Automatic segmentation of digitized data for reverse engineering applications

Reverse engineering is the process of developing a Computer Aided Design (CAD)model and a manufacturing database for an existing part. This process is used in CAD modeling of part prototypes, in designing molds, and in automated inspection of parts with complex surfaces. The work reported in this paper is on the automatic segmentation of 3-Dimensional (3-D) digitized data captured by a laser scanner or a Coordinate Measuring Machine (CMM) for reverse engineering applications. Automatic surface segmentation of digitized data is achieved using a combination of region and edge based approaches. It is assumed that the part surface contains planar as well as curved surfaces that are embedded in a base surface. The part surface should be visible to a single scanning probe (21/2D object). Neural network algorithms are developed for surface segmentation and edge detection. A back propagation network is used to segment part surfaces into surface primitives which are homogenous in their intrinsic differential geometric properties. The method is based on the computation of Gaussian and mean curvatures of the surface. They are obtained by locally approximating the object surface using quadratic polynomials. The Gaussian and mean curvatures are used as input to the neural network which outputs an initial region-based segmentation in the form of a curvature sign map. An edge based segmentation is also performed using the partial derivatives of depth values. Here, the output of the Laplacian operator and the unit surface normal are computed and used as input to a Self-Organized Mapping (SOM) network. This network is used to find the edge points on the digitized data. The combination of the region based and the edge based approaches, segment the data into primitive surface regions. The uniqueness of our approach is in automatic calculation of the threshold level for segmentation, and on the adaptability of the method to various noise levels in the digitized data. The developed algorithms and sample results are described in the paper     

Design model generation for reverse engineering using multi-sensors

Reverse engineering is the process of creating a design model and a manufacturing database for an existing part or prototype. The applications of reverse engineering are in redesigning of existing partstools or prototype parts where the CAD model of the part is not available. Reverse engineering, for the most part, is performed as an interactive process where the designer identifies the surface features from digitized data and then models the surfaces accordingly. This paper presents the algorithms and implementation results for a reverse engineering system which is intended to automatically create CAD representations of part prototypes. An integrated sensory system combining contact and non-contact sensors has been developed to digitize parts surfaces. The sensory system fuses data from machine vision and a coordinate measuring machine (CMM) in order to automatically digitize the part surface. Machine vision is used to capture the orthographic views of the part. The images of these orthographic views are processed and vectorized to create five views of the part in the form of an engineering drawing. The system utilizes the generated orthographic projections to automatically drive the CMM to capture a grid of point coordinates from the part surface. The CMM digitization process is guided by the segmentation provided from the orthographic views. The segmented data from the part surface is input to the surface modeling module of the system where parametric surfaces are fitted through the digitized points. The surfaces are then extended and intersected using the Hermite approximation method to develop the 3-D CAD model of the part. Accuracy and automation is achieved by combining global shape information obtained from part images with the accurate point data acquired by a CMM. Algorithms for surface segmentation, part digitization, surface extension, and surface intersection modeling are described in this paper.     

Sculptured surface reconstruction from CMM measurement data by a software iterative approach

The reverse engineering approach is being widely applied in designing and manufacturing of sculptured surfaces. The first step in the reverse engineering process is collection of data lying on the surface. When using a coordinate measuring machine (CMM) with a touch trigger probe for digitizing data points, the probe radius must be compensated according to normal vectors. Previous works were addressed on the iterative measurement procedure to reduce the error caused by the compensation. The major problem of iterative methods is time consumption in digitization. This paper proposes a new architecture based on look-up table that keeps the estimated normal vectors of the measurement data to refine the data points digitized by CMM. The digitized data are first fitted into several NURBS curves by interpolation. The skinning method is then applied to interpolate these curves. Thus a smooth NURBS surface can be constructed and more accurate normal vectors of the measurement points can be obtained to compensate for the probe radius. By using this software iterative technique, we need only one digitization procedure. Therefore, much time can be saved and the efficiency of reverse engineering can be improved.     

