Nearest neighbor weighted average customization for modeling faces

In this paper, we present an anatomically accurate generic wireframe face model and an efficient customization method for modeling human faces. We use a single 2D image for customization of the generic model. We employ perspective projection to estimate 3D coordinates of the 2D facial landmarks in the image. The non-landmark vertices of the 3D model are shifted using the translations of k nearest landmark vertices, inversely weighted by the square of their distances. We demonstrate on Photoface and Bosphorus 3D face data sets that the proposed method achieves substantially low relative error values with modest time complexity.     

融合视觉认知的工程视图理解方法

基于人的理解过程和方法,文中提出了工程视图理解的新算法框架。它允许用户参与到理解过程中,在出现歧义时,根据人的视觉认知规律进行“猜测”和“推理”,可得到与人的理解结果更为一致的解,并允许加入剖视图的处理。该文着重介绍该方法的算法思想,以及基元的划分与生成、剖视图处理、视觉推理等关键算法步骤。     

基于中轴表达的三维模型轮廓提取方法

三维网格模型的轮廓信息在网格检索、网格简化、网格重建中有着广泛应用。现有的轮廓提取方法较为复杂,需要分析和过滤网格模型的几何特征,计算量大且有时无法生成完整的轮廓信息。近年来,三维模型的中轴表达研究趋于成熟,在表达模型几何拓扑关系上有独特的优势。因此,提出了一种基于中轴表达的三维模型轮廓提取方法：首先提取三维模型的中轴表达信息,将中轴角点投影到三维模型表面;然后根据每个区域的拓扑关系选择适合的角点连接关系,将投影点连接形成模型区域轮廓;再针对投影过程中产生的误差进行分析和纠正;最后合并区域轮廓得到三维模型的完整轮廓。通过对多个模型数据库中代表性的三维网格模型进行实验和重建误差比较,该方法的平均重建质量较现有方法约有10%的提升,在重建质量和轮廓信息完整度方面优于现有方法。     

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.     

Photogrammetric reconstruction of free-form objects with curvilinear structures

The shapes of many natural or man-made objects have curve features. The images of such curves usually do not have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we introduce a photogrammetric method for recovering free-form objects with curvilinear structures. Our method chooses to obtain the topology and geometry of a sparse 3D wireframe of the object first instead of directly recovering a surface or volume model. Surface patches covering the object are then constructed to interpolate the curves in this wireframe while satisfying certain heuristics such as minimal bending energy. The result is an object surface model with curvilinear structures from a sparse set of images. We can produce realistic texture-mapped renderings of the object model from arbitrary viewpoints. Reconstruction results on multiple real objects are presented to demonstrate the effectiveness of our approach.     

基于直线平行垂直关系美化三维线框模型

针对计算机线图解释中直线间几何关系可能存在不准确,从而出现视觉 表达问题的不足,研究了基于直线平行垂直关系美化三维线框模型方法。首先,计算正视投 影空间中三维线框模型中棱线方向矢量并选择基准棱线;然后,采用直线间平行垂直约束对 线框模型中出现几何错误的直线进行校正,重新选择已校正棱线为基准棱线重复上述操作; 最后根据新的棱线参数确定三维线框模型顶点新坐标。通过算例结果表明,该方法能够有效 地解决线框模型中出现的平行垂直几何问题,达到线框模型视觉上的美化。     

Determination of the attitude of 3D objects from a singleperspective view

A method for finding analytical solutions to the problem of determining the attitude of a 3D object in space from a single perspective image is presented. Its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model, and on the search for the model attitude consistent with these projections. The geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight-degree equation in the general case. Using simple logical rules, it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3D objects because few admissible hypotheses are retained from the interpolation of the three line segments. Line matching by the prediction-verification procedure is thus less complex     

Recovering solid geometric object from single line drawing image

Many educational materials contain a lot of solid geometric figures. The solid geometric objects in these figures are usually drawn as 2D line drawings thus have lost their 3D information. This paper presents a method to recover the 3D information of the solid geometric object from single line drawing image taken from the geometric books, which would be used to help the users better present and understand the solid geometric object on their mobile devices. The main advantage of our method is the abilitYTo handle inaccurately processed sketches as opposed to the previous methods which require perfect line drawings as inputs. Our method consists of three main steps as follows. First, the sketch of the input line drawing image is automatically extracted and further represented as an undirected graph. Second, candidate 3D models from the pre-built 3D model database are found by graph similarity-based searching and sub-graph isomorphism matching. Third, for each candidate 3D model, the model parameters, the rotation and the translation aligning the model with the sketch are found by minimizing an objective function which is composed of the residuals between the vertices of the sketch and the 2D projections of the candidate model’s vertices, and an optimal reconstruction solution is further selected as the final result. Extensive experimental results demonstrate the effectiveness and robustness of our method for recovering the solid geometric object from single line drawing image.     

