Self-calibration from one circular motion sequence and two images

This paper describes a new method for self-calibration of camera with constant internal parameters under circular motion, using one sequence and two images captured with different camera orientations. Unlike the previous method, in which three circular motion sequences are needed with known motion, the new method computes the rotation angles and the projective reconstructions of the sequence and the images with circular constraint enforced, which is called a circular projective reconstruction, using a factorization-based method. It is then shown that the images of the circular points of each circular projective reconstruction can be readily obtained. Subsequently, the image of the absolute conic and the calibration matrix of the camera can be determined. Experiments on both synthetic and real image sequence are given, showing the accuracy and robustness of the new algorithm.     

Point set silhouettes via local reconstruction

We present an algorithm to compute the silhouette set of a point cloud. Previous methods extract point set silhouettes by thresholding point normals, which can lead to simultaneous over- and under-detection of silhouettes. We argue that additional information such as surface curvature is necessary to resolve these issues. To this end, we develop a local reconstruction scheme using Gabriel and intrinsic Delaunay criteria and define point set silhouettes based on the notion of a silhouette-generating set. The mesh umbrellas, or local reconstructions of one-ring triangles surrounding each point sample, generated by our method enable accurate silhouette identification near sharp features and close-by surface sheets, and provide the information necessary to detect other characteristic curves such as creases and boundaries. We show that these curves collectively provide a sparse and intuitive visualisation of point-cloud data.     

High-speed human motion recovery employing back projection

This paper describes a novel technique for high-speed human motion recovery. For 3-D human motion recovery, stereoscopic vision is a normal technique, as well as the employment of a magnetic field, but this cannot avoid the difficulty of marker tracking. In this article, a novel motion recovery technique is proposed based on the back projection of silhouette images. This technique has some advantages over others because it does not employ markers, and it has a simple architecture. In the experiment performed, the proposed motion recovery technique is implemented on a system containing a LAN, a host computer, and four pairs of camera and computer, and it achieves high-speed human motion recovery. This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2005     

Implicit surface reconstruction from contours

This paper presents a fast and efficient surface reconstruction method from contour data sets. The reconstructed surface is defined as an implicit surface. We need not create any geometric skeleton and the blending of the three dimensional contour functions enables us to avoid the correspondence and the branching problems that occur in geometrical methods. Tests carried out with medical scanner data-sets show that the reconstruction may be performed at interactive rates.     

基于旋转多视角深度配准的三维重建方法

针对在旋转平台上采集得到的多视角数据,提出一种有效的配准方法,同时结合双目立体视觉测量构建了完整的三维重建系统。通过拍摄旋转平台上多个视角下的标定板图像,提取标定板图像角点信息,计算出旋转平台坐标系和摄像机坐标系的空间位置关系,进一步推导出不同视角下的坐标转换关系,从而实现不同视角的数据配准。实验结果表明,基于本配准方法的旋转多视角双目测量系统具有较高的配准精度,能有效用于物体表面三维重建。     

Direct surface reconstruction from a moving sensor

A technique is described for surface reconstruction from a sequence of images when the sensor motion is known. The reconstruction takes the form of an orthographic depth map in a viewer-independent frame. Following a mathematical justification, the technique is illustrated with examples using noisy synthetic images.     

Surface reconstruction from scan paths

Given a finite set of points sampled from a surface, a particular important topic of surface reconstruction is to find a triangular mesh connecting the sampling points and approximating the surface. We introduce a new solution for this problem which takes into consideration hidden structural information in form of scan paths. The scan paths, which often are available in sampling data sets, allow us to cope with creases or ridges more reliably than algorithms assuming unstructured point clouds. Moreover, the consideration of scan paths leads to a better reconstruction of surface boundaries than other heuristics.     

Adaptive extraction and visualization of silhouette curves from volumetric datasets

An algorithm for silhouette extraction from volumetric data is presented. Trivariate tensor product B-spline functions are used to represent the data. An offline phase that arranges the data in a lookup table is employed to improve the computation time during an interactive session. A subdivision scheme is employed to extract the silhouette curves from an implicit trivariate B-spline function. The produced results are smooth, high-quality silhouette curves when compared to voxel-based silhouette extraction schemes.     

四元数样条插值的人体运动数据重构

为了得到平滑的人体动画,提出一种基于四元数的样条插值算法,利用提取的关键帧实现人体运动序列的有效重构。为减少重构误差、加快收敛速度,将已知关键帧集合作为初始条件,通过迭代算法求出样条曲线的控制点集合。利用样条曲线控制点计算贝塞尔曲线控制点,构造贝塞尔样条曲线段,将各段贝塞尔样条曲线段组合,构造一条基于四元数的样条曲线。根据德卡斯特里奥（de Casteljau）算法插值重构人体运动。实验结果表明,该算法在保证执行效率的同时,可得到光滑的插值结果,实现满足视觉要求的人体运动重构。     

A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.     

Splat-based surface reconstruction from defect-laden point sets

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface – a low-degree surface approximation – is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement. The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure.     

