WO2015196544A1 - 点云曲面重建方法及系统 - Google Patents

点云曲面重建方法及系统 Download PDF

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Publication number
WO2015196544A1
WO2015196544A1 PCT/CN2014/084714 CN2014084714W WO2015196544A1 WO 2015196544 A1 WO2015196544 A1 WO 2015196544A1 CN 2014084714 W CN2014084714 W CN 2014084714W WO 2015196544 A1 WO2015196544 A1 WO 2015196544A1
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Prior art keywords
point cloud
nurbs
curve
slice
reconstruction
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PCT/CN2014/084714
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English (en)
French (fr)
Inventor
黄惠
尹康学
科恩⋅丹尼尔
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中国科学院深圳先进技术研究院
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Publication of WO2015196544A1 publication Critical patent/WO2015196544A1/zh
Priority to US15/371,148 priority Critical patent/US10121283B2/en

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/10—Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/30—Polynomial surface description
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2210/00—Indexing scheme for image generation or computer graphics
    • G06T2210/56—Particle system, point based geometry or rendering

Definitions

  • the invention relates to a method and system for reconstructing a point cloud surface. Background technique
  • 3D modeling technology is one of the main bottlenecks that restrict various graphics applications in games, movies, and computer-aided design.
  • 3D scanning technology With the development of 3D scanning technology, a variety of 3D point cloud data has become readily available. However, these point cloud data often have serious noise and loss. The traditional point cloud surface reconstruction method is difficult to get good results.
  • the point cloud surface reconstruction technology mainly focuses on the automatic reconstruction method.
  • Common automatic algorithms include Poisson reconstruction, radial basis function based methods, and so on. These methods use the approximation algorithm of implicit functions to construct spatial surfaces. Although they are widely used in different degrees, when the point cloud data has large defects or the topology is unclear, these methods are very ineffective.
  • some scholars have begun experimenting with interactive methods to improve the quality of point cloud reconstruction. For example, the topology of the user-defined data is used to overcome the topological error after point cloud reconstruction, or the topology of the reconstructed surface is constrained by the user calibrating the inner and outer layers of the zero surface in the distance function.
  • the present invention provides a point cloud surface reconstruction method, the method comprising the steps of: a. extracting a skeleton curve of an input point cloud; b. editing the extracted skeleton curve, and specifying a sweep path; c. The edited skeleton curve acquires a point cloud slice, and the NURBS closed curve is fitted by the point cloud slice; d. A plurality of point cloud reconstructions are obtained along the specified sweep path combined with the fitted NURBS closed curve Generalized cylinder; e. Combine the plurality of generalized cylinders obtained by the above reconstruction into one surface, and perform a smooth operation on the intersection of the generalized cylinders to reconstruct the point cloud surface.
  • the method further includes: performing an interaction on the reconstructed point cloud surface to improve the quality of the reconstructed point cloud surface.
  • the editing includes: cutting, connecting, trimming, extending, deforming.
  • the step c includes: fitting the NURBS closed curve by using a curvature-based square distance minimization method, and allowing the user to correct the NURBS closed curve when the fitting effect is unsatisfactory.
  • the step d includes: sweeping the acquired point cloud slice along the specified sweep path, and ensuring that the obtained new point cloud slice curve matches the input point cloud; the closed curve for each NURBS is outward Interpolating, so that the NURBS surfaces after the extrapolation meet at the boundary, thereby detecting the correspondence of the control points of the different slice curves; after detecting the correspondence of the control points of the different slice curves, all the fits on the sweep path are The NURBS closure curves are combined.
  • the present invention also provides a point cloud surface reconstruction system, including an extraction module, an editing module, a fitting module, and a reconstruction module, wherein: the extraction module is configured to extract a skeleton curve of an input point cloud; Deriving a skeleton curve, and specifying a sweeping path; the fitting module is configured to acquire a point cloud slice along the edited skeleton curve, and use the point cloud slice to fit a NURBS closed curve; the reconstruction module For reconstructing a point cloud to obtain a plurality of generalized cylinders along the above-mentioned specified sweeping path, combined with the fitted NURBS closed curve; the reconstruction module is further configured to merge the plurality of generalized cylinders obtained by the above reconstruction into one surface And smoothing the intersection of the generalized cylinders to reconstruct the point cloud surface.
