Surface signatures: an orientation independent free-form surface representation scheme for the purpose of objects registration and matching

This paper introduces anew free-form surface representation scheme for the purpose of fast and accurate registration and matching. Accurate registration of surfaces is a common task in computer vision. The proposed representation scheme captures the surface curvature information (seen from certain points) and produces images, called "surface signatures," at these points. Matching signatures of different surfaces enables the recovery of the transformation parameters between these surfaces. We propose using template matching to compare the signature images. To enable partial matching, another criterion, the overlap ratio is used. This representation scheme can be used as a global representation of the surface as well as a local one and performs near real-time registration. We show that the signature representation can be used to recover scaling transformation as well as matching objects in 3D scenes in the presence of clutter and occlusion. Applications presented include: free-form object matching, multimodal medical volumes registration, and dental teeth reconstruction from intraoral images.     

3D reconstruction of free-formed line-like objects using NURBS representation

3D reconstruction of arbitrary free-formed objects is an important and challenging problem in computer vision. In this paper, we first discuss the importance of primitive selection in 3D reconstruction. Subsequently, a theorem, which reveals the perspective invariance of NURBS, is shown, making it a good choice as primitive in 3D reconstruction. Consequently, based on this theorem a new paradigm of free-formed line-like object reconstruction using NURBS as primitives is proposed. Furthermore, an approach for determining weights for 3D NURBS is presented, and the width effect of curved line-like objects is analyzed. Finally, experiments with line-like objects and machine part demonstrate the feasibility of our approach and prove the superiority of our approach over the point- or segment-based approaches as well as the B-spline-based reconstruction approach in terms of robustness and accuracy.     

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     

基于小波变换的三维网格物体盲水印方案

提出了一种基于小波变换的3D网格物体鲁棒性盲水印方案.首先将3D物体模型转换到仿射不变空间,抽取三维物体重心到顶点的距离生成一个一维的离散信号;将该离散信号进行小波变换,改变其高频系数以嵌入水印,然后经过小波逆变换生成带水印的3D物体模型.在仿射不变空间下,实现了3D物体模型对平移、旋转、比例变换的鲁棒性,采用小波变换使3D模型具有很强的水印不可见性以及一定的噪声鲁棒性.试验结果表明,该方法不仅对于旋转、平移、比例变换具有很强的鲁棒性,而且具有良好的水印不可见性.     

3D对象动态方位邻接关系及双向关联表示

3D空间对象方位关系的表示和分析在空间数据库、地理信息系统、人工智能和机器人学等领域具有重要的意义。为了分析和处理复杂的3D空间对象的方位关系,讨论了3种3D空间对象方位关系的立体表示模型：3DR7模型、3DR27模型和3DR39模型,给出了方位关系的交集序列;研究了3D空间对象方位关系的动态邻接关系和处理方法;进一步给出了3D空间对象方位关系的双向映射模型。研究成果为3D空间对象方位关系在空间数据库和地理信息系统等领域的应用奠定了基础。     

A spherical representation for recognition of free-form surfaces

Introduces a new surface representation for recognizing curved objects. The authors approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ellipsoid, until it fits the surface of the object. The authors define local regularity constraints that the mesh must satisfy. The authors then define a canonical mapping between the mesh describing the object and a standard spherical mesh. A surface curvature index that is pose-invariant is stored at every node of the mesh. The authors use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene. The authors show how the similarity between reference model and observed data can be evaluated and they show how the pose of the reference object in the observed scene can be easily computed using this representation. The authors present results on real range images which show that this approach to modelling and recognizing 3D objects has three main advantages: (1) it is applicable to complex curved surfaces that cannot be handled by conventional techniques; (2) it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search; and (3) even though it is based on a spherical mapping, the approach can handle occlusions and partial views     

Watermarking 3D objects for verification

We introduce and investigate the fundamental similarities and differences of watermarking 3D graphic models compared to 2D images, and propose some solutions to address a class of applications of digital watermarking-the verification of 3D polygonal models. To our knowledge, watermarking of 3D objects for verification purposes has not been addressed in any published literature. The proposed scheme, in its present form, is not intended for use in applications that require robust watermarks. One recent work in 3D data hiding addressed applications requiring robust means of hiding data. We first introduce digital watermarking, discuss its goals and application domains, and explain the different categories of watermarks. We believe the goals and applications will remain fairly similar for 2D images and 3D models     

Trimming of free-form objects for a B-Rep solid modeller

This paper describes a technique for trimming solid objects in a B-Rep solid modelling system. A B-Rep scheme based on the split-edge structure, which is suitable for the representation of trimmed surfaces, is first discussed. Algorithms for graph traversal, graph merging and graph splitting are then given in detail. Based on this B-Rep scheme, a technique for trimming objects is developed. The trimming process involves the evaluation of surface intersections, graph cutting along intersections and merging of appropriate graphs to obtain the required trimmed objects.     