面向IGES输出的曲面重构技术

针对反求工程中复杂曲面CAD建模专用软件（RE－SOFT）与其他商用CAD／CAM系统间进行信息流动的问题，提出一种面向IGES标准输出的复合三角Beizer曲面重构四边NURBS曲面技术；通过复合三角曲面的特征提取，对三角曲面进行分块、区域边界编辑及相邻区域光滑拼接，进而构造出G^1连续的光滑四边NURBS曲面模型并以IGES数据格式传输到其它CAD／CAM系统中进行后续处理，达到了既能充分利用三角曲面的优势又能实现专用CAD软件（RE－SOFT）与其他商用CAD／CAM系统集成的目的。     

二次曲面的NURBS最优化表示方法研究

为了解决非均匀有理B样条(NURBS)拟合二次曲面精度低、过程复杂的问题,提出了一种u、v参数化方向选择及求解出最优控制点个数选取范围的高效拟合二次曲面的方法。首先,根据二次曲面的形状特征确定u、v的参数化方向;然后,利用差值绝对值和均方根误差对不同控制点个数拟合出的各个重构曲面进行误差定量分析,根据定量分析的结果曲线求解拟合二次曲面的最优控制点个数的最小取值;最后,结合程序运行时间的关系曲线求解拟合二次曲面的最优控制点个数的最大取值。实例表明:较为常见的二次曲面的NURBS最优控制点个数的合理选取范围为201~541。该分析结果为NURBS标准分析表面的拟合过程中遇到的问题提供了理论支持和技术参考。     

Point-based approach to enhance the quality of geometric data for CAE applications

Commercial CAD surface modelling software is based almost exclusively on Bézier, B-spline and NURBS representations. These methods offer simple interactive shape modification and computationally efficient interrogations, but have some serious practical limitations. The root cause of all these problems is that the parametric polynomial methods are not geometry-based, and the trouble is compounded by the master geometry philosophy which treats the CAD model as if it were absolutely correct. An alternative purely geometric approach to surface modelling has been established, where the surface shape is characterised by a grid of points lying on the surface, but it is recognised that this approach would require major changes in existing CAE systems. This application paper explains the rationale to develop algorithms, which would plug into existing CAE software systems, so that the user could benefit from the point-based construction without disturbing the established mode of operation. The new point-based approach has achieved significant success in ensuring that form tools produce panels within a specified tolerance.     

NURBS machining and feed rate adjustment for high-speed cutting of complex sculptured surfaces

Owing to the enormous engineering advancement in modern industry, the competition in the development of advanced manufacturing technologies has been increasingly intense as can be seen in automobile, aerospace and various industries. Not only has product quality improved tremendously, but also the demand over production speed has become higher. Therefore, high-speed and high-accuracy production has become a very important goal of modern manufacturing companies. Thanks to ever increasing computer speed and the open architecture of new controllers in computer-controlled machines, the capability and flexibility of today's CNC machines allow us to machine contoured geometry using non-uniform rational B-spline (NURBS) curves directly from the free-form surfaces of a complex CAD/CAM model. As a result, machining accuracy and product quality can be greatly improved while machining time is also significantly reduced. This paper proposes a post-processing approach to convert G1 NC codes from most CAD/CAM systems to NURBS NC paths for highspeed contour machining. The NURBS interpolation strategy that takes into account the optimized cutting feed rate based on machine dynamic response and curvature of the NURBS curve is also developed. Experiments show that the implemented NURBS cutting can significantly improve machining accuracy and reduce cutting time and therefore satisfies the requirements of today's highspeed and-accuracy machining needs.     

基于C-B样条的三角形和四边形曲面生成

文章给出了基于C-B样条的由网格数据产生三角形和四边形曲面片的方法,C-B样条是由基底函数{sin t,cos t,t,1}导出的一种新型样条曲线,它可以克服现在正在使用的B样条和有理B样条为了满足数据网格的拓扑结构而增加多余的控制点,求导求积分复杂繁琐,阶数过高,从而讨论其连续拼接时增加了困难等缺点,如何将它推广成曲面就成为一个重要问题。作者利用边-顶点方法构造插值算子,再将这些算子进行凸性组合,将C-B样条曲线推广成三角形曲面片和四边形曲面片,它可以用于CAD的逆向工程中散乱数据的曲面重构。     

B-spline approximation in boundary face method for three-dimensional linear elasticity