  • the extraction module is configured to extract a skeleton curve of an input point cloud; Deriving a skeleton curve, and specifying a sweeping path
  • the fitting module is configured to acquire a point cloud slice along the
  • the system further includes an interaction module, configured to: perform interaction on the reconstructed point cloud surface, Thereby improving the quality of the reconstructed point cloud surface.
  • the editing includes: cutting, connecting, trimming, extending, deforming.
  • the fitting module is specifically configured to: fit using a curvature-based square distance minimization method
  • the NURBS closed curve allows the user to correct the NURBS closed curve when the fit is unsatisfactory.
  • the reconstruction module is specifically configured to: scan the acquired point cloud slice along the specified sweep path, and ensure that the obtained new point cloud slice curve matches the input point cloud; for each NURBS closed curve direction Extrapolating values, so that the NURBS surfaces after the extrapolation meet at the boundary, thereby detecting the correspondence relationship of the control points of the different slice curves; after detecting the correspondence relationship of the control points of the different slice curves, fitting the swept path All NURBS closure curves are combined.
  • the method and system for reconstructing a point cloud surface of the present invention can achieve the most accurate surface reconstruction with a minimum amount of interaction, and the beneficial effects are as follows: 1)
  • the point cloud data with severe missing can be processed:
  • the present invention adopts a skeleton curve and a tangential direction The two curves of the curve are represented as the middle, and the accuracy is still high when the data is seriously missing.
  • the reconstruction quality is high: it is more efficient and robust than the traditional fitting algorithm, so the reconstruction accuracy obtained is high; 3)
  • the interaction is simple: the present invention User interaction is required in the case of automatic calculation failure, and only interaction between the skeleton curve and the interaction of the face curve is required; 4) Good controllability: The present invention decomposes the three-dimensional interaction into two mutually orthogonal The curve interaction provides very good interactivity; 5)
  • the theoretical reconstruction effect can be perfect: Since the user is allowed to control two mutually orthogonal curves arbitrarily, in theory, as long as the user puts enough effort, the point cloud surface The accuracy of reconstruction can be reached
  • FIG. 1 is a flow chart of a method for reconstructing a point cloud surface according to the present invention
  • FIG. 2 is a schematic diagram of five basic operations for editing a skeleton of a point cloud according to the present invention
  • FIG. 3 is a hardware architecture diagram of a point cloud surface reconstruction system according to the present invention. detailed description
  • Step S401 automatically extracting a skeleton curve of the input point cloud.
  • the embodiment extracts the skeleton curve of the input point cloud by using an "L1-median value" algorithm.
  • Step S402 interactively editing the extracted skeleton curve and specifying a sweep path. details as follows:
  • this embodiment uses five basic operations to edit the skeleton curve of the input point cloud.
  • the following five basic operations are introduced one by one:
  • Cut Delete an edge from the skeleton curve representing the point cloud to cut off a branch of the skeleton curve; or delete a vertex with a degree greater than 2 from the skeleton curve representing the point cloud, thereby deleting a joint point.
  • Trim Deletes the end portion of a skeleton branch in the skeleton curve of the point cloud.
  • Deformation The user deforms the skeleton by dragging a point on the skeleton in the skeleton curve of the point cloud. This embodiment is implemented by a moving least squares deformation algorithm.
  • Step S403 obtaining a higher-quality point cloud slice along the edited skeleton curve, and fitting the NURBS closed curve by using the point cloud slice, and if the fitting effect is not good, allowing the user to interactively
  • the NURBS closed curve is corrected.
  • a higher quality point cloud slice is selected based on the edited skeleton curve to fit the NURBS closed curve.
