Matching wire frame objects from their two dimensional perspective projections

A wire frame object consists of a set of three dimensional arcs, each arc being a sequence of conics and line segments lying in the same plane, with different arcs being allowed to lie on different planes. Given a picture taken by a camera focusing on one wire frame object, we show how to determine what the object is and where it is situated relative to the camera when the camera viewing parameters are unknown.

To accomplish the object identification, we begin with a segmented picture. Then we construct a ray from the lens to each point on the boundary of every region. For each region, the collection of its associated rays is a cone. We show that by constructing cones, the two-dimensional to three-dimensional matching problem is transformed into an equivalent three-dimensional to three-dimensional matching problem.

This matching problem is expressed as a nonlinear optimization search procedure on the 6 camera viewing parameters: the 3 translation parameters and the 3 rotation parameters. A solution is found when a viewing position and optical axis is determined which is consistent with the world knowledge we have of possible curves and the observed image data.     

Constructing the generalized local Voronoi diagram from laser rangescanner data

We consider the problem of building local free space representation by a circular-base robot, operating in an unknown bounded planar environment populated by obstacles of arbitrary shape. In the unknown environment, the robot depends on its sensors; in our case, this is the laser range scanner. A new structure is represented, termed the generalized local Voronoi diagram (GLVD), constructed directly from sensory data, obtained from an observation of the local environment, that is from the visible region, GLVD is obtained by deleting some edges from the ordinary Voronoi diagram, which is generated by the measured scanned points from the visible region. Crucial for the acquisition of the GLVD is the clusterization of the scanned points. Clusterization means grouping of the scanned points into distinct clusters, each having a specific property, e.g., for a particular point in the cluster, the nearest neighboring point should not lie further than a prescribed distance away. The relevant part of GLVD, the portion of GLVD which is in accordance with the generalized Voronoi diagram of the environment, is determined. Eventual differences between these two structures are discussed and experimental results are presented. With the superposition of several GLVDs we show that this structure can be used to construct a global map of the environment, for which the position and the orientation of the robot is needed     

Automatic Camera Placement for Image-Based Modeling

We present an automatic camera placement method for generating image-based models from scenes with known geometry. Our method first approximately determines the set of surfaces visible from a given viewing area and then selects a small set of appropriate camera positions to sample the scene from. We define a quality measure for a surface as seen, or covered, from the given viewing area. Along with each camera position, we store the set of surfaces which are best covered by this camera. Next, one reference view is generated from each camera position by rendering the scene. Pixels in each reference view that do not belong to the selected set of polygons are masked out.
The image-based model generated by our method, covers every visible surface only once, associating it with a camera position from which it is covered with quality that exceeds a user-specified quality threshold. The result is a compact non-redundant image-based model with controlled quality.
The problem of covering every visible surface with a minimum number of cameras (guards) can be regarded as an extension to the well-known Art Gallery Problem. However, since the 3D polygonal model is textured, the camera-polygon visibility relation is not binary; instead, it has a weight — the quality of the polygon's coverage.     

Three-dimensional object representation and invariant recognitionusing continuous distance transform neural networks

3D object recognition under partial object viewing is a difficult pattern recognition task. In this paper, we introduce a neural-network solution that is robust to partial viewing of objects and noise corruption. This method directly utilizes the acquired 3D data and requires no feature extraction. The object is first parametrically represented by a continuous distance transform neural network (CDTNN) trained by the surface points of the exemplar object. The CDTNN maps any 3D coordinate into a value that corresponds to the distance between the point and the nearest surface point of the object. Therefore, a mismatch between the exemplar object and an unknown object can be easily computed. When encountered with deformed objects, this mismatch information can be backpropagated through the CDTNN to iteratively determine the deformation in terms of affine transform. Application to 3D heart contour delineation and invariant recognition of 3D rigid-body objects is presented.     

一种具有自终止特性的视点规划方法

提出了一种具有自终止特性的对未知物体模型自动3维测量的视点规划方法。首先在寻找最优视点阶段，利用群矢量链方法获得视觉传感器在下一个视点的观测方向，而视觉传感器在空间的确切位置参数是通过计算矢量场内的边界积分获得，其中获得最大边界积分的空间位置被定为下一个最优视点。同时为了保证对未知物体模型自动3维测量过程具有自终止特性，根据高斯定理，提出由测量所得的点云直接计算出物体体积的方法，并将连续两个视点下物体体积的变化量作为终止测量的依据来判断规划过程是否需要终止或继续。实验结果表明，该具有自终止特性的视点规划方法是可行而且有效的。     

