A novel plane extraction approach using supervised learning

This paper presents a novel approach for the classification of planar surfaces in an unorganized point clouds. A feature-based planner surface detection method is proposed which classifies a point cloud data into planar and non-planar points by learning a classification model from an example set of planes. The algorithm performs segmentation of the scene by applying a graph partitioning approach with improved representation of association among graph nodes. The planarity estimation of the points in a scene segment is then achieved by classifying input points as planar points which satisfy planarity constraint imposed by the learned model. The resultant planes have potential application in solving simultaneous localization and mapping problem for navigation of an unmanned-air vehicle. The proposed method is validated on real and synthetic scenes. The real data consist of five datasets recorded by capturing three-dimensional(3D) point clouds when a RGBD camera is moved in five different indoor scenes. A set of synthetic 3D scenes are constructed containing planar and non-planar structures. The synthetic data are contaminated with Gaussian and random structure noise. The results of the empirical evaluation on both the real and the simulated data suggest that the method provides a generalized solution for plane detection even in the presence of the noise and non-planar objects in the scene. Furthermore, a comparative study has been performed between multiple plane extraction methods.     

改进ICP算法实现多视点云精确配准研究

复杂面形的三维整体测量能否顺利完成取决于不同视下测得的三维点云的配准精度。研究表明:采用点到点,点到三角面配准方法易受噪声干扰,采用面形比较计算量大,且在平面和标准球面情况下容易失效。以粗配准标记点所在的立方体区域为重合区域,使用点到点的多邻接三角面距离最近的点对作为初始匹配点,并根据几何结构最大相似原则对所求得的多个粗匹配点对进行筛选,再对筛选后的点对应用最近点迭代(ICP)算法。改进后的ICP算法实现了重合区域的快速自动定位,实现了不同视下点云的快速精确配准,在多个实例下获得了配准精度优于0.01 mm的实验结果。     

Point fingerprint: a new 3-D object representation scheme

This paper proposes a new, efficient surface representation method for surface matching. A feature carrier for a surface point, which is a set of two-dimensional (2-D) contours that are the projections of geodesic circles on the tangent plane, is generated. The carrier is named point fingerprint because its pattern is similar to human fingerprints and plays a role in discriminating surface points. Corresponding points on surfaces from different views are found by comparing their fingerprints. The point fingerprint is able to carry curvature, color, and other information which can improve matching accuracy, and the matching process is faster than 2-D image comparison. A novel candidate point selection method based on the fingerprint irregularity is introduced. Point fingerprint is successfully applied to pose estimation of real range data.     

海量散乱点的曲面重建算法研究

基于海量散乱点的曲面重建在机械产品测量造型、计算机视觉、根据切片数据的医学图像重建等领域中有重要应用.给出了一种以物体表面上不附加任何几何和拓扑信息(包括测点法矢、曲面边界信息)的散乱点集为处理对象,自动生成物体表面的三角网格模型的算法.该算法首先根据测点的邻近测点估算曲面在该测点处的法矢,并采用优化的顺序对法矢方向进行调整以使各测点处的法矢都指向曲面外侧,最后用步进立方体算法输出三角网格模型.采用新的方法计算切平面,不但进一步提高了效率,而且改善了曲面边界及尖锐棱边区域的重建效果.还提出并解决了法矢方向传播中可能出现的局部“孤岛”问题.同时,提出了一种对海量数据进行空间划分的算法,从而大大提高了海量数据的处理效率.应用实例表明,算法效果良好     

CSG-EESI: a new solid representation scheme and a conversion expertsystem

A representation scheme is proposed for describing 3-D mechanical parts and structural bodies which are formed from planes and quadratic faces. Since the method combines features of the constructive solid geometry (CSG) representation and an extension of the enhanced (EESI) spherical image representation (ESI), it is designated the CSG-EESI. In this scheme, the body model is roughly divided into two levels: the higher level corresponds to a restricted CSG tree that contains the structural information describing how the various subparts form the body; the lower level contains the geometric information for those simple subparts and represents them by an extension of enhanced spherical images. The scheme can be used both as the medium between pictorial models and relational models and as an internal model to facilitate the recognition of bodies. An expert system written in C-PROLOG on a VAX 11/750 is presented that converts BR-like models into the CSG-EESI representation is presented     

