Octree generation from object silhouettes in perspective views

Octrees are useful for object representation when fast access to coarse spatial occupancy information is necessary. This paper presents an efficient algorithm for generating octrees from multiple perspective views of an object. The algorithm first obtains a polygonal approximation of the object silhouette. This polygon is then decomposed into convex components. For each convex component, a pyramid is formed treating the view point as its apex and the convex components as a cross section. The octree representation of each of these pyramids is obtained by performing intersection detection of the object with the cubes corresponding to octree nodes. The intersection detection step is made efficient by decomposing it into a coarse-to-fine sequence of intersection tests. The octree for one silhouette is obtained by taking the union of octrees obtained for each component. An intersection of octrees corresponding to different viewing directions gives the final octree of the object. An implementation of the algorithm is given. The accuracy of the octree representation of the objects is evaluated. The ratio of the actual volume of the object to the volume of the object reconstructed from the octree representation is used as a performance index of the algorithm.     

Linear octrees by volume intersection

The paper describes a new algorithm for constructing a 3D approximation of an object from three orthogonal 2D silhouettes. The 2D views are represented as binary arrays and 3D approximation is obtained as a linear octree. The algorithm makes use of volume intersection of three cylinders obtained by sweeping three views in respective directions. The algorithm takes less time than an existing algorithm which makes use of three quadtrees and an octree for 2D and 3D image representation, respectively. Unlike the previous algorithm, the present algorithm does not require any preprocessing stage or condensation. It is Shown that the proposed algorithm is of o(T), where T is the total number of nodes in the resulting octree.     

Hidden Octree Node Removal as a Pipeline Process

A processing pipeline solution to the generation and display of octree encoded 3-D objects is described. Particular emphasis is given to an algorithm which removes that part a of linear octree code which describes parts of the object which are invisible from a prescribed viewing position. The scope of the algorithm is restricted to viewing directions which are parallel to the Cartesian axes and to orthogonal projections. The algorithm is specifically designed to operate as a single stage within a pipeline of processes.     

Octree Representation and Its Applications in CAD

In this paper,a survey of octree representation and its applications in CAD is presented.The octree representation may be categorized as pure octree representation and polytree(or extended octree),and the latter is actually a boundary representation decomposed by octree.Linear octree which is a variant of regular octree representation has the advantage of saving memory space.The mapping between Cartesian coordinates and node addresses in linear octree is discussed.Then,algorithms for converting a boundary representation of 3D object into an octree are investiged and major approaches for transforming an octree encoded object are presented.After that,some of the applications of octree representation in CAD are listed,in particular,the applications in solid modeling,in accelerating ray tracing and in generating meshes for FEM.     

Viewing Transformations of Voxel-Based Objects Via Linear Octrees

This article gives three viewing-transformation algorithms for displaying on a screen 3D pictures represented by linear octrees. All the procedures take advantage of the recursive labeling used to identify the successive decomposition of an object into octants. The first algorithm performs transformations directly on the linear octree, while the second and third algorithms determine the 3D border of the given object first and then project onto the screen the surface voxels thus found. All the algorithms perform the viewing transformations in O(RN) time, where R is the resolution of the picture and N is the number of elements in the linear octree. One of the algorithms provides views of the object at different layers of gray level, while another allows internal views.     

An algorithm for converting the boundary representation of a CAD model to its octree representation

Present CAD systems store the solid model of an object using a convenient representation. Boundary models and CSG (Constructive Solid Geometry) models are the most frequently used representations. Based on recent research findings, octree representation of an object presents a promising approach in solving problems in the areas of Computer Graphics, Manufacturing and Robotics. The most notable use of octree representations is in CAD-based robotic path planning problems. Octree models have also been used in fast rendering of 3-D solid models using ray tracing methods. This paper presents an algorithm for converting the boundary representation of polyhedral models to its octree representation. Such an algorithm would provide the link between an object generated using a solid modelling system and the application involving an octree representation of an object. The algorithm is demonstrated by converting a polyhedral boundary model of a sample object to its octree representation.     

