面向逆向工程的小波技术研究与应用
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摘要
逆向工程是实现新产品开发的一个重要手段，越来越受到各国工业界和学术界的高度重视。针对目前逆向工程中存在的自动化程度低，通用性差，缺乏自适应性等问题，引入小波技术这一新的时频工具。以提高质量和效率为目标，对逆向工程中数据预处理技术、数据精简、准均匀B样条曲线光顺、NURBS曲面重构、小波分解技术和重构曲面CAD模型精度分析等关键技术进行了研究和探讨。
研究了基于CMM点云数据的坐标变换、坐标归一化、分层和排序技术。根据坐标值的集中程度来自动识别固定轴，实现数据的分层。以点集之间的距离作为准则，采用了首尾判断的方法进行排序，建立了层内数据的拓扑关系。
研究了异常噪声点的剔除方法。结合数理统计的3σ法则，通过计算平均值和标准差来确定阈值，提出了弦高法的自适应阈值计算方法，具有良好的自适应性。
研究了基于小波技术的点云数据降噪方法。运用小波技术进行降噪，通过对信号进行多次小波分解，分解后得到近似系数和细节系数，再对细节系数作用软阈值抑制噪声，然后重建信号达到降噪的目的。
数据精简技术的关键是在精简数据的同时，最大限度地保留点云数据的原有特征。在研究现有数据精简技术的基础上，提出了基于提升格式的第二代小波进行分层数据精简的新方法。
研究了准均匀B样条曲线光顺技术，提出了基于提升格式的第二代小波曲线光顺新方法。从多分辨率分析的概念入手，详细推导了B样条曲线的小波表示，简要介绍了半正交B样条小波，给出了B样条小波分解和重构的快速算法。运用第二代小波基本原理，经过分裂、预测和更新等步骤，详细推导了均匀B样条曲线的第二代小波表示，实现了基于第二代小波的曲线光顺。
研究了任意控制点B样条曲线小波光顺技术，通过插入节点以增加控制点个数的方法，构造出满足小波光顺要求的精细曲线。
在进行非均匀有理B样条(NURBS)曲面重构时，为了生成矩形域网格，针对数据点的分布不均匀性，采用累积弦长法构造非均匀节点矢量，构造插值于扫描线上数据点的非均匀B样条曲线，再对其均匀采样，保证了曲面的插值精度。完成了曲面重构。
研究了双三次准均匀B样条曲面的多分辨分解算法。确定了满足小波分解条件的重采样点数，实现了点云数据的曲面重构和多级小波分解的无缝集成。
从误差来源的角度进行论述，具体分析了影响重构曲面CAD模型精度的各种因素。简要介绍了模型精度评价方法，定性地给出了为提高模型精度的误差处理策略。通过光顺性检查和误差检查用实例验证了NURBS曲面重构算法和曲面小波分解算法的可行性和准确性。
采用面向对象的编程技术，开发了原型系统，获得了良好的应用。
Reverse Engineering(RE) is one important method to develop new product, which hasreceived more and more high attention both from industry and academia. Aiming at thecurrent questions in RE such as low automation and generality, lacking adaptivity, the newtime-frequency tool- wavelet technology is introduced。With a view to raise quality andefficiency, the key technologies including data treatments, data simplification, quasi-uniform B-spline curve fairness, NURBS surface reconstruction, wavelet decompositionand accuracy analysis of CAD model of reconstructed surface are researched anddiscussed.
Coordinate transformation, coordinate fusion, delamination and ordering of cloudydata based on CMM are researched. According to the concentrating extent of coordinatevalue, fixed axis is identified automatically, so delaminating data is realized. On theprinciple of distance between data set, the method of judging beginning and end is adoptedto order, and so topology information within same layer is established.
The deleting method of abnormal noises is researched. Incorporating the, 3σlaw ofmathematical statistics, by means of calculating mean and standard error to determinatethreshold, the adaptive counting threshold method is put forward, which has welladaptivity.