Shape and motion from simultaneous equations with closed-loop solution

This paper proposes a method for simultaneously estimating 2D image motion and 3D object shape and motion from only two frames. The problem is formulated in a system of equations, including the differential epipolar constraint, a newly derived optical flow equation and surface normal constraint, under the assumption of perspective projection, rigid motion, Lambertian reflectance and distant lighting. A closed-loop solver is constructed based on the simultaneous equations to export accurate estimate for optical flow as well as dense shape and motion. Experimental results are also provided.     

Shape from shading using the facet model

In this paper, the facet model is used in the recovery of surface orientation from single and multiple images. Two methods for determining surface orientation from image shading are presented. The first method works in the single image domain and is formulated as a non-linear optimization problem. Since three-dimensional scene information available in a single image is usually ambiguous, the optimization procedure can result in multiple solutions. The possibility of adding boundary constraints to the optimization process is also investigated. In the second method, additional images are obtained from the same viewing position, but with changing illumination direction. With these additional images, local surface orientation is determined uniquely by a linear optimization procedure. Experimental results of the shape-from-shading methods are also described.     

Provably correct reconstruction of surfaces from sparse noisy samples

Automated three-dimensional surface reconstruction is a very large and still fast growing area of applied computer vision and there exists a huge number of heuristic algorithms. Nevertheless, the number of algorithms which give formal guarantees about the correctness of the reconstructed surface is quite limited. Moreover such theoretical approaches are proven to be correct only for objects with smooth surfaces and extremely dense samplings with no or very few noise. We define an alternative surface reconstruction method and prove that it preserves the topological structure of multi-region objects under much weaker constraints and thus under much more realistic conditions. We derive the necessary error bounds for some digitization methods often used in discrete geometry, i.e. supercover and m-cell intersection sampling. We also give a detailed analysis of the behavior of our algorithm and compare it with other approaches.     

Continuous global optimization in surface reconstruction from an oriented point cloud

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, and allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.     

Composite freeform surface reconstruction using recursive interpolating subdivision scheme

Composite freeform surface reconstruction from 3D scanned data of a physical model has become a more and more important topic in the field of CAD/CAE/CAM. By repeated application of a fixed set of recursive interpolation subdivision schemes on the initial mesh of the 3D sparse scanned data of a physical model, a polygonal model of composite freeform surface can be constructed. In the paper, the algorithm for constructing the initial triangular mesh from 3D sparse scanned data is presented. The unified recursive interpolating subdivision scheme for triangular mesh is proposed. A special quad-tree data structure is suggested to store all the necessary information of the vertices and elements of the polygonal model. Examples of composite surface reconstruction are provided to explain the distinguished superiority of subdivision scheme for reconstructing the arbitrary topological complex surface.     

基于Shape from Shading的医学图像三维重建

通过对由医疗成像设备获取的二维灰度图像进行形状重建,得到的三维立体原型能帮助医学诊断人员确诊病情。介绍了Shape from Shading的实现原理和扫描电镜成像系统的简单构成,提出了一种基于线性逼近的用于解决SEM反射映射函数的实现方法,并将之应用于红血细胞的三维图像重构,得到的细胞图形非常接近其真实形状。     

A graph-spectral method for surface height recovery

This paper describes a graph-spectral method for 3D surface integration. The algorithm takes as its input a 2D field of surface normal estimates, delivered, for instance, by a shape-from-shading or shape-from-texture procedure. We commence by using the surface normals to obtain an affinity weight matrix whose elements are related to the surface curvature. The weight matrix is used to compute a row-normalized transition probability matrix, and we pose the recovery of the integration path as that of finding the steady-state random walk for the Markov chain defined by this matrix. The steady-state random walk is given by the leading eigenvector of the original affinity weight matrix. By threading the surface normals together along the path specified by the magnitude order of the components of the leading eigenvector we perform surface integration. The height increments along the path are simply related to the traversed path length and the slope of the local tangent plane. The method is evaluated on needle-maps delivered by a shape-from-shading algorithm applied to real-world data and also on synthetic data. The method is compared with the local geometric height reconstruction method of Bors, Hancock and Wilson, and the global methods of Horn and Brooks and Frankot and Chellappa.     

Spatio-temporal shape building from image sequences using lateral interaction in accumulative computation

To be able to understand the motion of non-rigid objects, techniques in image processing and computer vision are essential for motion analysis. Lateral interaction in accumulative computation for extracting non-rigid shapes from an image sequence has recently been presented, as well as its application to segmentation from motion. In this paper, we introduce a modified version of the first multi-layer architecture. This version uses the basic parameters of the LIAC model to spatio-temporally build up to the desired extent the shapes of all moving objects present in a sequence of images. The influences of LIAC model parameters are explained in this paper, and we finally show some examples of the usefulness of the model proposed.     

Optimization-based approach for curve and surface reconstruction

This paper introduces an optimization-based approach for the curve reconstruction problem, where piecewise linear approximations are computed from sets of points sampled from target curves. In this approach, the problem is formulated as an optimization problem. To be more concrete, at first the Delaunay triangulation for the sample points is computed, and a weight is assigned with each Delaunay edge. Then the problem becomes minimization or maximization of the total weights of the edges that constitute the reconstruction. This paper proposes one exact method and two approximate methods, and shows that the obtained results are improved both theoretically and empirically. In addition, the optimization-based approach is further extended to three dimensions, where surfaces are to be reconstructed, and the quality of the reconstructions is examined.