Surface mapping brain function on 3D models

A flexible graphics system for displaying functional and anatomic data on arbitrary collections of surfaces on or within the brain is presented. The system makes it possible to show complex, convoluted surfaces with the shading cues necessary to understand their shapes; to vary viewpoint, object position, illumination, and perspective easily; to show multiple-objects in one view, with or without transparency, in order to examine internal surfaces and intersecting objects in relation to each other; and to superimpose quantitative information on biological or otherwise defined surfaces anywhere within the volume, thus furthering understanding of both quantitative and positional information in its global context. These display techniques are applied to a new form of biological surface model, the removed surface. The surface-removal method creates a set of surfaces internal to a given object, so that, given a specified distance, every point on the created surfaces is equidistant from the surface of the enclosing object. The method is based on thresholding a derived scalar field, the minimum distance field. Models made by this method have applications in 3-D neurobiology and provide an alternative to cutaways for viewing patterns of internal functional activity     

Introducing a new problem: shape-from-silhouette when the relative positions of the viewpoints is unknown

3D shapes can be reconstructed from 2D silhouettes by back-projecting them from the corresponding viewpoints and intersecting the resulting solid cones. However, in many practical cases as observing an aircraft or an asteroid, the positions of the viewpoints with respect to the object are not known. In these cases, the relative position of the solid cones is not known and the intersection cannot be performed. The purpose of this paper is introducing and stating in a theoretical framework the problem of understanding 3D shapes from silhouettes when the relative positions of the viewpoints are unknown. The results presented provide a first insight into the problem. In particular, the case of orthographic viewing directions parallel to the same plane is thoroughly discussed, and sets of inequalities are presented which allow determining objects compatible with the silhouettes.     

Analysis of global and local extrema of regularizing functionals in the problem of the reconstruction of images observed through randomly inhomogeneous media

An approach to the reconstruction problem of undistorted images of objects observed through randomly inhomogeneous media is considered. The approach is based on the solution to the integral equation of the first kind (convolution equation) with an unknown kernel and inaccurately defined right-hand side. It is demonstrated that the procedure for the construction of an inverse operator needed for the solution is determined by the minimization of the nonlinear regularizing multiextremum functional, which takes into account the a priori data regarding the positive intensity distribution in the image of an object. The analysis of the structure of the multiextremum functional is presented. The estimates of the reconstructed images that correspond to the global and local extrema are studied. The results of a numerical experiment on the reconstruction of the optical image of an object observed through the turbulent atmosphere are presented.     

High-quality splatting on rectilinear grids with efficient cullingof occluded voxels

Splatting is a popular volume rendering algorithm that pairs good image quality with an efficient volume projection scheme. The current axis-aligned sheet-buffer approach, however, bears certain inaccuracies. The effect of these is less noticeable in still images, but clearly revealed in animated viewing, where disturbing popping of object brightness occurs at certain view angle transitions. In previous work, we presented a new variant of sheet-buffered splatting in which the compositing sheets are oriented parallel to the image plane. This scheme not only eliminates the condition for popping, but also produces images of higher quality. In this paper, we summarize this new paradigm and extend it in a number of ways. We devise a new solution to render rectilinear grids of equivalent cost to the traditional approach that treats the anisotropic volume as being warped into a cubic grid. This enables us to use the usual radially symmetric kernels, which can be projected without inaccuracies. Next, current splatting approaches necessitate the projection of all voxels in the iso-interval(s), although only a subset of these voxels may eventually be visible in the final image. To eliminate these wasteful computations we propose a novel front-to-back approach that employs an occlusion map to determine if a splat contributes to the image before it is projected, thus skipping occluded splats. Additional measures are presented for further speedups. In addition, we present an efficient list-based volume traversal scheme that facilitates the quick modification of transfer functions and iso-values     

Optimal Path Planning for an Object in a Random Search Region

This paper considers the planning problem of an object’s optimal path that passes through a random search region. The problem specifics consist in that the search region is a priori unknown but the algorithmic and technical characteristics of search means are known. Two variational statements of the integral risk minimization problem with and without path length constraints are suggested. Program modules for their numerical solution are also developed.     

The research of an automatic object reconstruction method based on limit visible region of the laser-scanning vision system

This paper presents an automatic multi-view selection approach for 3D reconstruction by means of a laser scanning vision system. It is realized based on the visual region of the laser scanning vision system. The candidate next best view (NBV) position is obtained by computing the unknown space area according to the limit visual region of the vision system. The final NBV position, which can acquire the maximal visual area, is obtained by comparing the above candidate’s view positions. Experimental results show successful implantation of the proposed view planning method for digitization and reconstruction of freeform objects.     

约束可满足方法对单幅图片的三维猜测与个体识别

从二维图像提取到的特征点相对位置信息,利用对于目标物体的先验知识如边缘比例、夹角特征等,形成基于投影成像规则的变量约束方程,从而将物体姿态计算问题转化为一个非线性优化问题,通过多个局部约束线索形成全局约束,能够迅速对物体的姿态做出比较准确的估计,从而推算出视角等信息.实现这个转化的一个前提假设是,对于我们理解图像中物体的姿态,特征位置点的相对位置而不是绝对位置,起着关键作用.因此计算是在一个假设的深度上进行的,从效果来看这样的假设并不影响物体的住姿计算.本文的方法计算量小,利用几何特征来识别稳定、可靠、泛化能力好,实践证明使用几何特征的约束可满足方法能获得关于姿态的极少量可能解,识别出的姿态在各条边之间的比例关系上具有不变性,继而可以将其应用于不变性识别的实际问题之中.     

