Image‐based modeling of 3D objects with curved surfaces

This paper addresses an image‐based method for modeling 3D objects with curved surfaces based on the non‐uniform rational B‐splines (NURBS) representation. The user fits the feature curves on a few calibrated images with 2D NURBS curves using the interactive user interface. Then, 3D NURBS curves are constructed by stereo reconstruction of the corresponding feature curves. Using these as building blocks, NURBS surfaces are reconstructed by the known surface building methods including bilinear surfaces, ruled surfaces, generalized cylinders, and surfaces of revolution. In addition to them, we also employ various advanced techniques, including skinned surfaces, swept surfaces, and boundary patches. Based on these surface modeling techniques, it is possible to build various types of 3D shape models with textured curved surfaces without much effort. Copyright © 2007 John Wiley & Sons, Ltd.     

三维破碎物体多尺度拼接技术

在分析三维物体碎片轮廓曲线的特征和表示的基础上,研究多尺度小波轮廓描述符的计算,提出了一种多尺度下轮廓曲线特征提取及基于多尺度分析的三维物体碎片拼接方法.轮廓曲线经多尺度小波变换平滑后,提取曲率和挠率构成特征矢量;在选择了基于小波轮廓描述符的三维曲线匹配起点后,比较2条轮廓曲线的特征矢量以判断轮廓的相似性,并将轮廓匹配的2块相邻物体碎片拼接,实现破碎物体复原.最后通过实验验证了该方法的有效性.     

Globally minimal surfaces by continuous maximal flows

In this paper, we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or suboptimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias.     

3D object recognition using invariants of 2D projection curves

This paper presents a new method for recognizing 3D objects based on the comparison of invariants of their 2D projection curves. We show that Euclidean equivalent 3D surfaces imply affine equivalent 2D projection curves that are obtained from the projection of cross-section curves of the surfaces onto the coordinate planes. Planes used to extract cross-section curves are chosen to be orthogonal to the principal axes of the defining surfaces. Projection curves are represented using implicit polynomial equations. Affine algebraic and geometric invariants of projection curves are constructed and compared under a variety of distance measures. Results are verified by several experiments with objects from different classes and within the same class.     

Point Signatures: A New Representation for 3D Object Recognition

Few systems capable of recognizing complex objects with free-form (sculptured) surfaces have been developed. The apparent lack of success is mainly due to the lack of a competent modelling scheme for representing such complex objects. In this paper, a new form of point representation for describing 3D free-form surfaces is proposed. This representation, which we call the point signature, serves to describe the structural neighbourhood of a point in a more complete manner than just using the 3D coordinates of the point. Being invariant to rotation and translation, the point signature can be used directly to hypothesize the correspondence to model points with similar signatures. Recognition is achieved by matching the signatures of data points representing the sensed surface to the signatures of data points representing the model surface.The use of point signatures is not restricted to the recognition of a single-object scene to a small library of models. Instead, it can be extended naturally to the recognition of scenes containing multiple partially-overlapping objects (which may also be juxtaposed with each other) against a large model library. No preliminary phase of segmenting the scene into the component objects is required. In searching for the appropriate candidate model, recognition need not proceed in a linear order which can become prohibitive for a large model library. For a given scene, signatures are extracted at arbitrarily spaced seed points. Each of these signatures is used to vote for models that contain points having similar signatures. Inappropriate models with low votes can be rejected while the remaining candidate models are ordered according to the votes they received. In this way, efficient verification of the hypothesized candidates can proceed by testing the most likely model first. Experiments using real data obtained from a range finder have shown fast recognition from a library of fifteen models whose complexities vary from that of simple piecewise quadric shapes to complicated face masks. Results from the recognition of both single-object and multiple-object scenes are presented.     

Thesaurus-based 3D Object Retrieval with Part-in-Whole Matching

Research in content-based 3D retrieval has already started, and several approaches have been proposed which use in different manner a similarity assessment to match the shape of the query against the shape of the objects in the database. However, the success of these solutions are far from the success obtained by their textual counterparts. A major drawback of most existing 3D retrieval solutions is their inability to support partial queries, that is, a query which does not need to be formulated by specifying a whole query shape, but just a part of it, for example a detail of its overall shape, just like documents are retrieved by specifying words and not whole texts. Recently, researchers have focused their investigation on 3D retrieval which is solved by partial shape matching. However, at the extent of our knowledge, there is still no 3D search engine that provides an indexing of the 3D models based on all the interesting subparts of the models. In this paper we present a novel approach to 3D shape retrieval that uses a collection-aware shape decomposition combined with a shape thesaurus and inverted indexes to describe and retrieve 3D models using part-in-whole matching. The proposed method clusters similar segments obtained trough a multilevel decomposition of models, constructing from such partition the shape thesaurus. Then, to retrieve a model containing a sub-part similar to a given query, instead of looking on a large set of subparts or executing partial matching between the query and all models in the collection, we just perform a fast global matching between the query and the few entries in the thesaurus. With this technique we overcame the time complexity problems associated with partial queries in large collections.     