  • a curvature-based square distance minimization method is used to fit a NURBS closed curve from a two-dimensional point cloud slice.
  • Step S404 reconstructing the point cloud along the specified sweep path and combining the fitted NURBS closed curve to obtain a plurality of generalized cylinders.
  • the specific steps are as follows:
  • the acquired point cloud slice is swept along the user-specified sweep path, and the obtained new point cloud slice curve is matched with the input point cloud.
  • each NURBS closed curve is interpolated outward, so that the NURBS surfaces after the extrapolation meet at the boundary, so that The correspondence between the control points of different slice curves is detected. Extrapolation is achieved by minimizing the following formula:
  • Cj is a NURBS curve obtained by extrapolation
  • E d ( Cj ) is the error between Cj and the corresponding two-dimensional point cloud slice
  • E m (Ci, Cj ) is between Ci and Cj
  • ⁇ is a constant parameter, and the embodiment generally takes 0.1 as the value of ⁇ . From the beginning, continuously outward, the adjacent slice curves are obtained one by one.
  • Step S405 Combine the plurality of generalized cylinders obtained by the above reconstruction into one surface, and perform a smoothing operation on the intersection of the generalized cylinders to reconstruct the point cloud surface.
  • the generalized cylinder calculated along the user-specified sweep path is converted into a distance field, and the distance is combined using CSG and operated, and then the surface is generated according to the distance field, and then pulled.
  • the Plass smoothing operation smoothes the joints of different generalized cylinders to obtain a final surface.
  • Step S406 Perform interaction on the reconstructed point cloud surface to improve the quality of the reconstructed point cloud surface.
  • the interaction operations mainly include: specifying sharp features and modifying the reconstructed surface. details as follows:
  • Specify sharp features Allows the user to draw a stroke on a two-dimensional screen, and then finds the NURBS curve intersected on the generalized cylinder. By modifying the weight of the NURBS control point, the reconstructed surface has sharp features consistent with user requirements.
  • Modify the reconstructed surface Sometimes the automatically calculated point cloud surface does not necessarily meet the user's requirements. In this case, the user can select any NURBS curve on the generalized cylinder and modify the final surface by editing its control point.
  • FIG. 3 it is a hardware architecture diagram of the point cloud surface reconstruction system of the present invention.
  • the system includes an extraction module, an editing module, a fitting module, a reconstruction module, and an interaction module.
  • the extraction module is configured to automatically extract a skeleton curve of the input point cloud. Specifically, the embodiment extracts the skeleton curve of the input point cloud by using the "L1-median value” algorithm.
  • the editing module is for interactively editing the extracted skeleton curve and specifying a sweep path. details as follows:
  • this embodiment uses five basic operations to edit the skeleton curve of the input point cloud.
  • the following five basic operations are introduced one by one:
  • Cut Delete an edge from the skeleton curve representing the point cloud to cut off a branch of the skeleton curve; or delete a vertex with a degree greater than 2 from the skeleton curve representing the point cloud, thereby deleting a joint point.
  • Trim Deletes the end portion of a skeleton branch in the skeleton curve of the point cloud.
  • Deformation The user deforms the skeleton by dragging a point on the skeleton in the skeleton curve of the point cloud. This embodiment is implemented by a moving least squares deformation algorithm.
  • the fitting module is configured to obtain a high-quality point cloud slice along the edited skeleton curve, and use the point cloud slice to fit a NURBS closed curve, and if the fitting effect is not good, the user is allowed to interact.
  • the NURBS closure curve is corrected.
  • a higher quality point cloud slice is selected based on the edited skeleton curve to fit the NURBS closed curve.
  • a curvature-based square distance minimization method is used to fit a NURBS closed curve from a two-dimensional point cloud slice.
  • the reconstruction module is configured to reconstruct a point cloud according to the specified sweep path and the fitted NURBS closed curve to obtain a plurality of generalized cylinders. details as follows:
  • the acquired point cloud slice is swept along the user-specified sweep path, and the obtained new point cloud slice curve is matched with the input point cloud.