Generating octrees from object silhouettes in orthographic views

An algorithm to construct the octree representation of a three-dimensional object from silhouette images of the object is described. The images must be obtained from thirteen viewing directions corresponding to the three face views, six edge views, and four corner views of an upright cube. These views where chosen because they provide a simple relationship between pixels in the image and the octant labels in the octree, thus replacing the computation of detecting intersections between the octree space and the objects by a table lookup operation. The average ratio of the object volume to the octree volume is found to be greater than 90%. The sequential use made of the chosen viewing directions results in a coarse-to-fine acquisition of occupancy information. The number and order of the viewpoints used provides a mechanism for trading accuracy of the representation against the computational effort needed to obtain the representation     

The analysis and recognition of real-world textures in threedimensions

The observed image texture for a rough surface has a complex dependence on the illumination and viewing angles due to effects such as foreshortening, local shading, interreflections, and the shadowing and occlusion of surface elements. We introduce the dimensionality surface as a representation for the visual complexity of a material sample. The dimensionality surface defines the number of basis textures that are required to represent the observed textures for a sample as a function of ranges of illumination and viewing angles. Basis textures are represented using multiband correlation functions that consider both within and between color band correlations. We examine properties of the dimensionality surface for real materials using the Columbia Utrecht Reflectance and Texture (CUReT) database. The analysis shows that the dependence of the dimensionality surface on ranges of illumination and viewing angles is approximately linear with a slope that depends on the complexity of the sample. We extend the analysis to consider the problem of recognizing rough surfaces in color images obtained under unknown illumination and viewing geometry. We show, using a set of 12,505 images from 61 material samples, that the information captured by the multiband correlation model allows surfaces to be recognized over a wide range of conditions. We also show that the use of color information provides significant advantages for three-dimensional texture recognition     

An efficient method for fully automatic 3D digitization of unknown objects

Our goal is to develop a complete and automatic scanning strategy with minimum prior information about the object shape. We aim to establish a methodology for the automation of the 3D digitization process. The paper presents a novel approach to determine the Next Best View (NBV) for an efficient reconstruction of highly accurate 3D models. Our method is based on the classification of the acquired surfaces into Well Visible and Barely Visible combined with a best view selection algorithm based on mean shift, which avoids unreachable positions. Our approach is applicable to all kinds of range sensors. To prove the efficiency and the robustness of our method, test objects are first scanned manually by experts in 3D digitization from the VECTEO company. The comparison of results between manual and automatic scanning shows that our method is very efficient and faster than trained experts. The 3D models of the different objects are obtained with a strongly reduced number of acquisitions while moving efficiently the ranging device. The obtained results prove the effectiveness and the versatility of our 3D reconstruction approach for industrial applications.     

Automatic high-resolution optoelectronic photogrammetric 3D surface geometry acquisition system

A fast, high-resolution, automatic, non-contact 3D surface geometry measuring system using a photogrammetric optoelectronic technique based on lateral-photoeffect diode detectors has been developed. Designed for the acquisition of surface geometries such as machined surfaces, biological surfaces, and deformed parts, the system can be used in design, manufacturing, inspection, and range finding. A laser beam is focused and scanned onto the surface of the object to be measured. Two cameras in stereo positions capture the reflected light from the surface at 10 kHz. Photogrammetric triangulation quickly transforms the pair of 2D signals created by the camera detectors into 3D coordinates of the light spot. Because only one small spot on the object is illuminated at a time, the stereo correspondence problem is solved in real time. The resolution is determined by a 12-bit A/D converter and can be improved up to 25 60025 600 by oversampling. The irregular 3D data can be regularized for use with image-based algorithms. Received: 8 October 1996 / Accepted: 3 February 1997     

How far 3D shapes can be understood from 2D silhouettes

Each 2D silhouette of a 3D unknown object O constrains O inside the volume obtained by back-projecting the silhouette from the corresponding viewpoint. A set of silhouettes specifies a boundary volume R obtained by intersecting the volumes due to each silhouette. R more or less closely approximates O, depending on the viewpoints and the object itself. This approach to the reconstruction of 3D objects is usually referred to as volume intersection. This correspondence addresses the problem of inferring the shape of the unknown object O from the reconstructed object R. For doing this, the author divides the points of the surface of R into hard points, which belong to the surface of any possible object originating R, and soft points, which may or may not belong to O. The author considers two cases: In the first case R is the closest approximation of O which can be obtained from its silhouettes, i.e., its visual hull; in the second case, R is a generic reconstructed object. In both cases the author supplies necessary and sufficient conditions for a point to be hard and gives rules for computing the hard surfaces