In this paper, basis functions generated from B-spline or Non-Uniform Rational B-spline (NURBS), are used for approximating the boundary variables to solve the 3D linear elasticity Boundary Integral Equations (BIEs). The implementation is based on the BFM framework in which both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces to keep the exact geometric information in the BIEs. In order to reduce the influence of tensor product of B-spline and make the discretization of a body surface easier, the basis functions defined in global intervals are translated into local form. B-spline fitting function built with the local basis functions is converted into an interpolation type of function in which the nodal values of the boundary variables are used for control points. Numerical tests for 3D linear elasticity problems show that the BFM with B-spline basis functions outperforms that with the well-known Moving Least Square (MLS) approximation.     

Optimal cutter size determination for 2½-axis finish machining of NURBS profile parts

A curve model of non-uniform rational B-spline (NURBS) has been widely adopted in mainstream CAD/CAM software systems to design complicated geometries of mechanical parts, for example, the curved profiles of pockets, sides, and islands. NURBS profile parts (the profiles include NURBS curves for pockets and islands) are produced in 2½-axis rough and finish machining. In rough machining of the parts, several end-mills with different sizes are employed for high cutting efficiency, and in finish machining, a single end-mill is usually used to cut along the profiles for high surface quality. To accurately produce the geometries with NURBS curves in finish machining, the cutter size should be optimised in order to eliminate gouging and save machining time. Although this topic has been a research focus for a decade, optimal cutter size determination still remains as a technical challenge. To rise to this challenge, our work proposes a new approach to determining the largest allowable size for the cutter to move along all the profiles (including NURBS curves) in 2½-axis finish machining without global and local gouging. The salient feature of this approach is that an original model of the cutter size is formulated and an effective solver–the particle swarm optimisation method–is employed to compute the largest allowable cutter size. This intelligent approach is more efficient and accurate than the conventional computational method based on the test examples in this work. It can also be applied to global and local gouging detection for NURBS profile machining. Our research work has great potential to advance CNC machining techniques.     

T‐spline finite element method for the analysis of shell structures

A T‐spline surface is a nonuniform rational B‐spline (NURBS) surface with T‐junctions, and is defined by a control grid called T‐mesh. The T‐mesh is similar to a NURBS control mesh except that in a T‐mesh, a row or column of control points is allowed to terminate in the inner parametric space. This property of T‐splines makes local refinement possible. In the present study, shell formulation based on the T‐spline finite element method (FEM) is presented. Shell formulation based on NURBS or T‐splines has fundamental limitations because rotational DOFs, which are necessary in the shell formulation, cannot be defined on control points. In this study, the simple mapping scheme, in which every control point is mapped into one geometric point on the surface, is employed to eliminate the limitations. Using this mapping scheme, T‐spline FEM can be easily extended to the analysis of shells. The proposed shell formulation is verified through various benchmarking problems. This study is a part of the efforts by the authors for the integration of CAD–CAE processes. Copyright © 2009 John Wiley & Sons, Ltd.     

A 2D topology optimisation algorithm in NURBS framework with geometric constraints

In this paper, the solid isotropic material with penalisation (SIMP) method for topology optimisation of 2D problems is reformulated in the non-uniform rational BSpline (NURBS) framework. This choice implies several advantages, such as the definition of an implicit filter zone and the possibility for the designer to get a geometric entity at the end of the optimisation process. Therefore, important facilities are provided in CAD postprocessing phases in order to retrieve a consistent and well connected final topology. The effect of the main NURBS parameters (degrees, control points, weights and knot-vector components) on the final optimum topology is investigated. Classic geometric constraints, as the minimum and maximum member size, have been integrated and reformulated according to the NURBS formalism. Furthermore, a new constraint on the local curvature radius has been developed thanks to the NURBS formalism and properties. The effectiveness and the robustness of the proposed method are tested and proven through some benchmarks taken from literature and the results are compared with those provided by the classical SIMP approach.     