  • each NURBS closed curve is interpolated outward, so that the NURBS surfaces after the extrapolation meet at the boundary, so that The correspondence between the control points of different slice curves is detected. Extrapolation is achieved by minimizing the following formula:
  • Cj is a NURBS curve obtained by extrapolation
  • E d ( Cj ) is the error between Cj and the corresponding two-dimensional point cloud slice
  • E m (Ci, Cj ) is between Ci and Cj
  • ⁇ is a constant parameter, and the embodiment generally takes 0.1 as the value of ⁇ . From the beginning, continuously outward, the adjacent slice curves are obtained one by one.
  • the reconstruction module is further configured to combine the plurality of generalized cylinders obtained by the above reconstruction into one surface, and perform a smoothing operation on the intersection of the generalized cylinders to reconstruct the point cloud surface.
  • the generalized cylinder calculated along the user-specified sweep path is converted into a distance field, and the distance is combined together using CSG, and then the surface is generated according to the distance field, and then the Laplace smoothing operation is performed. Smoothing the joints of different generalized cylinders to obtain a final surface.
  • the interaction module is configured to interact with the reconstructed point cloud surface to improve the quality of the reconstructed point cloud surface.
  • the interaction mainly includes: specifying a sharp feature and modifying the reconstructed surface. details as follows:
  • Specify sharp features Allows the user to draw a stroke on a two-dimensional screen, and then finds the NURBS curve intersected on the generalized cylinder. By modifying the weight of the NURBS control point, the reconstructed surface has sharp features consistent with user requirements.
