3D CAD model matching from 2D local invariant features

The matching of particular types of CAD models to existing physical models can provide invaluable support to the process of CAD design and reuse. To meet the demand for fast and robust algorithms to detect predefined models in database, an local invariant model matching approach is proposed in this paper. It first maps the 3D CAD model to 2D principal image plane by its first two principal components, and then finds affine invariant key points in the 2D image. The CAD model matching problem is implemented as key points matching. Experimental results show the proposed 3D model retrieval method performs fairly well in retrieving similar models from a database of 3D CAD models.     

Combining Points and Tangents into Parabolic Polygons

Image and geometry processing applications estimate the local geometry of objects using information localized at points. They usually consider information about the tangents as a side product of the points coordinates. This work proposes parabolic polygons as a model for discrete curves, which intrinsically combines points and tangents. This model is naturally affine invariant, which makes it particularly adapted to computer vision applications. As a direct application of this affine invariance, this paper introduces an affine curvature estimator that has a great potential to improve computer vision tasks such as matching and registering. As a proof-of-concept, this work also proposes an affine invariant curve reconstruction from point and tangent data.     

On Rational Geometry of Conic Sections

Simple geometric objects and transformations appear in representations and algorithms of geometric facilities in computer applications such as modelling, robotics, or graphics. Usually, these applications only support objects and transformations fully describable by rational parameters, and a computer display of points of the objects at least implicitly requires points with rational coordinates. In this setting we investigate some basic questions of the geometry of rational conic sections, when the geometry is defined by the group of rational projective transformations, the group of rational affine transformations, or the group of rational rigid transformations. Some results follow classical results, while others turn out to be quite different. In particular, we obtain a complete classification scheme for nondegenerate rational conics for rational affine geometry and a constructive method for production of a minimal set of representatives of all equivalence classes.     

基于多尺度轮廓段的形状特征提取与识别

形状识别是计算机视觉与模式识别领域的重要研究内容。形状的特征选取与描述是形状识别的研究热点。针对现有识别方法的不足，提出一种通过对不同长度轮廓段进行描述，进行特征提取的方法。对每个形状均在6种尺度下进行特征提取，每种尺度选取5种轮廓段特征参数，实现了对形状的特征描述。在形状识别阶段，使用动态时间规整（DTW）算法度量形状描述子之间的匹配距离，实现形状识别。分别在Kimia99、Kimia216和MPEG-7数据库中进行算法验证，结果表明基于多尺度轮廓段的形状特征描述子具有旋转、缩放、平移和局部遮挡不变性，识别率优于现有算法。     

Recursive turtle programs and iterated affine transformations

We provide a formal proof of equivalence between the class of fractals created by recursive-turtle programs (RTP) and iterated affine transformations (IAT). We begin by reviewing RTP (a geometric interpretation of non-bracketed L-systems with a single production rule) and IAT (iterated function systems restricted to affine transformations). Next, we provide a simple extension to RTP that generalizes RTP from conformal transformations to arbitrary affine transformations. We then present constructive proofs of equivalence between the fractal geometry generated by RTP and IAT that yield conversion algorithms between these two methods. We conclude with possible extensions and a few open questions for future research.     

Self-calibration of an affine camera from multiple views

A key limitation of all existing algorithms for shape and motion from image sequences under orthographic, weak perspective and para-perspective projection is that they require the calibration parameters of the camera. We present in this paper a new approach that allows the shape and motion to be computed from image sequences without having to know the calibration parameters. This approach is derived with the affine camera model, introduced by Mundy and Zisserman (1992), which is a more general class of projections including orthographic, weak perspective and para-perspective projection models. The concept of self-calibration, introduced by Maybank and Faugeras (1992) for the perspective camera and by Hartley (1994) for the rotating camera, is then applied for the affine camera.This paper introduces the 3 intrinsic parameters that the affine camera can have at most. The intrinsic parameters of the affine camera are closely related to the usual intrinsic parameters of the pin-hole perspective camera, but are different in the general case. Based on the invariance of the intrinsic parameters, methods of self-calibration of the affine camera are proposed. It is shown that with at least four views, an affine camera may be self-calibrated up to a scaling factor, leading to Euclidean (similarity) shape réconstruction up to a global scaling factor. Another consequence of the introduction of intrinsic and extrinsic parameters of the affine camera is that all existing algorithms using calibrated affine cameras can be assembled into the same framework and some of them can be easily extented to a batch solution.Experimental results are presented and compared with other methods using calibrated affine cameras.     

形状和颜色混合不变量在图像检索中的应用

多视觉特征的图像检索是当前基于内容的图像检索领域的重要方向.已有的多特征的检索主要通过线性加权的方法对特征进行组合,但这种组合方式仅实现了代数意义上的合并,未能真正利用和发掘特征间存在的相互关系,并且权重值不容易确定,检索结果易受权重值的影响.针对这一问题,提出一种形状-颜色混合不变特征的构造方法,特征提取的过程包含同时对形状、颜色信息的抽取,直接构造出能够同时对形状仿射变换和颜色对角-偏移变换具有不变性的特征,也称作形状-颜色矩不变量.首先分别在图像的2维几何空间、3维颜色空间定义形状核、颜色核,然后对形状核、颜色核的乘积进行多重积分,最后做规范化,就得到一个不变量.理论上,通过选择不同的形状核、颜色核可以推导出无穷多的不变量.实验结果表明,该方法优于加权组合特征的方法;与加权特征、局部特征相比,形状-颜色矩不变量对于同一物体不同成像条件下的近复制图像、整体属性相似的图像、大体类似的物体图像等表现出较高的检索性能及效率.     

On advances in differential-geometric approaches for 2D and 3D shape analyses and activity recognition

In this paper we summarize recent advances in shape analysis and shape-based activity recognition problems with a focus on techniques that use tools from differential geometry and statistics. We start with general goals and challenges faced in shape analysis, followed by a summary of the basic ideas, strengths and limitations, and applications of different mathematical representations used in shape analyses of 2D and 3D objects. These representations include point sets, curves, surfaces, level sets, deformable templates, medial representations, and other feature-based methods. We discuss some common choices of Riemannian metrics and computational tools used for evaluating geodesic paths and geodesic distances for several of these shape representations. Then, we study the use of Riemannian frameworks in statistical modeling of variability within shape classes.Next, we turn to models and algorithms for activity analysis from various perspectives. We discuss how mathematical representations for human shape and its temporal evolutions in videos lead to analyses over certain special manifolds. We discuss the various choices of shape features, and parametric and non-parametric models for shape evolution, and how these choices lead to appropriate manifold-valued constraints. We discuss applications of these methods in gait-based biometrics, action recognition, and video summarization and indexing.For reader convenience, we also provide a short overview of the relevant tools from geometry and statistics on manifolds in the Appendix.     

Mapping of industry building product model for detailed thermal simulation and analysis

Industry Foundation Classes (IFC) is an emerging data standard that promotes the interoperability of digital building product object models, or building product models (BPMs). Implementing IFC-based applications allows reducing data duplication, especially in the aspect of building geometry. With appropriate data mapping engines, an existing BPM may be readily used for performance-based simulation which requires significantly less effort compared with the traditional means. As a result, it is possible to make use of many available proprietary tools to provide additional services such as early-stage building design support. SEMPER-II (S2), which is an active, multi-domain, space-based, object-oriented design support tool for integrated building performance computing, was developed before the IFC standard was established. In order to perform building performance simulations based on the IFC compliant data models expressed through the eXtensible Markup Language (XML) based formats, an add-on data mapping engine has been developed as a front-end application in S2. The data mapping engine extracts all necessary information embedded in the XML data files, which is obtained directly from IFC compliant CAD drawings, and converts the data into the internal data format of S2.This process demonstrates a seamless link between an IFC compliant industry building product model (e.g. CAD) and the Shared Object Model (SOM) of S2 to facilitate building performance simulations.     

Methodbases and product models as bases for integrated design and manufacturing

Modelbases and product models are essential for integrated data processing in a company. Design data, process planning data and administrative data have to be put together to give a pool of information for one particular product. Therefore the existing CAD/CAM-systems have to be increased concerning their capabilities of storing and retrieving product information and their functional equipment and efficiency. The paper describes the concepts and first results of a methodbase system and the included product models.