A viewing pipeline for discrete solid modeling

We describe the architecture of BIN, a discrete solid modeler, placing special emphasis on the structure of the viewing subsystem. In contrast to most quadtree and octree systems BIN operates directly on a compact linear bitstring representation of images residing in external storage. Anticipating a pipelined hardware implementation, the system is based on connecting distinct programs to each other through Unix pipes. The system is dimension independent in the sense that a single program operates on both 2D and 3D (and kD) models, where applicable. We present a discussion of the structure and the interchangeable components of an octree viewing pipeline, together with an overview of the methods used in the BIN system, several of which are novel.     

A volumetric fusion technique for surface reconstruction from silhouettes and range data

Optical triangulation, an active reconstruction technique, is known to be an accurate method but has several shortcomings due to occlusion and laser reflectance properties of the object surface, that often lead to holes and inaccuracies on the recovered surface. Shape from silhouette, on the other hand, as a passive reconstruction technique, yields robust, hole-free reconstruction of the visual hull of the object. In this paper, a hybrid surface reconstruction method that fuses geometrical information acquired from silhouette images and optical triangulation is presented. Our motivation is to recover the geometry from silhouettes on those parts of the surface which the range data fail to capture. A volumetric octree representation is first obtained from the silhouette images and then carved by range points to amend the missing cavity information. An isolevel value on each surface cube of the carved octree structure is accumulated using local surface triangulations obtained separately from range data and silhouettes. The marching cubes algorithm is then applied for triangulation of the volumetric representation. The performance of the proposed technique is demonstrated on several real objects.     

Recognition by linear combinations of models

An approach to visual object recognition in which a 3D object is represented by the linear combination of 2D images of the object is proposed. It is shown that for objects with sharp edges as well as with smooth bounding contours, the set of possible images of a given object is embedded in a linear space spanned by a small number of views. For objects with sharp edges, the linear combination representation is exact. For objects with smooth boundaries, it is an approximation that often holds over a wide range of viewing angles. Rigid transformations (with or without scaling) can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations. Three alternative methods of determining the transformation that matches a model to a given image are proposed     

广义线性八元树表示及物体的广义三维重建

提出物体的广义线性八元树表示法,推广线性八元树的构造方法完成物体的广义三 维重建--广义线性八元树表示,从而为物体三维重建降低约束、增加灵活性.     

一种改进的八元树三维目标表示方法

利用八元树表示三维物体是一种十分有效的方法。传统指针表示的八元树结构具有占据内存容量大、节点间关系少等缺点。在分析了物体的空间布局和八元树结构的基础上,文章提出了一种改进的八元树三维表示方法。从医学图像三维重建的实验结果看,提出的方法可行并且在内存存储结构和访问方式等方面优于传统的表示方法。     

基于图像的对象环绕视图生成方法研究

基于图像的环绕视图生成应用IBMR替代传统的三维对象建模的方法,对虚拟场景中的对象进行建模和表现。该文探讨了基于图像的建模与渲染在环境表现和对象表现上的区别,提出了环绕视域空间划分的对象采样方法,通过建立相邻样本之间的特征点匹配关系,计算样本之间的相对关系,进行视图的平行变换和合成。     

Describing a Robot's Workspace Using a Sequence of Views from a Moving Camera

This correspondence describes a method of building and maintaining a spatial respresentation for the workspace of a robot, using a sensor that moves about in the world. From the known camera position at which an image is obtained, and two-dimensional silhouettes of the image, a series of cones is projected to describe the possible positions of the objects in the space. When an object is seen from several viewpoints, the intersections of the cones constrain the position and size of the object. After several views have been processed, the representation of the object begins to resemble its true shape. At all times, the spatial representation contains the best guess at the true situation in the world with uncertainties in position and shape explicitly represented. An octree is used as the data structure for the representation. It not only provides a relatively compact representation, but also allows fast access to information and enables large parts of the workspace to be ignored. The purpose of constructing this representation is not so much to recognize objects as to describe the volumes in the workspace that are occupied and those that are empty. This enables trajectory planning to be carried out, and also provides a means of spatially indexing objects without needing to represent the objects at an extremely fine resolution. The spatial representation is one part of a more complex representation of the workspace used by the sensory system of a robot manipulator in understanding its environment.     