Optimized stereo reconstruction of free-form space curves based on a nonuniform rational B-spline model

Analytical reconstruction of 3D curves from their stereo images is an important issue in computer vision. We present an optimization framework for such a problem based on a nonuniform rational B-spline (NURBS) curve model that converts reconstruction of a 3D curve into reconstruction of control points and weights of a NURBS representation of the curve, accordingly bypassing the error-prone point-to-point correspondence matching. Perspective invariance of NURBS curves and constraints deduced on stereo NURBS curves are employed to formulate the 3D curve reconstruction problem into a constrained nonlinear optimization. A parallel rectification technique is then adopted to simplify the constraints, and the Levenberg-Marquardt algorithm is applied to search for the optimal solution of the simplified problem. The results from our experiments show that the proposed framework works stably in the presence of different data samplings, randomly posed noise, and partial loss of data and is potentially suitable for real scenes.     

Research and implementation of NURBS interpolator with continuous feedrate for high-speed machining

Using non-uniform rational B-splines (NURBS) rather than piecewise lines and arc segments as a toolpath makes it much easier to achieve high-speed control in die and mould machining. When NURBS is used as a toolpath, two issues must be solved. The first is how to convert the discrete cutter location (CL) data offset from a CAD model into a NURBS curve. The second is how to maintain low velocity fluctuation while interpolating the NURBS curve with limited calculation time. This study proposes a NURBS toolpath generation method from line segments and a real-time NURBS interpolator for CNC machines to achieve the goal of high-speed machining. A CL data simplification method with shape holding is presented based on identifying and correcting the defect point from the original CL data, and removing redundant CL data within shape-maintaining requirements. Then the conversion of all simplified CL data to NURBS curves is done by applying NURBS fitting or interpolation with optional directional constraints. A precise method based on nonlinear mapping between the NURBS's parameter and arc length is proposed and implemented to obtain a continuous feedrate and machining quality. The simulation performed on CL points for a wave surface demonstrates that the proposed approach reduces the NC blocks to 6% while staying within the tolerance of deviation. The machining experiment shows that the proposed approach can increase machining quality while reducing machining time by about 22%.     

贵州少数民族文化遗产的逆向工程应用研究

以少数民族文化遗产的保护和开发方法研究为目的,从实物测量、三维CAD模型、曲面模型评价体系、CAD模型重建等方面详细阐述了逆向工程技术在文化遗产保护方面的应用.选用有代表性的贵州少数民族文物--布依族酒壶、水壶以及木制傩戏面具作为研究对象,采用Hiscanner 激光扫描测头对其进行数据采集,扫描得到的点云数据可刻录到光盘上作为文物数据永久保存;更进一步地,采用目前流行的逆向工程软件Geomagic studio对点云数据进行数据精简、数据滤波、数据修补、提取特征线等处理后得到NURBS曲面;为保证曲面模型重建的精度,在曲面重建模型后对其误差评价,通过控制误差的方式指导曲面模型重建,使重建的文物曲面模型能真实完整地反映原状;最后,在功能强大的三维造型软件Solidworks中导入重构的NURBS曲面进行曲面缝合、放样等,将其生成实体CAD模型,并对模型的局部特征进行适当的再设计以实现文物实体模型的优化.对该模型进行快速成型制造可得到文物复制品或成品模具,即实现逆向工程技术在文化遗产保护中的应用研究.逆向工程技术应用于少数民族文化遗产文物保护是一个全新的课题,该项技术的应用能进一步推动文化遗产保护措施的发展,也能为类似课题的研究提供借鉴.     

NURBS-based 3-D anthropomorphic computational phantoms for radiation dosimetry applications

Computational anthropomorphic phantoms are computer models used in the evaluation of absorbed dose distributions within the human body. Currently, two classes of the computational phantoms have been developed and widely utilised for dosimetry calculation: (1) stylised (equation-based) and (2) voxel (image-based) phantoms describing human anatomy through the use of mathematical surface equations and 3-D voxel matrices, respectively. However, stylised phantoms have limitations in defining realistic organ contours and positioning as compared to voxel phantoms, which are themselves based on medical images of human subjects. In turn, voxel phantoms that have been developed through medical image segmentation have limitations in describing organs that are presented in low contrast within either magnetic resonance or computed tomography image. The present paper reviews the advantages and disadvantages of these existing classes of computational phantoms and introduces a hybrid approach to a computational phantom construction based on non-uniform rational B-spline (NURBS) surface animation technology that takes advantage of the most desirable features of the former two phantom types.