Denoising cloudy data based wavelet technology is researched. Using wavelet tech-nology to denoise is the process of decomposing signal with wavelet, acquiring approxi-mate coefficients and detail coefficients, acting detailed coefficients with soft threshold tosuppress noises, then reconstructing signal to get the goal of denoising.
The key of simplifying data technique is retaining original features of cloudy datautmost. On the basis of researching current simplification technique, new method usingsecond generation wavelet based on lifting to simplification data is proposed.
Quasi-uniform B-spline curve fairness technique is studied and new method of curvefairness with second generation wavelet based on lifting is presented. From the conceptionof MRA, wavelet representation of B-spline curve is reasoned in detail, semi-orthogonalB-spline wavelet is introduced and B-spline wavelet fast algorithm of decomposing andreconstructing are given.Using the fundamental principle of second generation wavelet,after split, prediction and update, second generation wavelet representation of B-splinecurve is reasoned detailedly, and curve fairness based on second generation is realized.
Fairness technique of B-spline curves with arbitrary control points based on wavelet isstudied. Refined curves meeting with the requirement of wavelet fairness are constructedby means of inserting knots to increase control points number.
As reconstructing Non-Uniform Rational B-Spline (NURBS) surface, In order togenerate rectangle field grids, with non-uniform data points, a method of accumulatingchord length is presented to create non-uniform knots vector, Non-uniform B-Spline curveis constructed and interpolated on scanning line data points, then sampling it uniformly; Sothe accuracy of interpolated surface is guaranteed.
The fast algorithms of quasi-uniform bi-cubic B-spline wavelet and decomposing dualcubic quasi-uniform B-spline surface are given. Re-sample point number which meets thecondition of wavelet decomposition is determined and seamless integration of surfacereconstruction and multi-rank decomposing it is realized.
From the source of error, all sort of factors of influencing CAD model precision ofreconstructed surface are analyzed concretely. Evaluation methods of model precision areintroduced briefly and strategies dealing with error are proposed qualitatively. Thefeasibility and accuracy of algorithms of NURBS surface reconstruction anddecomposition with wavelet are verified through testing fairness and error.
Adopting object-oriented programming technique, prototype system with wellapplication is tapped.
研究了基于CMM点云数据的坐标变换、坐标归一化、分层和排序技术。根据坐标值的集中程度来自动识别固定轴，实现数据的分层。以点集之间的距离作为准则，采用了首尾判断的方法进行排序，建立了层内数据的拓扑关系。
研究了异常噪声点的剔除方法。结合数理统计的3σ法则，通过计算平均值和标准差来确定阈值，提出了弦高法的自适应阈值计算方法，具有良好的自适应性。
研究了基于小波技术的点云数据降噪方法。运用小波技术进行降噪，通过对信号进行多次小波分解，分解后得到近似系数和细节系数，再对细节系数作用软阈值抑制噪声，然后重建信号达到降噪的目的。
数据精简技术的关键是在精简数据的同时，最大限度地保留点云数据的原有特征。在研究现有数据精简技术的基础上，提出了基于提升格式的第二代小波进行分层数据精简的新方法。
研究了准均匀B样条曲线光顺技术，提出了基于提升格式的第二代小波曲线光顺新方法。从多分辨率分析的概念入手，详细推导了B样条曲线的小波表示，简要介绍了半正交B样条小波，给出了B样条小波分解和重构的快速算法。运用第二代小波基本原理，经过分裂、预测和更新等步骤，详细推导了均匀B样条曲线的第二代小波表示，实现了基于第二代小波的曲线光顺。
研究了任意控制点B样条曲线小波光顺技术，通过插入节点以增加控制点个数的方法，构造出满足小波光顺要求的精细曲线。
在进行非均匀有理B样条(NURBS)曲面重构时，为了生成矩形域网格，针对数据点的分布不均匀性，采用累积弦长法构造非均匀节点矢量，构造插值于扫描线上数据点的非均匀B样条曲线，再对其均匀采样，保证了曲面的插值精度。完成了曲面重构。
研究了双三次准均匀B样条曲面的多分辨分解算法。确定了满足小波分解条件的重采样点数，实现了点云数据的曲面重构和多级小波分解的无缝集成。
从误差来源的角度进行论述，具体分析了影响重构曲面CAD模型精度的各种因素。简要介绍了模型精度评价方法，定性地给出了为提高模型精度的误差处理策略。通过光顺性检查和误差检查用实例验证了NURBS曲面重构算法和曲面小波分解算法的可行性和准确性。
采用面向对象的编程技术，开发了原型系统，获得了良好的应用。
