Estimation of three-dimensional objects from orthographic views with inconsistencies

Many algorithms to construct 3-D solid objects from orthographic views assume the bottom-up approach. This paper describes a method for identifying conflictions found in inconsistent views which improbably present complete objects and estimating solid objects. The sources of inconsistencies are extra segments, missing segments and incorrect classifications of line types (visible lines or hidden lines). In order to supply candidates for missing segments, probable segments are generated not from three views but from two views. The signs appearing in each step of the bottom-up algorithm are examined, and then the heuristic method for selecting more probable segments is developed. The estimation of solid objects and identification of incoherences are useful, for example, to detect improper input of three views and incorrect recognition of engineering drawings.     

Reconstruction of 3D interacting solids of revolution from 2D orthographic views

3D CAD is replacing 2D CAD to improve efficiency of product design and manufacturing. Therefore, converting legacy 2D drawings into 3D solid models is required. CSG based approaches reconstruct solid models from orthographic views more efficiently than traditional B-rep based approaches. A major limitation of CSG based approaches has been the limited domain of objects that can be handled. This paper aims at extending the capabilities of CSG based approaches by proposing a hint-based recognition of interacting solids of revolution. This approach can handle interacting solids of revolution as well as isolated solids of revolution.     

Polyhedral objects identification through the orthographic projection views generation

This paper presents a new method to automatic recognition of polyhedra. Given images taken from different viewpoints of designated polyhedra, algorithms are developed to interpret them as the same object. Based on the heuristic inference of the polyhedral scene regularities and the gradient space analysis, this method will restore the 3-D information of the polyhedra. The 3-D data is used for the generation of the orthographic projection views of the observed object which consist of the top view, the front view, and the side view.     

Reconstruction of intersecting curved solids from 2D orthographic views

This paper presents a new approach to reconstruct curved solids composed of elementary volumes intersecting with one another from three-view engineering drawings. Intersection curves arising from two intersecting curved surfaces are mostly higher order spatial curves, which cannot be described exactly by 2D orthographic projections and normally represented as smooth curves passing through several key points or even simplified as arcs or lines. Approximated sketches of higher order intersection curves in 2D views result in the invalidation of existing methods that need the exact projection information as input. Based on some heuristic hints, our method is able to recover the complete and correct half-profiles of the intersecting elementary volumes using the least traces left by them, which ensure the correctness of solution solids constructed finally. Several examples are provided to show the validation of the described method.     

应用多个正交视角轮流逼近3维目标的坐标

为实现目标的快速、精确3维定位和跟踪,提出一种正交摄像机视频定位系统及其坐标轮流逼近的迭代定位算法。系统中平面摄像机光轴按照正交方式布置,拍摄方向均指向原点。不同于现有的大部分计算机视觉方法,本算法中没有影响定位效率和精度问题的图像配准操作。证明了迭代算法的收敛性。数值验证和实际试验表明,本算法计算简单、误差稳定性好,收敛快,因此具有良好的应用潜力。     

3D geometry reconstruction from orthographic views: A method based on 3D image processing and data fitting

Industrial esthetic designers typically produce hand-drawn sketches in the form of orthographic projections. A subsequent translation from 2D-drawings to 3D-models is usually necessary. This involves a considerably time consuming process, so that some automation is advisable.     

Handling sectional views in volume-based approach to automatically construct 3D solid from 2D views

This paper presents an algorithm for solid model reconstruction from 2D sectional views based on volume-ba`sed approach. None of the existing work in automatic reconstruction from 2D orthographic views have addressed sectional views in detail. It is believed that the volume-based approach is better suited to handle different types of sectional views. The volume-based approach constructs the 3D solid by a boolean combination of elementary solids. The elementary solids are formed by sweep operation on loops identified in the input views. The only adjustment to be made for the presence of sectional views is in the identification of loops that would form the elemental solids. In the algorithm, the conventions of engineering drawing for sectional views, are used to identify the loops correctly. The algorithm is simple and intuitive in nature. Results have been obtained for full sections, offset sections and half sections. Future work will address other types of sectional views such as removed and revolved sections and broken-out sections.     

Using motion from orthographic views to verify 3-D point matches

The specific problem addressed by the authors is how to detect the true match of a fourth point from among candidate matches in a situation in which three points have already been matched. The two sets of points to be matched are both subject to measurement errors. The depth error is more dominant than errors in the other two coordinates; however, the exact statistical distribution of the measurement errors is not known. The authors present a new method for solving the problem. The method is based on the technique of motion analysis using orthographic views. It discards the noisy z (depth) coordinates and uses only the x and y coordinates of the points to verify the match. The effect of depth errors on the motion estimate is completely prevented. Results show that this method is substantially more effective than previous methods that use all three coordinates     

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     

Effectiveness of applying 2D static depictions and 3D animations to orthographic views learning in graphical course

This study provides experiment results as an educational reference for instructors to help student obtain a better way to learn orthographic views in graphical course. A visual experiment was held to explore the comprehensive differences between 2D static and 3D animation object features; the goal was to reduce the possible misunderstanding factors in the learning process. This empirical study provided one hundred and twenty Taiwanese freshmen four types of visualization, which includes two 2D static depictions (2DT, 2DR), and two 3D animations (3DT, 3DR), to meet five surface styles on orthographic views. The responses to views ability test and interviews illustrated that applying 3D animations shows better performance in understanding the appearances and features of objects constructed by oblique and double-curved surfaces. The application of 3D animations results also demonstrates a better visual comprehension for students, especially when objects are constructed by the complicated features.     