线框模型投影图的消隐

不具有表面信息的三维线框模型投影到二维平面上,不能利用现有的立体投影消隐的方法来消除被遮挡线。提出利用包围盒与有向三角形相结合的方法,找出投影图中的相交边,通过投影模型计算距离并判断其相互的遮挡关系。引入遮挡矩阵存储遮挡信息弥补了投影降维后造成的深度信息损失。利用遮挡矩阵更新表示顶点间拓扑关系的连接矩阵,得到不含隐藏线的投影图。实验表明,算法稳定而高效。     

Identification of faces in a 2D line drawing projection of awireframe object

An important key to reconstructing a three-dimensional object depicted by a two-dimensional line drawing projection is face identification. Identification of edge circuits in a 2D projection corresponding to actual faces of a 3D object becomes complex when the projected object is in wireframe representation. This representation is commonly encountered in drawings made during the conceptual design stage of mechanical parts. When nonmanifold objects are considered, the situation becomes even more complex. This paper discusses the principles underlying face identification and presents an algorithm capable of performing this identification. Face-edge-vertex relationships applicable to nonmanifold objects are also proposed. Examples from a working implementation are given     

Recovering the position and orientation of free-form objects fromimage contours using 3D distance maps

The accurate matching of 3D anatomical surfaces with sensory data such as 2D X-ray projections is a basic problem in computer and robot assisted surgery, In model-based vision, this problem can be formulated as the estimation of the spatial pose (position and orientation) of a 3D smooth object from 2D video images. The authors present a new method for determining the rigid body transformation that describes this match. The authors' method performs a least squares minimization of the energy necessary to bring the set of the camera-contour projection lines tangent to the surface. To correctly deal with projection lines that penetrate the surface, the authors consider the minimum signed distance to the surface along each line (i.e., distances inside the object are negative). To quickly and accurately compute distances to the surface, the authors introduce a precomputed distance map represented using an octree spline whose resolution increases near the surface. This octree structure allows the authors to quickly find the minimum distance along each line using best-first search. Experimental results for 3D surface to 2D projection matching are presented for both simulated and real data. The combination of the authors' problem formulation in 3D, their computation of line to surface distances with the octree-spline distance map, and their simple minimization technique based on the Levenberg-Marquardt algorithm results in a method that solves the 3D/2D matching problem for arbitrary smooth shapes accurately and quickly     

Constructing a wire-frame from views on arbitrary view planes for objects with conic sections inclined to all view planes

A new and efficient approach to construct a 3D wire-frame of an object from its orthographic projections is described. The input projections can be two or more and can include regular and complete auxiliary views. Each view may contain linear, circular and other conic sections. The output is a 3D wire-frame that is consistent with the input views.The approach can handle auxiliary views containing curved edges. This generality derives from a new technique to construct 3D vertices from the input 2D vertices (as opposed to matching coordinates that is prevalent in current art). 3D vertices are constructed by projecting the 2D vertices in a pair of views on the common line of the two views. The construction of 3D edges also does not require the addition of silhouette and tangential vertices and subsequently splitting edges in the views. The concepts of complete edges and n-tuples are introduced to obviate this need. Entities corresponding to the 3D edge in each view are first identified and the 3D edges are then constructed from the information available with the matching 2D edges. This allows the algorithm to handle conic sections that are not parallel to any of the viewing directions. The localization of effort in constructing 3D edges is the source of efficiency of the construction algorithm as it does not process all potential 3D edges.Working of the algorithm on typical drawings is illustrated.     

A new generalized computational framework for finding objectorientation using perspective trihedral angle constraint

This paper investigates a fundamental problem of determining the position and orientation of a three-dimensional (3-D) object using a single perspective image view. The technique is focused on the interpretation of trihedral angle constraint information. A new closed form solution based on Kanatani's formulation is proposed. The main distinguishing feature of the authors' method over the original Kanatani formulation is that their approach gives an effective closed form solution for a general trihedral angle constraint. The method also provides a general analytic technique for dealing with a class of problem of shape from inverse perspective projection by using “angle to angle correspondence information.” A detailed implementation of the authors' technique is presented. Different trihedral angle configurations were generated using synthetic data for testing the authors' approach of finding object orientation by angle to angle constraint. The authors performed simulation experiments by adding some noise to the synthetic data for evaluating the effectiveness of their method in a real situation. It has been found that the authors' method worked effectively in a noisy environment which confirms that the method is robust in practical application     

基于三视图的三维形体重建技术

基于工程图纸的三维形体的重建技术是根据形体的二维视图中的几何信息和拓扑信息,生成相应的三维形体,这是一个从爸维到高维的构造过程,文中提出了一个三维形体重建算法,该算法首先根据三视图生成形体的线框图,然后应用左邻边搜索策略求出线框图内的所有面及相应的极小环,最后利用Ｍｏｅｂｉｕｓ规则及工程图的性质,删除重建过程中生成的非法元素,该方法利用二几何基元和三维几何基元的几何性质及生成关系,减少了重建过程中     

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.     

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     

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.     

多面体线框模型的表面识别技术

提出一种综合利用线框模型几何信息和拓扑信息的表面识别算法。首先利用平行投影法将3维线框模型投影到2维平面上,隐藏被遮挡边和悬边悬链;然后在可见投影边线图中,根据各个顶点的关联边序列,按照顺时针最小转角原则搜索最小回路;最后根据Moebius规则和二流形体的性质,及时删除不是表面投影的非法回路和图中的完备边,并调整回路的方向,使其均指向体外。通过各类典型立体的表面识别实验表明,算法具有广泛的立体适应能力和较高的效率。