  • Modify the reconstructed surface Sometimes the automatically calculated point cloud surface does not necessarily meet the user's requirements. In this case, the user can select any NURBS curve on the generalized cylinder and modify the final surface by editing its control point.

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Abstract

本发明涉及一种点云曲面重建方法，包括如下步骤：提取输入点云的骨架曲线；编辑所述提取的骨架曲线，并指定扫掠路径；沿着所述编辑后的骨架曲线获取点云切片，利用所述点云切片拟合出NURBS闭合曲线；沿着上述指定的扫掠路径，结合拟合出的NURBS闭合曲线，对点云重建得到多个广义圆柱；将上述重建得到的多个广义圆柱合并为一个曲面，并对所述广义圆柱的相交处进行平滑操作重建点云曲面。本发明能够以最少量的交互实现最精确的点云曲面重建，可以处理缺失严重的点云数据，且曲面重建质量高，可控性好。

Description

点云曲面重建方法及系统 技术领域
本发明涉及一种点云曲面重建方法及系统。 背景技术
3D 建模技术是制约着游戏、 电影、 计算机辅助设计等领域的各种图形学 应用的主要瓶颈之一。 随着 3D扫描技术的发展， 各种各样的三维点云数据开 始变得容易获得。但是， 这些点云数据往往有严重的噪声和缺失， 传统的点云 曲面重建方法很难得到很好的效果。
目前点云曲面重建技术主要集中在自动重建方法上。常见的自动算法有泊 松重建、基于径向基函数的方法等。这些方法利用隐式函数的逼近算法来构造 空间曲面， 虽然在不同程度上广为应用，但是当点云数据具有较大缺失或者拓 扑结构不清晰的时候， 这些方法的效果都很差。 除此之外， 已经有一些学者开 始尝试使用交互方法来提高点云重建的质量。例如， 通过用户定义数据的拓扑 结构来克服点云重建后的拓扑错误，或者通过用户在距离函数标定零曲面内外 层来约束重建曲面的拓扑结构。
目前的交互式点云曲面重建方法都没有得到很好的效果，原因主要在于四 个方面： 第一， 这些交互重建技术仍然建立在自动重建算法之上， 当数据缺失 较严重时， 引入的交互不足以改善极糟糕的自动重建结果； 第二， 仍然采用了 简单的光滑假设， 当数据有尖锐特征时难以得到很好的结果； 第三， 这些交互 方法太复杂， 用户难以使用； 第四， 这些方法都不够成熟可靠， 以至于很难被 广泛使用。 发明内容 有鉴于此， 有必要提供一种点云曲面重建方法及系统。
本发明提供一种点云曲面重建方法， 该方法包括如下歩骤： a.提取输入点 云的骨架曲线； b.编辑所述提取的骨架曲线， 并指定扫掠路径； c.沿着所述编 辑后的骨架曲线获取点云切片， 利用所述点云切片拟合出 NURBS闭合曲线； d. 沿着上述指定的扫掠路径， 结合拟合出的 NURBS闭合曲线，对点云重建得到多 个广义圆柱； e.将上述重建得到的多个广义圆柱合并为一个曲面， 并对所述广 义圆柱的相交处进行平滑操作重建点云曲面。
其中， 该方法还包括歩骤： 对上述重建的点云曲面进行交互操作， 从而提 高所述重建的点云曲面的质量。
所述的编辑包括： 切断、 连接、 修剪、 延长、 变形。
所述的歩骤 c包括：采用基于曲率的平方距离极小化方法拟合 NURBS闭合 曲线， 对拟合效果不满意时允许用户对所述 NURBS闭合曲线进行修正。
所述的歩骤 d包括： 沿着指定的扫掠路径对获取的点云切片进行扫掠， 同 时保证获得的新点云切片曲线和输入的点云相匹配；对每个 NURBS闭合曲线向 外插值， 使外插之后的 NURBS曲面在边界处相遇， 从而检测不同切片曲线的控 制点的对应关系； 在检测不同切片曲线的控制点的对应关系之后，将所述扫掠 路径上拟合的所有 NURBS闭合曲线结合到一起。
本发明还提供一种点云曲面重建系统， 包括提取模块、 编辑模块、 拟合模 块及重建模块， 其中： 所述提取模块用于提取输入点云的骨架曲线； 所述编辑 模块用于编辑所述提取的骨架曲线， 并指定扫掠路径； 所述拟合模块用于沿着 所述编辑后的骨架曲线获取点云切片，利用所述点云切片拟合出 NURBS闭合曲 线； 所述重建模块用于沿着上述指定的扫掠路径， 结合拟合出的 NURBS闭合曲 线，对点云重建得到多个广义圆柱； 所述重建模块还用于将上述重建得到的多 个广义圆柱合并为一个曲面，并对所述广义圆柱的相交处进行平滑操作重建点 云曲面。