An Application of Surface Reconstruction from Rotational Motion

For surface reconstruction using motion, objects are placed on a rotating disc in front of a single camera. For camera calibration the method by Tsai was implemented, extended (calculation of distorted from undisturbed coordinates) and optimized (e.g. with respect to the number of calibration planes and points in each plane) (1). The way the calibration results can be used for this special case of surface reconstruction of objects on a rotating disc is described. Motion vectors calculated from point correspondences are used as input for this calculation of 3-D point positions. In two theorems, new reconstruction formulae are given. Experimentally, accurate depth values could be obtained for sparse object surface points. It is suggested to combine these exact values with "surface drafts" calculated by approaches based on reflectance properties.     

Discrete plane segmentation and estimation from a point cloud using local geometric patterns

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discretegeometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. In contrast to the continuous case, there exist a finite number of local geometric patterns （LGPs） appearing on discrete planes. Moreover, such an LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate the values of parameters of a discrete plane by minimizing its thickness.     

Local Shape from Mirror Reflections

We study the problem of recovering the 3D shape of an unknown smooth specular surface from a single image. The surface reflects a calibrated pattern onto the image plane of a calibrated camera. The pattern is such that points are available in the image where position, orientations, and local scale may be measured (e.g. checkerboard). We first explore the differential relationship between the local geometry of the surface around the point of reflection and the local geometry in the image.We then study the inverse problem and give necessary and sufficient conditions for recovering surface position and shape.We prove that surface position and shape up to third order can be derived as a function of local position, orientation and local scale measurements in the image when two orientations are available at the same point (e.g. a corner). Information equivalent to scale and orientation measurements can be also extracted from the reflection of a planar scene patch of arbitrary geometry, provided that the reflections of (at least) 3 distinctive points may be identified.We validate our theoretical results with both numerical simulations and experiments with real surfaces.     

Efficient and automatic plane detection approach for 3-D rock mass point clouds

The detection of planar regions from three-dimensional (3-D) laser scanning point clouds has become more and more significant in many scientific fields, including 3-D reconstruction, augmented reality and analysis of discontinuities. In rock engineering, planes extracted from rock mass point clouds are the foundational step to build 3-D numerical models of rock mass, which is significant in analysis of rock stability. In the past, several approaches have been proposed for detecting planes from TLS point clouds. However, these methods have difficulties in processing rock points because of the uniqueness of rock. This paper introduces a novel and efficient method for plane detection from 3-D rock mass point clouds. Firstly, after filtering the raw point clouds of rock mass acquired through laser scanning, the point cloud is split into some small voxels according to the specified resolution. Then, for the purpose of acquisition of high-quality growth units, an accurate coplanarity test process is used in each voxel. Meanwhile, the accurate neighborhood information can be built according to the result of coplanarity test. Finally, small voxels are clustered into a completed plane by region growing and the procedure of postprecessing. The performance of this method was tested in one icosahedron point cloud and three rock mass point clouds. Compared with the existing methods, the results demonstrate superior performance of our method in the field of plane detection.

     

Tangential Distance Fields for Mesh Silhouette Problems

We consider a tangent-space representation of surfaces that maps each point on a surface to the tangent plane of the surface at that point. Such representations are known to facilitate the solution of several visibility problems, in particular, those involving silhouette analysis. In this paper, we introduce a novel class of distance fields for a given surface defined by its tangent planes. At each point in space, we assign a scalar value which is a weighted sum of distances to these tangent planes. We call the resulting scalar field a 'tangential distance field' (TDF). When applied to triangle mesh models, the tangent planes become supporting planes of the mesh triangles. The weighting scheme used to construct a TDF for a given mesh and the way the TDF is utilized can be closely tailored to a specific application. At the same time, the TDFs are continuous, lending themselves to standard optimization techniques such as greedy local search, thus leading to efficient algorithms. In this paper, we use four applications to illustrate the benefit of using TDFs: multi-origin silhouette extraction in Hough space, silhouette-based view point selection, camera path planning and light source placement.     