Shape differentiation of freeform surfaces using a similarity measure based on an integral of Gaussian curvature

Freeform surfaces are popularly used to design and model complex 3D objects. These 3D models are stored as computerized models in databases. To facilitate data retrieval and shape matching, a major challenge lies in defining and computing the level of similarity between two or more freeform surfaces. In order to explore the useful 3D information associated with the surfaces, an integrated approach based on the integral of Gaussian curvature is proposed to develop the measures of similarity of freeform surfaces. Specifically, the integral of Gaussian curvature is mapped into the 2D space, and a shape-based measure is developed using statistical methods to compute the level of similarity. For smooth surfaces, a fast approximation algorithm is developed to calculate the curvature of individual subregions. In cases where the target surface has a complex topological structure or a smooth surface is not available, the integral of Gaussian curvature for the discrete surface is first calculated at each vertex, followed by mapping onto a 2D spherical coordinate. The distance measure focuses on the local geometry, which is critical to investigate models with a certain level of resemblance such as products in a family. This proposed approach can be applied to surfaces under various transformations, as well as 3D data from various sources.     

基于立体视觉的高光物体恢复深度图的方法

基于立体视觉的物体深度图提取,在工业检测等许多方面均有较高的应用价值,但对于工程领域里的高光物体带来的误差,研究不多。为了较好地恢复具有高光反射的物体表面的三维深度信息,论文提出一种与立体视觉结合的多光源法去除高光的技术,使得后续的立体匹配更加可靠,深度计算更加准确。实验首先采用多光源法获取高光反射物体的多组图像,再经过图像预处理、摄像机标定、高光去除、立体匹配等步骤,结果证明这种方法有效地恢复了具有相对大面积的高光区域表面的物体的三维深度信息。     

基于面部曲线弹性匹配的三维人脸识别方法

提出一种基于面部径向曲线弹性匹配的三维人脸识别方法。使用人脸曲 面上的多条曲线表征人脸曲面,提取三维人脸上从鼻尖点发射的多条面部径向曲线,对其进 行分层弹性匹配和点距对应匹配,根据人脸不同部位受表情影响程度不同,对不同曲线识别 相似度赋予不同权重进行加权融合作为总相似度用于识别。测试结果表明该方法具有很好的 识别性能,并且对表情、遮挡和噪声具有较好的鲁棒性。     

非均匀有理B样条曲线优化匹配组合

目的 为了解决从曲线库(轮廓线集合)中筛选出与期望曲线相匹配的相似曲线段问题,研究基于Kabsch算法的NURBS(非均匀有理B样条)曲线优化匹配组合方法。方法 首先提出一种基于Kabsch算法的曲线相似性判断方法,针对两条NURBS曲线上相同个数点阵,经最优旋转和平移变换得到其最小均方根偏差,进而依据基于最小均方根偏差和相似度指标判断曲线相似性;在此基础上,提出一种类似二分查找法的曲线优化匹配组合方法,对于给定相似度和最小搜索步长,通过曲线分割和相似性判断得到期望曲线分割段数最少的相似组合曲线。结果 给定一条期望的3D曲线,在相似度为0.025和最小搜索步长为0.05情况下,采用所提方法从包含4条3D曲线的曲线库中依次筛选出10段基元构建相似组合曲线。结论 提出了一种新的NURBS曲线优化匹配组合方法,实验结果表明,对不同期望曲线能高效稳定构建相对应的相似组合曲线,适用于类似碎片拼接重构问题。     

Multiresolution analysis as an approach for tool path planning in NC machining

Wavelets permit multiresolution analysis of curves and surfaces. A complex curve can be decomposed using wavelet theory into lower resolution curves. The low-resolution (coarse) curves are similar to rough-cuts and high-resolution (fine) curves to finish cuts in NC machining. In this paper, we investigate the applicability of multiresolution analysis using B-spline wavelets to NC machining of contoured 2D objects. High-resolution curves are used close to the object boundary similar to conventional offsetting while lower resolution curves are used farther away from the object boundary. Experimental results indicate that wavelet-based tool path planning improves machining efficiency. Tool path length is reduced, sharp corners are smoothed out thereby reducing uncut areas and larger tools can be selected for rough-cuts.     

3-D object recognition using bipartite matching embedded indiscrete relaxation

The authors show how large efficiencies can be achieved in model-based 3-D vision by combining the notions of discrete relaxation and bipartite matching. The computational approach presented is capable of pruning large segments of search space-an indispensable step when the number of objects in the model library is large and when recognition of complex objects with a large number of surfaces is called for. Bipartite matching is used for quick wholesale rejection of inapplicable models and for the determination of compatibility of a scene surface with a potential model surface taking into account relational considerations. The time complexity function associated with those aspects of the procedure that are implemented via bipartite matching is provided. The algorithms do not take more than a couple of iterations, even for objects with more than 30 surfaces     

Feature-based 3D morphing based on geometrically constrained spherical parameterization

Current trends in free form editing motivate the development of a novel editing paradigm for CAD models beyond traditional CAD editing of mechanical parts. To this end, we need robust and efficient 3D mesh deformation techniques such as 3D structural morphing.In this paper, we present a feature-based approach to 3D morphing of arbitrary genus-0 polyhedral objects that is appropriate for CAD editing. The technique is based on a sphere parameterization process built on an optimization technique that uses a target function to maintain the correspondence between the initial polygons and the mapped ones, while preserving topology and connectivity through a system of geometric constraints. Finally, we introduce a fully automated feature-based technique that matches surface areas (feature regions) with similar topological characteristics between the two morphed objects and performs morphing according to this feature correspondence list. Alignment is obtained without user intervention based on pattern matching between the feature graphs of the two morphed objects.     

Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.