us not only to connect vertices from successive slices in a reasonable way but also to solve the branching problem by creating intermediate contours where adjacent contours differ too much. Last but not least we show how the 2D distance fields used in the reconstruction step can be converted to a 3D distance field that can be advantageously exploited for distance calculations during a subsequent simplification step.     

Integration of Hough Transform of lines and planes in the framework of conformal geometric algebra for 2D and 3D robot vision

This paper presents the application of 2D and 3D Hough Transforms together with conformal geometric algebra to build 3D geometric maps using the geometric entities of lines and planes. Among several existing techniques for robot self-localization, a new approach is proposed for map matching in the Hough domain. The geometric Hough representation is formulated in such a way that one can easily relate it to the conformal geometric algebra framework; thus, the detected lines and planes can be used for algebra-of-incidence computations to find geometric constraints, useful when perceiving special configurations in 3D visual space for exploration, navigation, relocation and obstacle avoidance. We believe that this work is very useful for 2D and 3D geometric pattern recognition in robot vision tasks.     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

利用2D射影变换求解空间复杂结构的3D不变量

3D不变量作为不随姿态、视点等成像条件变化而变化的特征参量，可以广泛应用于计算机视觉的多重领域．通过分析2D射影变换矩阵求解的多种可能性，由单纯基于点集对应的思路扩展到利用点集、线集、点、线组合等其它方法，从而拓宽了建立两射影平面对应关系的应用条件．由此提出了一种基于多种点线组合构造虚元素的方法，结合实元素和虚元素可以巧妙提取空间复杂结构下的多种3D不变量，以用于目标识别和描述当中．实验结果验证了方法的有效性。     

Learning Variable-Length Markov Models of Behavior

In recent years there has been an increased interest in the modeling and recognition of human activities involving highly structured and semantically rich behavior such as dance, aerobics, and sign language. A novel approach for automatically acquiring stochastic models of the high-level structure of an activity without the assumption of any prior knowledge is presented. The process involves temporal segmentation into plausible atomic behavior components and the use of variable-length Markov models for the efficient representation of behaviors. Experimental results that demonstrate the synthesis of realistic sample behaviors and the performance of models for long-term temporal prediction are presented.     

A new approach to 3D reconstruction without camera calibration

In this paper, we present a new approach for 3D scene reconstruction based on projective geometry without camera calibration. Previous works use at least six points to build two projective reference planes. Our contribution is to reduce the number of reference points to four by exploiting some geometrical shapes contained in the scene. The first implemented algorithm allows the reconstruction of a fourth point on each reference plane. The second algorithm is devoted to the 3D reconstruction. We obtained the expected good results and the proposed method is to equip a mobile robot moving in a structured environment.