Solid reconstruction from orthographic opaque views using incremental extrusion

The reconstruction of 3-D solids from 2-D projections is an important research topic in reverse engineering. The reconstruction can be grouped into two categories: single-view approach and multiple-view approach. Each approach can be classified as wireframe, BRep or CSG. However, not many CSG approaches have been reported in the literature. The methods are also restricted to uniform-thickness objects or require user interaction. The method proposed in this paper employs the CSG approach. A 3-D solid computer model is reconstructed from 2-D line drawings of six orthographic opaque views, viz. top, front, left, right, bottom and rear views. Firstly, the six views are grouped into three pairs. For each pair of views, segmented areas from one of the two views (called g-view) is incrementally extruded according to the information in the neighbouring view (called d-view). Extrusion primitive solids are generated during the incremental extrusion. All primitive solids are then unioned into an extrusion solid. Finally, all extrusion solids are intersected to give a unique 3-D solution object.     

Solid reconstruction using recognition of quadric surfaces from orthographic views

The reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided.     

Invariant object recognition in the visual system with novel views of 3D objects

To form view-invariant representations of objects, neurons in the inferior temporal cortex may associate together different views of an object, which tend to occur close together in time under natural viewing conditions. This can be achieved in neuronal network models of this process by using an associative learning rule with a short-term temporal memory trace. It is postulated that within a view, neurons learn representations that enable them to generalize within variations of that view. When three-dimensional (3D) objects are rotated within small angles (up to, e.g., 30 degrees), their surface features undergo geometric distortion due to the change of perspective. In this article, we show how trace learning could solve the problem of in-depth rotation-invariant object recognition by developing representations of the transforms that features undergo when they are on the surfaces of 3D objects. Moreover, we show that having learned how features on 3D objects transform geometrically as the object is rotated in depth, the network can correctly recognize novel 3D variations within a generic view of an object composed of a new combination of previously learned features. These results are demonstrated in simulations of a hierarchical network model (VisNet) of the visual system that show that it can develop representations useful for the recognition of 3D objects by forming perspective-invariant representations to allow generalization within a generic view.     

Geometric assistance for visual reasoning and construction of solids with curved surfaces from 2D orthographic views

As the extensive use of solid models becomes widespread, it is important to have a mechanism by which existing engineering drawings can be converted into solid models. Therefore, a geometric assistance that can aid in visual reasoning and constructing of solid models is beneficial. In this paper, we present key operations for a system called the Assistant for Reasoning and Construction of Solids (ARCS), which provides this assistance given a set of two orthographic views. The geometric domain of ARCS encompasses curved solids with cylindrical and spherical surfaces, such as those found in typical mechanical parts. We have devised the Cylindrical and Spherical Warping operations to create cylindrical and spherical surfaces, which use interactive computer graphics that guide a human user to curved faces of a solid. These operations are then illustrated with examples using ARCS to create the solid models of typical mechanical parts from their orthographic projections.     

Model-based recognition of 3D objects from single images

In this work, we treat major problems of object recognition which have received relatively little attention lately. Among them are the loss of depth information in the projection from a 3D object to a single 2D image, and the complexity of finding feature correspondences between images. We use geometric invariants to reduce the complexity of these problems. There are no geometric invariants of a projection from 3D to 2D. However, given certain modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions can be either a particular model or a generic assumption about a class of models. Here, we use such assumptions for single-view recognition. We find algebraic relations between the invariants of a 3D model and those of its 2D image under general projective projection. These relations can be described geometrically as invariant models in a 3D invariant space, illuminated by invariant “light rays,” and projected onto an invariant version of the given image. We apply the method to real images     

无序图像三维重构中的图像选择技术

针对无序图像的三维重构问题,本文提出了一种图像选择算法,在三维重构算法运行之前,首先利用图像间的全局运动估计,去除冗余的图像,有效的减少了问题的规模,同时保持图像间的大部分连接关系,并能够较好地防止出现退化情况。为了验证本文的算法,针对一系列图像进行了测试,实验结果证明,作为三维重构的一个预处理过程,提高了三维重构算法的运行效率和算法的鲁棒性,具有很高的实用价值。     

Lines in one orthographic and two perspective views

We introduce a linear algorithm to recover the Euclidean motion between an orthographic and two perspective cameras from straight line correspondences filling the gap in the analysis of motion estimation from line correspondences for various projection models. The general relationship between lines in three views is described by the trifocal tensor. Euclidean structure from motion for three perspective views is a special case in which the relationship is defined by a collection of three matrices. Here, we describe the case of two calibrated perspective views and an orthographic view. Similar to the other cases, our linear algorithm requires 13 or more line correspondences to recover 27 coefficients of the trifocal tensor.