Model construction and shape recognition from occluding contours

A technique is presented for recognizing a 3D object (a model in an image library) from a single 2D silhouette using information such as corners (points with high positive curvatures) and occluding contours, rather than straight line segments. The silhouette is assumed to be a parallel projection of the object. Each model is stored as a set of the principal quadtrees, from which the volume/surface octree of the model is generated. Feature points (i.e. corners) are extracted to guide the recognition process. Four-point correspondences between the 2D feature points of the observed object and 3D feature points of each model are hypothesized, and then verified by applying a variety of constraints to their associated viewing parameters. The result of the hypothesis and verification process is further validated by 2D contour matching. This approach allows for a method of handling both planar and curved objects in a uniform manner, and provides a solution to the recognition of multiple objects with occlusion as demonstrated by the experimental results     

A solution to the next best view problem for automated surfaceacquisition

A solution to the “next best view” (NBV) problem for automated surface acquisition is presented. The NBV problem is to determine which areas of a scanner's viewing volume need to be scanned to sample all of the visible surfaces of an a priori unknown object and where to position/control the scanner to sample them. A method for determining the unscanned areas of the viewing volume is presented. In addition, a novel representation, positional space, is presented which facilitates a solution to the NBV problem by representing what must be and what can be scanned in a single data structure. The number of costly computations needed to determine if an area of the viewing volume would be occluded from some scanning position is decoupled from the number of positions considered for the NBV, thus reducing the computational cost of choosing one. An automated surface acquisition systems designed to scan all visible surfaces of an a priori unknown object is demonstrated on real objects     

Octree creation via C.S.G. definition

The common method for generating the octrees of complex objects, is based upon generating the octrees of several pre-defined primitives and applying Boolean operations on them. Regardless how the octrees representing the primitives are generated (top-down or bottom-up) the octree of a desired object is obtained by performing Boolean operations among the primitives comprising the object according to the object's CSG (constructive solid Geometry) representation. When carrying out this procedure, most of the computing and memory resources are used for generating and storing the octants comprising the primitives. However, the majority of those octants are not required for the representation of the final object. In this paper the extention of the top-down approach to the CSG level (i.e., generating the octree of an object directly from its CSG representation) is proposed. With this method there is no need to generate the octrees of the primitives comprising the object nor to perform Boolean operations on them. Moreover, only these octants which belong to the final object are generated.     

Feature space trajectory methods for active computer vision

We advance new active object recognition algorithms that classify rigid objects and estimate their pose from intensity images. Our algorithms automatically detect if the class or pose of an object is ambiguous in a given image, reposition the sensor as needed, and incorporate data from multiple object views in determining the final object class and pose estimate. A probabilistic feature space trajectory (FST) in a global eigenspace is used to represent 3D distorted views of an object and to estimate the class and pose of an input object. Confidence measures for the class and pose estimates, derived using the probabilistic FST object representation, determine when additional observations are required as well as where the sensor should be positioned to provide the most useful information. We demonstrate the ability to use FSTs constructed from images rendered from computer-aided design models to recognize real objects in real images and present test results for a set of metal machined parts.     

Multiview registration of 3D scenes by minimizing error between coordinate frames

This paper addresses the problem of large-scale multiview registration of range images captured from unknown viewing directions. To reduce the computational burden, we separate the local problem of pairwise registration on neighboring views from the global problem of distribution of accumulated errors. We define the global problem as an optimization over the graph of neighboring views, and we show how the graph can be decomposed into a set of cycles such that the optimal transformation parameters for each cycle can be solved in closed form. We then describe an iterative procedure that can be used to integrate the solutions for the set of cycles across the graph of views. This method for error distribution does not require point correspondences between views, and can be used to integrate any method of pairwise registration or robot odometry.     

Learning to detect objects in images via a sparse, part-based representation

We study the problem of detecting objects in still, gray-scale images. Our primary focus is the development of a learning-based approach to the problem that makes use of a sparse, part-based representation. A vocabulary of distinctive object parts is automatically constructed from a set of sample images of the object class of interest; images are then represented using parts from this vocabulary, together with spatial relations observed among the parts. Based on this representation, a learning algorithm is used to automatically learn to detect instances of the object class in new images. The approach can be applied to any object with distinguishable parts in a relatively fixed spatial configuration; it is evaluated here on difficult sets of real-world images containing side views of cars, and is seen to successfully detect objects in varying conditions amidst background clutter and mild occlusion. In evaluating object detection approaches, several important methodological issues arise that have not been satisfactorily addressed in the previous work. A secondary focus of this paper is to highlight these issues, and to develop rigorous evaluation standards for the object detection problem. A critical evaluation of our approach under the proposed standards is presented.