Reverse Engineering(RE) is one important method to develop new product, which hasreceived more and more high attention both from industry and academia. Aiming at thecurrent questions in RE such as low automation and generality, lacking adaptivity, the newtime-frequency tool- wavelet technology is introduced。With a view to raise quality andefficiency, the key technologies including data treatments, data simplification, quasi-uniform B-spline curve fairness, NURBS surface reconstruction, wavelet decompositionand accuracy analysis of CAD model of reconstructed surface are researched anddiscussed.
Coordinate transformation, coordinate fusion, delamination and ordering of cloudydata based on CMM are researched. According to the concentrating extent of coordinatevalue, fixed axis is identified automatically, so delaminating data is realized. On theprinciple of distance between data set, the method of judging beginning and end is adoptedto order, and so topology information within same layer is established.
The deleting method of abnormal noises is researched. Incorporating the, 3σlaw ofmathematical statistics, by means of calculating mean and standard error to determinatethreshold, the adaptive counting threshold method is put forward, which has welladaptivity.
Denoising cloudy data based wavelet technology is researched. Using wavelet tech-nology to denoise is the process of decomposing signal with wavelet, acquiring approxi-mate coefficients and detail coefficients, acting detailed coefficients with soft threshold tosuppress noises, then reconstructing signal to get the goal of denoising.
The key of simplifying data technique is retaining original features of cloudy datautmost. On the basis of researching current simplification technique, new method usingsecond generation wavelet based on lifting to simplification data is proposed.
Quasi-uniform B-spline curve fairness technique is studied and new method of curvefairness with second generation wavelet based on lifting is presented. From the conceptionof MRA, wavelet representation of B-spline curve is reasoned in detail, semi-orthogonalB-spline wavelet is introduced and B-spline wavelet fast algorithm of decomposing andreconstructing are given.Using the fundamental principle of second generation wavelet,after split, prediction and update, second generation wavelet representation of B-splinecurve is reasoned detailedly, and curve fairness based on second generation is realized.
Fairness technique of B-spline curves with arbitrary control points based on wavelet isstudied. Refined curves meeting with the requirement of wavelet fairness are constructedby means of inserting knots to increase control points number.
As reconstructing Non-Uniform Rational B-Spline (NURBS) surface, In order togenerate rectangle field grids, with non-uniform data points, a method of accumulatingchord length is presented to create non-uniform knots vector, Non-uniform B-Spline curveis constructed and interpolated on scanning line data points, then sampling it uniformly; Sothe accuracy of interpolated surface is guaranteed.
The fast algorithms of quasi-uniform bi-cubic B-spline wavelet and decomposing dualcubic quasi-uniform B-spline surface are given. Re-sample point number which meets thecondition of wavelet decomposition is determined and seamless integration of surfacereconstruction and multi-rank decomposing it is realized.
From the source of error, all sort of factors of influencing CAD model precision ofreconstructed surface are analyzed concretely. Evaluation methods of model precision areintroduced briefly and strategies dealing with error are proposed qualitatively. Thefeasibility and accuracy of algorithms of NURBS surface reconstruction anddecomposition with wavelet are verified through testing fairness and error.
Adopting object-oriented programming technique, prototype system with wellapplication is tapped.
引文
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