Wavelet-based affine invariant representation: a tool forrecognizing planar objects in 3D space

A technique is developed to construct a representation of planar objects undergoing a general affine transformation. The representation can be used to describe planar or nearly planar objects in a three-dimensional space, observed by a camera under arbitrary orientations. The technique is based upon object contours, parameterized by an affine invariant parameter and the dyadic wavelet transform. The role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation. A dissimilarity function is also developed and used to distinguish among different object representations. This function makes use of the extrema on the representations, thus making its computation very efficient. A study of the effect of using different wavelet functions and their order or vanishing moments is also carried out. Experimental results show that the performance of the proposed representation is better than that of other existing methods, particularly when objects are heavily corrupted with noise     

3D free-form surface registration and object recognition

A new technique to recognise 3D free-form objects via registration is proposed. This technique attempts to register a free-form surface, represented by a set of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmamaala% aabaGaaGymaaqaaiaaikdaaaGaamiraaaa!38F8!\[2\frac{1}{2}D\] sensed data points, to the model surface, represented by another set of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmamaala% aabaGaaGymaaqaaiaaikdaaaGaamiraaaa!38F8!\[2\frac{1}{2}D\] model data points, without prior knowledge of correspondence or view points between the two point sets. With an initial assumption that the sensed surface be part of a more complete model surface, the algorithm begins by selecting three dispersed, reliable points on the sensed surface. To find the three corresponding model points, the method uses the principal curvatures and the Darboux frames to restrict the search over the model space. Invariably, many possible model 3-typles will be found. For each hypothesized model 3-tuple, the transformation to match the sensed 3-tuple to the model 3-tuple can be determined. A heuristic search is proposed to single out the optimal transformation in low order time. For realistic object recognition or registration, where the two range images are often extracted from different view points of the model, the earlier assumption that the sensed surface be part of a more complete model surface cannot be relied on. With this, the sensed 3-tuple must be chosen such that the three sensed points lie on the common region visible to both the sensed and model views. We propose an algorithm to select a minimal non-redundant set of 3-tuples such that at least one of the 3-tuples will lie on the overlap. Applying the previous algorithm to each 3-tuple within this set, the optimal transformation can be determined. Experiments using data obtained from a range finder have indicated fast registration for relatively complex test cases. If the optimal registrations between the sensed data (candidate) and each of a set of model data are found, then, for 3D object recognition purposes, the minimal best fit error can be used as the decision rule.     

3D sketching for aesthetic design using fully free-form deformation features

This paper addresses the designers’ activity and in particular the way designers express an object shape in 2D sketches through character lines and how these lines form a basis for sketching shapes in 3D. The tools currently available in commercial CAS/CAD systems to manipulate the digital models are still not sufficiently suited to support design. In this paper, the so-called fully free-form deformation features (δ-F⁴) are introduced as a modelling method to take into account the curve-oriented stylists’ way of working. Both the advantages of a free-form surface deformation method and a feature-based approach are merged to define these high-level modelling entities allowing for a direct manipulation of surfaces through a limited number of intuitive parameters. Such features incorporate several characteristics designed to handle the uncertainties and/or inconsistencies of the designer's input during a sketching activity. In addition, a δ-F⁴ classification is proposed to enable a fast access to the desired shape according to its semantics and characteristics.     

Geometric algorithms for rapidly reconfigurable mold manufacturing of free-form objects

This paper presents geometric algorithms for developing a re-configurable tooling system for fabrication of freeform objects. The proposed method involves a mold block, with n faces, in which the mold cavity is formed by moving a set of discrete pins on each face of the block. The part surfaces are approximated in the mold cavity using the pins from the suitable mold block faces. The geometric algorithms detailed in this paper analyze the part and determine the face of mold block from which the part model is approximated best. Further, the algorithms detect possible interference between pins from different faces, and suitably alter the approximating face to alleviate interferences. By moving these pins in and out of the mold block, the shape of the mold cavity is reconfigured rapidly to suit the changes in part geometry. Since, the proposed method approximates free-form objects with discrete pins, a surface-error calculation method is also developed to control the accuracy. Computer implementation and examples are also presented in this paper.     

FEG structures for representation and recognition of 3-D polyhedral objects

The paper proposes a fast O(n ^2.5) recognition algorithm for partially occluded 3D polyhedral objects, where n is the number of the polyhedron vertices.Our approach is based on the generate and test mechanism using the alignment approach as its basic recognition tool. The first stage is to align one face of the unknown polyhedron with one face of one library model (generate). The second stage is a recursive test procedure that checks the matching of the remaining faces. A new structure called FEG—Face Edge Graph is introduced. This structure stores information about the 2D coordinates of each face and the identity of its adjacent faces.A very low complexity is achieved by using a divide and conquer strategy. Instead of trying to recognize the whole object at once, we divide it and conquer (recognize) it face by face. This is done by reducing the recognition problem to generalized subgraph matching problem in which two subgraphs are equal not only when they are isomorphic, but also when they represent the same part of the same object. A special mechanism handles false splitting and false merging of adjacent faces as a result of wrong segmentation.The process lends itself to hierarchical parallel processing in that the matching with each library model may be carried out independently, and also for each model—processing at the pixel level may also be done in parallel.We evaluated our approach with several real range data images as well as some synthetic objects. Four of these cases are reported here.     

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.     

Algorithms for optimal partial matching of free-form objects with scaling effects

A free-form object matching problem is addressed in this paper. Two methods are proposed to solve a partial matching problem with scaling effects and no prior information on correspondence or the rigid body transformation involved. The first method uses umbilical points, which behave as fingerprints of a surface and their qualitative properties can be used for matching purposes. The second method uses an optimization scheme based on the extension of the KH curvature matching method [Comput. Aided Design 35 (2003) 913], first introduced in the context of a matching problem without scaling effects. Two types of curvatures, the Gaussian and the mean curvatures, are used to establish correspondences between two objects. The curvature matching method is formulated in terms of minimization of an objective function depending on the unknown scaling factor, and the rigid body transformation parameters. The accuracy and complexity of the proposed methods as well as the convergence for the optimization approach are analyzed. Examples illustrate the two methods.     

再现3D对象

多亏有了Google上的一种免费工具,3D建模变得不再是一个痛苦而笨拙的过程。Jerome Turner介绍SketchUp的主要功能。