6DoF haptic rendering using distance maps over implicit representations

This paper presents a haptic rendering scheme based on distance maps over implicit surfaces. Using the successful concept of support planes and mappings, a support plane mapping formulation is used so as to generate a convex representation and efficiently perform collision detection. The proposed scheme enables, under specific assumptions, the analytical reconstruction of the rigid 3D object’s surface, using the equations of the support planes and their respective distance map. As a direct consequence, the problem of calculating the force feedback can be analytically solved using only information about the 3D object’s spatial transformation and position of the haptic interaction point. Moreover, several haptic effects are derived by the proposed mesh-free haptic rendering formulation. Experimental evaluation and computational complexity analysis demonstrates that the proposed approach can reduce significantly the computational cost when compared to existing methods.     

基于平面的便携式结构光系统柔性标定方法

对于便携式结构光系统, 该系统必须适合方便使用. 因此, 针对该系统的标定方法也必须采用方便且便宜的设备, 诸如具有两个或三个正交平面或者需要额外固定措施的一些设备则不宜采用. 同时针对快速三维获取的目的, 应该采用估计便携式结构光系统投影矩阵的方法. 本文针对便携式结构光系统的上述应用需求, 提出了一种基于平面的便携式结构光系统柔性标定方法. 该方法需要一个标定模板和一个参考模板. 标定模板被固定在一个平面上, 而参考模板则通过LCD投影仪被投射到该平面上. 通过交比和极几何约束, 可以获得分别对投影仪和相机的世界坐标系和图像坐标系的点对应坐标. 通过这些点对应坐标, 即可完成整个系统的标定. 实验结果表明该方法具有很高的准确性和鲁棒性．     

Three-dimensional model acquisition for medical robotics-assisted burn debridement system

This paper discusses the principles for the acquisition of a three-dimensional (3-D) computational model of the treatment area of a burn victim for a vision-servo-guided robot which ablates the victim's burned skin tissue by delivering a high-energy laser light to the burned tissue. The medical robotics assistant system consists of: a robot whose end effector is equipped with a laser head, whence the laser beam emanates, and a vision system which is used to acquire the 3-D coordinates of some points on the body surface; 3-D surface modeling routines for generating the surface model of the treatment area; and control and interface hardware and software for control and integration of all the system components. Discussion of the vision and surface modeling component of the medical robotics assistant system is the focus of this paper. The robot-assisted treatment process has two phases: an initial survey phase during which a model of the treatment area on the skin is built and used to plan an appropriate trajectory for the robot in the subsequent phase—the treatment phase, during which the laser surgery is performed. During the survey phase, the vision system employs a camera to acquire points on the surface of the patient's body by using the camera to capture the contour traced by a plane of light generated by a low power laser, distinct from the treatment laser. The camera's image is then processed. Selected points on the camera's two-dimensional image frame are used as input to a process that generates 3-D body surface points as the intersection point of the plane of light and the line of sight between the camera's image point and the body surface point. The acquired body surface points are then used to generate a computational model of the treatment area using the non-uniform rational B-splines (NURBS) surface modeling technique. The constructed NURBS surface model is used to generate a treatment plan for the execution of the treatment phase. The robot plan for treatment is discussed in another paper. The prototype of the entire burn treatment system is at an advanced stage of development and tests of the engineering principles on inanimate objects, discussed herein, are being conducted.     

