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.     

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     

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.     

Computing the aspect graph for line drawings of polyhedral objects

An algorithm for computing the aspect graph for polyhedral objects is described. The aspects graph is a representation of three-dimensional objects by a set of two-dimensional views. The set of viewpoints on the Gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same. At the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes. It is shown that for polyhedral objects there are two fundamental visual events: (1) the projections of an edge and a vertex coincide; and (2) the projections of three nonadjacent edges intersect at a point. The geometry of the object is reflected in the locus of the accidental viewpoints. The algorithm computes the partition together with a representative view for each region of the partition     

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.     

Automatic Generation of Multiresolution Boundary Representations

The paper focuses on automatic simplification algorithms for the generation of a multiresolution family of solid models from an initial boundary representation of a polyhedral solid. An algorithm for general polyhedra based on an intermediate octree representation is proposed. Simplified elements of the multiresolution family approximate the initial solid within increasing tolerances. A discussion among different octree-based simplification methods and the standard marching cubes algorithm is presented.     

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.     

基于图片序列的三维表面重建

根据非透明物体内部不可见的实际,提出了一种基于图片序列的三维表面重建算法.该算法首先利用传统的八叉树算法重建出物体的三维模型,然后利用一种新颖的表面点提取算法提取出物体表面点,最后利用这些表面点进行三角网格剖分,进而重建出光滑的三维物体表面.在表面点的提取过程中,算法对处于不同状态(处于立方体的顶点、棱、面)的点赋予不...     

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.     

Efficiently computing and representing aspect graphs of polyhedralobjects

An efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented. The aspect graph is an approach to representing 3-D objects by a set of 2-D views, for the purpose of object recognition. In this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change. The viewing data of an object is the partition of the viewpoint space together with a representative view in each region. The algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection     

Obtaining complete 2 D view representation of polyhedra using concept of seedling single-view area

This article deals with construction of complete 2 D exact view models of polyhedral objects for visual identification systems. In particular, a new method and an algorithm views generation using the view sphere with perspective concept are described. A set of views generated by this method forms a complete view representation of the object. The method of ensuring completeness of the view representation by controlling covering of the view space (by single-view areas) is used in the presented algorithm. The perspective projection used for calculating the views, the total, tight covering of the view sphere by the single-view areas and -dimensionality of the views ensure, in our opinion, unambiguous and proper identification of polyhedral objects. The method consists in calculating single (any) view, determining the corresponding single-view area (so-called seedling single-view area) and then spiral propagation of neighbouring single-view areas until the whole view sphere is covered by them (i.e., until the border register containing the border between the covered and uncovered parts of the view sphere becomes empty). Having a complete set of single-view areas, we get a complete set of views as well. A method of determining single-view areas for convex polyhedra is also presented.     

Polyhedral object recognition by indexing

In computer vision, the indexing problem is the problem of recognizing a few objects in a large database of objects while avoiding the help of the classical image-feature-to-object-feature matching paradigm. In this paper we address the problem of recognizing three-dimensional (3-D) polyhedral objects from 2-D images by indexing. Both the objects to be recognized and the images are represented by weighted graphs. The indexing problem is therefore the problem of determining whether a graph extracted from the image is present or absent in a database of model graphs. We introduce a novel method for performing this graph indexing process which is based both on polynomial characterization of binary and weighted graphs and on hashing. We describe in detail this polynomial characterization and then we show how it can be used in the context of polyhedral object recognition. Next we describe a practical recognition-by-indexing system that includes the organization of the database, the representation of polyhedral objects in terms of 2-D characteristic views, the representation of this views in terms of weighted graphs and the associated image processing. Finally, some experimental results allow the evaluation of the system performance.     

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.     

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.     

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.     

A new global accessibility algorithm for a polyhedral model with convex polygonal facets

Global accessibility information of a CAD model has been utilized widely in various manufacturing applications. This information needs fast-computing to improve the efficiency of manufacturability analysis. It needs compact representation to increase the effective utilization in its process-planning task. We propose a new geometric algorithm to explicitly find the global accessibility cones (GAC) of a polyhedral model. The proposed algorithm has three main steps. The first is concave region extraction, collecting facets that are not on the convex hull of the entire model. Second, inaccessibility of convex polygonal facets in these concave regions is analyzed in order to find their inaccessibility cones (IAC). The method is done in 2D instead of 3D. Finally, to compute GACs of those facets, the complement of the IACs union is determined for an exact solution, while the slicing-method is proposed to find a near-exact solution. In this paper, geometric examples are demonstrated and a comparison of the computational complexity with existing algorithms is provided.     

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.     

Representation and shape matching of 3-d objects

A three-dimensional scene analysis system for the shape matching of real world 3-D objects is presented. Various issues related to representation and modeling of 3-D objects are addressed. A new method for the approximation of 3-D objects by a set of planar faces is discussed. The major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3-D scene analysis. The method is a sequential region growing algorithm. It is not applied to range images, but rather to a set of 3-D points. The 3-D model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object, applying the necessary transformations and then approximating the surface by polygons. A stochastic labeling technique is used to do the shape matching of 3-D objects. The technique matches the faces of an unknown view against the faces of the model. It explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification. It is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels. The objective here is to match the individual views of the object taken from any vantage point. Details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting.