Skewed rotational symmetry detection from a 2D line drawing of a 3D polyhedral object

This paper introduces a new algorithm for detecting skewed rotational symmetry in a 2D line drawing of a 3D polyhedral object by locating the possibly-multiple symmetry axes. The drawing is converted into an edge–vertex graph from which the algorithm finds the faces of the object and the sets of topologically symmetric edges and vertices. It then checks that each set of vertices is rotationally symmetric geometrically by analyzing the distribution of the vertices around the circumference of the best-fit ellipse. The object is rotationally skewed symmetric if the best fit ellipses of all the vertex sets have parallel axes, equal ratio of major radius to minor radius and centers on the axis of rotation. A tolerance is used in the calculation to allow for inaccuracies in the line drawings. A set of experimental results is presented showing that the algorithm works well.     

3D reconstruction of polyhedral objects from single parallel projections using cubic corner

This paper presents a direct method to recover the geometry of the 3D polyhedron depicted in a single parallel projection. It uses two sets of information, the list of faces in the object, obtained automatically from the drawing, and a user-identified cubic corner, to compute for the coordinates of the vertices in the drawing and thus establish the 3D geometry of the whole polyhedron. The algorithm exploits the topological structure of the polyhedron, implicit in the connectivities between the faces, resulting in a complexity that is linear in the number of faces. The method is extended to objects with no cubic corners as well. The algorithm works well for recovering objects from accurate line drawings, producing accurate 3D objects. A simple extension to the algorithm allows it to handle inaccurate drawings such as sketches, and produce 3D objects that are consistent with our human perception of the drawings.     

3D Reconstruction from 2D Line Drawings only with Visible Vertices and Edges

The human vision system can reconstruct a 3D object easily from single 2D line drawings even if the hidden lines of the object are invisible. Now, there are many methods have emulated this ability, but when the hidden lines of the object are invisible, these methods cannot reconstruct a complete 3D object. Therefore, we put forward a new algorithm to settle this hard problem. Our approach consists of two steps： （1） infer the invisible vertices and edges to complete the line drawing, （2） propose a vertex-based optimization method to reconstruct a 3D object.     

3D reconstruction of complex curved objects from line drawings

An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve this problem, but they can't solve this problem when the geometric structure of a curved object becomes complex. This paper proposes a novel approach to reconstructing a complex curved 3D object from single 2D line drawings. Our approach has three steps:(1) decomposing a complex line drawing into several simpler line drawings and transforming them into polyhedron;(2) reconstructing the 3D wireframe of curved object from these simpler line drawings and generating the curved faces;(3) combining the 3D objects into the complete objects. A number of examples are given to demonstrate the ability of our approach to successfully perform reconstruction of curved objects which are more complex than previous methods.     

Plane-based optimization for 3D object reconstruction from single line drawings

In previous optimization-based methods of 3D planar-faced object reconstruction from single 2D line drawings, the missing depths of the vertices of a line drawing (and other parameters in some methods) are used as the variables of the objective functions. A 3D object with planar faces is derived by finding values for these variables that minimize the objective functions. These methods work well for simple objects with a small number N of variables. As N grows, however, it is very difficult for them to find expected objects. This is because with the nonlinear objective functions in a space of large dimension N, the search for optimal solutions can easily get trapped into local minima. In this paper, we use the parameters of the planes that pass through the planar faces of an object as the variables of the objective function. This leads to a set of linear constraints on the planes of the object, resulting in a much lower dimensional nullspace where optimization is easier to achieve. We prove that the dimension of this nullspace is exactly equal to the minimum number of vertex depths which define the 3D object. Since a practical line drawing is usually not an exact projection of a 3D object, we expand the nullspace to a larger space based on the singular value decomposition of the projection matrix of the line drawing. In this space, robust 3D reconstruction can be achieved. Compared with two most related methods, our method not only can reconstruct more complex 3D objects from 2D line drawings, but also is computationally more efficient.     

Decomposition of complex line drawings with hidden lines for 3D planar-faced manifold object reconstruction

Three-dimensional object reconstruction from a single 2D line drawing is an important problem in computer vision. Many methods have been presented to solve this problem, but they usually fail when the geometric structure of a 3D object becomes complex. In this paper, a novel approach based on a divide-and-conquer strategy is proposed to handle the 3D reconstruction of a planar-faced complex manifold object from its 2D line drawing with hidden lines visible. The approach consists of four steps: 1) identifying the internal faces of the line drawing, 2) decomposing the line drawing into multiple simpler ones based on the internal faces, 3) reconstructing the 3D shapes from these simpler line drawings, and 4) merging the 3D shapes into one complete object represented by the original line drawing. A number of examples are provided to show that our approach can handle 3D reconstruction of more complex objects than previous methods.     

Topology based 2D engineering drawing and 3D model matching for process plant

Process plant models mainly include 3D models and 2D engineering drawings. Matching calculation between these CAD models has wide applicability in model consistency check and retrieval. In process plant, engineering design standards make 2D engineering drawing and 3D model differ in geometry, proportion and structure, leading to the inapplicability of current shape-feature based matching approaches. Since connection relationships between components are the core of a process plant, a topology based algorithm is proposed. Firstly, by exploiting components as vertices and relationships as edges, both 2D engineering drawing and 3D model are preprocessed into graph structures. Then each model’s relationship types are extracted from the graph. Finally, regarding the extracted relationship types as primary feature, feature similarity is calculated to measure the matching degree between their corresponding models. The proposed algorithm is geometric deformation invariant. Experiments with industrial applications are presented, which demonstrates the effectiveness and feasibility of the proposed algorithm.     

Overcoming superstrictness in line drawing interpretation

Presents an algorithm for correcting incorrect line drawings-incorrect projections of a polyhedral scene. Such incorrect drawings arise, e.g., when an image of a polyhedral world is taken, the edges and vertices are extracted, and a drawing is synthesized. Along the way, the true positions of the vertices in the 2D projection are perturbed due to digitization errors and the preprocessing. As most available algorithms for interpreting line drawings are "superstrict," they judge these noisy inputs as incorrect and fail to reconstruct a three-dimensional scene from them. The presented method overcomes this problem by moving the positions of all vertices until a very close correct drawing is found. The closeness criterion is to minimize the sum of squared distances from each vertex in the input drawing to its corrected position. With this tool, any superstrict method for line drawing interpretation is now practical, as it can be applied to the corrected version of the input drawing     

Extracting 3D model feature lines based on conditional random fields

We propose a 3D model feature line extraction method using templates for guidance. The 3D model is first projected into a depth map, and a set of candidate feature points are extracted. Then, a conditional random fields (CRF) model is established to match the sketch points and the candidate feature points. Using sketch strokes, the candidate feature points can then be connected to obtain the feature lines, and using a CRF-matching model, the 2D image shape similarity features and 3D model geometric features can be effectively integrated. Finally, a relational metric based on shape and topological similarity is proposed to evaluate the matching results, and an iterative matching process is applied to obtain the globally optimized model feature lines. Experimental results showed that the proposed method can extract sound 3D model feature lines which correspond to the initial sketch template.     

手绘图风格的三维模型线条渲染

现有的三维模型线条渲染方法,由于模型是网格结构,渲染得到线条图由大量的小线段组成,导致图形中有许多明显的棱角和孤立线段.提出了一种新的手绘图风格的三维模型线条渲染方法,将观察到的三维模型转化成简洁、自然的线条图.算法首先采用Suggestive Contours方法得到模型的特征线段集,通过分析线段的空间信息,将小线段连接成若干长线条,并用三次B样条曲线插值这些线条,然后引入B样条小波对线条进行简化.实验结果表明,本文的方法可以很好地连接这些线段集,得到平滑、简洁的手绘风格模型线条图.     

Labeling Line Drawings with Hidden-Part-Drawn of Planar Object with Trihedral Vertices

Although line drawings consist of only line segments on a plane, they convey much information about the three-dimensional object structures. For a computer interpreting line drawings, some intelligent mechanism is required to extract three-dimensional information from the two-dimensional line drawings. In this paper, a new labeling theory and method are proposed for the two-dimensional line drawing with hidden-part-draw of a three-dimensional planar object with trihedral vertices. Some rules for labeling line drawing are established. There are 24 kinds of possible junctions for line drawing with hidden-part-draw, in which there are 8 possible Y and 16 W junctions. The three problems are solved that Sugihara's line drawing labeling technique exists. By analyzing the projections of the holes in manifold planar object, we have put forward a labeling method for the line drawing. Our labeling theory and method can discriminate between correct and incorrect hidden-part-draw natural line drawings. The hidden-part-draw natural line drawings can be labeled correctly by our labeling theory and method, whereas the labeling theory of Sugihara can only label the hidden-part-draw unnatural line drawings in which some visible lines must be drawn as hidden lines, and some invisible lines must be drawn as continuous lines.     

Identification of sections from engineering drawings based on evidence theory

View identification is the basic process for solid reconstruction from engineering drawings. A new method is presented to label various views from a section-involved drawing and identify geometric planes through the object at which the sections are to be located. In the approach, a graph representation is developed for describing multiple relationships among various views in the 2D drawing space, and a reasoning technique based on evidence theory is implemented to validate view relations that are used to fold views and sections in the 3D object space. This is the first automated approach which can handle multiple sections in diverse arrangements, especially accommodating the aligned section for the first time. Experimental results are given to show that the proposed solution makes a breakthrough in the field and builds a promising basis for further expansibility, although it is not a complete one.     

三维物体的形态图表达方法

三维物体的表达方法是计算机视觉中的关键问题之一，现有的各种三维物体表达方法虽然在各自的识别中得到应用，但都存在各自的局限性，用形态图表达三维物体是一种以视点为中心的表达方法，由于它列举了一个物体所有可能的“定性”形象，即它可使用最少的二维投影线图（特征视图）来表达一个完整的三维物体，因此使三维物体识别转化为2D与2D的匹配，该文首先定义了二维线图拓扑结构等价的判别准则，然后给出了构造透明物体形态图的方法，最后根据拓扑结构等价准则来得到不透明物体的形态图和特征图，并用圆锥与圆柱相交的实例进行了验证。     

New grouping and fitting methods for interactive overtraced sketches

This paper describes a new method for recognizing overtraced strokes to 2D geometric primitives, which are further interpreted as 2D line drawings. This method can support rapid grouping and fitting of overtraced polylines or conic curves based on the classified characteristics of each stroke during its preprocessing stage. The orientation and its endpoints of a classified stroke are used in the stroke grouping process. The grouped strokes are then fitted with 2D geometry. This method can deal with overtraced sketch strokes in both solid and dash linestyles, fit grouped polylines as a whole polyline and simply fit conic strokes without computing the direction of a stroke. It avoids losing joint information due to segmentation of a polyline into line-segments. The proposed method has been tested with our freehand sketch recognition system (FSR), which is robust and easier to use by removing some limitations embedded with most existing sketching systems which only accept non-overtraced stroke drawing. The test results showed that the proposed method can support freehand sketching based conceptual design with no limitations on drawing sequence, directions and overtraced cases while achieving a satisfactory interpretation rate.     

Efficient and robust 3D line drawings using difference-of-Gaussian

Line drawings are widely used for sketches, animations, and technical illustrations because they are effective and easy to draw. The existing computer-generated lines, such as suggestive contours, apparent ridges, and demarcating curves, adopt the two-pass framework: in the first pass, certain geometric features or properties are extracted or computed in the object space; then in the second pass, the line drawings are rendered by iterating each polygonal face or edge. It is known these approaches are very sensitive to the mesh quality, and usually require appropriate preprocessing operations (e.g. smoothing, remeshing, etc.) to the input meshes. This paper presents a simple yet robust approach to generate view-dependent line drawings for 3D models. Inspired by the image edge detector, we compute the difference-of-Gaussian of illumination on the 3D model. With moderate assumption, we show all the expensive computations can be done in the pre-computing stage. Our method naturally integrates object- and image-spaces in that we compute the geometric features in the object space and then adopt a simple fragment shader to render the lines in the image space. As a result, our algorithm is more efficient than the existing object-space approaches, since the lines are generated in a single pass without iterating the mesh edges/faces. Furthermore, our method is more flexible and robust than the existing algorithms in that it does not require the preprocessing on the input 3D models. Finally, the difference-of-Gaussian operator can be extended to the anisotropic setting guided by local geometric features. The promising experimental results on a wide range of real-world models demonstrate the effectiveness and robustness of our method.     

Identifying faces in a 2D line drawing representing a manifold object

A straightforward way to illustrate a 3D model is to use a line drawing. Faces in a 2D line drawing provide important information for reconstructing its 3D geometry. Manifold objects belong to a class of common solids and most solid systems are based on manifold geometry. In this paper, a new method is proposed for finding faces from single 2D line drawings representing manifolds. The face identification is formulated based on a property of manifolds: each edge of a manifold is shared exactly by two faces. The two main steps in our method are (1) searching for cycles from a line drawing and (2) searching for faces from the cycles. In order to speed up the face identification procedure, a number of properties, most of which relate to planar manifold geometry in line drawings, are presented to identify most of the cycles that are or are not real faces in a drawing, thus reducing the number of unknown cycles in the second searching. Schemes to deal with manifolds with curved faces and manifolds each represented by two or more disjoint graphs are also proposed. The experimental results show that our method can handle manifolds previous methods can handle, as well as those they cannot.     

What the back of the object looks like: 3D reconstruction from line drawings without hidden lines

The human vision system can interpret a single 2D line drawing as a 3D object without much difficulty even if the hidden lines of the object are invisible. Many reconstruction methods have been proposed to emulate this ability, but they cannot recover the complete object if the hidden lines of the object are not shown. This paper proposes a novel approach to reconstructing a complete 3D object, including the shape of the back of the object, from a line drawing without hidden lines. First, we develop theoretical constraints and an algorithm for the inference of the topology of the invisible edges and vertices of an object. Then we present a reconstruction method based on perceptual symmetry and planarity of the object. We show a number of examples to demonstrate the success of our approach.     

具有相切面的曲面立体线画图标记研究

为了更好地理解三维景物，介绍了前人对线画图标记的研究成果，同时建立了一种标记具有相切面的曲面立体线画图的方法，并给出了具有相切面的曲面立体线画图的标记规则。由于线画图中的节点是由三面角构成的顶点的投影，因此对于画出隐藏线的具有相切面的曲面立体线画图，其合法的节点标记形式有38种，其中Y型节点有6种，W型节点有18种，V型节点有14种。新的标记方法适用于由平面立体和曲面立体组合而成的复杂立体线画图。