Direct boolean intersection between acquired and designed geometry

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data).We use the moving least-squares (MLS) surface as the underlying surface representation for acquired point-sampled geometry. Based on the MLS surface definition, we derive closed formula for computing curvature of planar curves on the MLS surface. A set of intersection algorithms including line and MLS surface intersection, curvature-adaptive plane and MLS surface intersection, and polygonal mesh and MLS surface intersection are successively developed. Further, an algorithm for NURBS and MLS surface intersection is then developed. It first adaptively subdivides NURBS surfaces into polygonal mesh, and then intersects the mesh with the MLS surface. The intersection points are mapped to the NURBS surface through the Gauss-Newton method.Based on the above algorithms, a prototype system has been implemented. Through various examples from the system, we demonstrate that direct Boolean intersection between designed geometry and acquired geometry offers a useful and effective means for the shape modeling applications where point-cloud data is involved.     

Occlusions as a guide for planning the next view

A strategy for acquiring 3-D data of an unknown scene, using range images obtained by a light stripe range finder is addressed. The foci of attention are occluded regions, i.e., only the scene at the borders of the occlusions is modeled to compute the next move. Since the system has knowledge of the sensor geometry, it can resolve the appearance of occlusions by analyzing them. The problem of 3-D data acquisition is divided into two subproblems due to two types of occlusions. An occlusion arises either when the reflected laser light does not reach the camera or when the directed laser light does not reach the scene surface. After taking the range image of a scene, the regions of no data due to the first kind of occlusion are extracted. The missing data are acquired by rotating the sensor system in the scanning plane, which is defined by the first scan. After a complete image of the surface illuminated from the first scanning plane has been built, the regions of missing data due to the second kind of occlusions are located. Then, the directions of the next scanning planes for further 3-D data acquisition are computed     

Near laser-scan quality 3-D face reconstruction from a low-quality depth stream

We propose a method to produce near laser-scan quality 3-D face models of a freely moving user with a low-cost, low resolution range sensor in real-time. Our approach does not require any prior knowledge about the geometry of a face and can produce faithful geometric models of any star-shaped object. We use a cylindrical representation, which enables us to efficiently process the 3-D mesh by applying 2-D filters.We use the first frame as a reference and incrementally build the model by registering each subsequent cloud of 3-D points to the reference using the ICP (Iterative Closest Point) algorithm implemented on a GPU (Graphics Processing Unit). The registered point clouds are merged into a single image through a cylindrical representation. The noise from the sensor and from the pose estimation error is removed with a temporal integration and a spatial smoothing of the successively incremented model. To validate our approach, we quantitatively compare our model to laser scans, and show comparable accuracy.¹     

Free-Form Simulation of Sequential Etching and Surface Characterization for 3-D MEMS Fabrication

A new diffusion-based simulation model of isotropic wet etching and free-form surface characterization method for 3-D free-form microelectromechanical systems (MEMS) fabrication is presented in this paper. To simulate the etching process, a diffusion-based model solved by the finite-element method (FEM) has been developed, allowing extraction of more accurate etch-front data at discrete time steps. In the developed method, free-form MEMS objects are modeled as B-spline functions with material concentration. Finite elements are generated by discretization in the parametric domain of the free-form object and mapping back to the Euclidean space. Points on the etch front are extracted using a Z-map method. The extracted point data are characterized to obtain a B-spline representation of the etch-front surface. Examples from the isotropic etching simulation of 2-D and 3-D objects with both regular and free-form geometry are presented. The developed method allows the simulation of 3-D objects with free-form input and free-form mask opening and facilitates the simulation of sequential etching of free-form objects with irregular mask openings. This paper also discusses applications of the developed method in MEMS process planning that can be realized by taking advantage of the better control of geometry that it provides in MEMS fabrication.     

单目平行线约束下的空间点坐标恢复

提出一种从单目像机拍摄的二维投影图像中恢复空间点三维坐标的简化算法.假定摄像机与空间中的一对平行线的位置关系已知,同时摄像机坐标系下平行线所在平面中的任意空间点在像平面中的投影也已知,通过射影几何可得图像坐标到目标点三维空间坐标的转换系数,即坐标转换因数,从而估计出三维空间点的坐标.实验中通过对人体行走轨迹进行估计来测试算法性能,结果表明算法简单有效,计算开销小.