其中，该系统还包括交互模块用于：对上述重建的点云曲面进行交互操作， 从而提高所述重建的点云曲面的质量。
所述的编辑包括： 切断、 连接、 修剪、 延长、 变形。
所述的拟合模块具体用于： 采用基于曲率的平方距离极小化方法拟合
NURBS闭合曲线， 对拟合效果不满意时允许用户对所述 NURBS闭合曲线进行修 正。
所述的重建模块具体用于：沿着指定的扫掠路径对获取的点云切片进行扫 掠， 同时保证获得的新点云切片曲线和输入的点云相匹配； 对每个 NURBS闭合 曲线向外插值， 使外插之后的 NURBS曲面在边界处相遇， 从而检测不同切片曲 线的控制点的对应关系； 在检测不同切片曲线的控制点的对应关系之后，将所 述扫掠路径上拟合的所有 NURBS闭合曲线结合到一起。
本发明点云曲面重建方法及系统，能够以达到以最少量的交互实现最精确 的曲面重建的目的， 有益效果如下： 1 ) 可以处理缺失严重的点云数据： 本发 明采用骨架曲线和切向曲线两种曲线作为中间表示，在数据严重缺失时依然精 度很高； 2 ) 重建质量高： 比传统的拟合算法更加高效鲁棒， 因此获得的重建 精度很高； 3 ) 交互简单： 本发明在自动计算失败的情况下才需要用户交互， 并且只需要对骨架曲线的交互和对切面曲线的交互两种交互； 4 ) 可控性好： 本发明将三维交互分解为两种相互正交的曲线交互，提供了非常好的可交互性; 5 ) 理论重建效果可以达到完美： 由于允许用户任意的控制两种相互正交的曲 线， 因而， 理论上只要用户付出足够多的努力， 点云曲面重建的精度可以达到
附图说明
图 1为本发明点云曲面重建方法的流程图；
图 2为本发明对点云的骨架进行编辑的五种基本操作示意图;
图 3为本发明点云曲面重建系统的硬件架构图。 具体实施方式
下面结合附图及具体实施例对本发明作进一歩详细的说明。
参阅图 1所示， 是本发明点云曲面重建方法较佳实施例的作业流程图。 歩骤 S401 , 自动提取输入点云的骨架曲线。具体而言，本实施例采用 "L1- 中值"算法提取所述输入点云的骨架曲线。
歩骤 S402 , 交互式地编辑所述提取的骨架曲线， 并指定扫掠路径。 具体 如下：
如图 2所示，本实施例采用五种基本操作对所述输入点云的骨架曲线进行 编辑。 以下对所述五种基本操作进行逐一介绍：
( 1 ) 切断： 从表示点云的骨架曲线图中删除一条边， 以切断骨架曲线的 一条分支； 或者从表示点云的骨架曲线图中删除一个度数大于 2的顶点， 从而 删除一个结合点。
( 2 ) 连接： 连接表示点云的骨架曲线图上的两个终端结点， 从而将两条 分支连接为一条。
( 3 ) 修剪： 删除点云的骨架曲线图中一个骨架分支的末端部分。
( 4 ) 延长： 从点云的骨架曲线图中骨架分支的端点处沿着末端切向继续 向前生长；
( 5 ) 变形： 用户通过拖动点云的骨架曲线图中骨架上的一个点， 对骨架 实施形变。 本实施例采用移动最小二乘变形算法实现。
歩骤 S403 , 沿着所述编辑后的骨架曲线获取质量较高的点云切片， 利用 所述点云切片拟合出 NURBS闭合曲线， 如果拟合效果不好， 则允许用户交互式 地对所述 NURBS闭合曲线进行修正。 具体歩骤如下：
根据所述编辑后的骨架曲线选取质量较高的点云切片，来拟合 NURBS闭合 曲线。 本实施例采用基于曲率的平方距离极小化方法从二维点云切片中拟合 NURBS闭合曲线。
若拟合效果不精确，则允许用户交互式地拖动所述 NURBS闭合曲线控制点 对其修正。
歩骤 S404 , 沿着上述指定的扫掠路径， 结合拟合出的 NURBS闭合曲线， 对点云进行重建得到多个广义圆柱。 具体歩骤如下：
本实施例沿着用户指定的扫掠路径对上述获取的点云切片进行扫掠，同时 保证获得的新点云切片曲线和输入的点云相匹配。
在上述获取的二维点云切片和从二维点云切片拟合的 NURBS 闭合曲线的 基础上，对每个 NURBS闭合曲线向外插值， 使外插之后的 NURBS曲面在边界处 相遇， 从而可以检测不同切片曲线的控制点的对应关系。通过极小化如下公式 来实现外插：
argminc . (£'£i (c/ ) + aEm ci, Cj))
其中， 为原始 NURBS曲线， Cj为外插得到的一条 NURBS曲线， Ed(Cj)表示 Cj与相应二维点云切片之间的误差， Em (Ci, Cj )表示 Ci和 Cj之间的相对变形程度， α为一个常数参数， 本实施例一般取 0. 1 作为 α的值。 从 开始， 不断向外， 逐个求出相邻的切片曲线。
在检测到不同切片曲线的控制点的对应关系之后，将所述扫掠路径上上一 歩拟合的所有 NURBS闭合曲线结合到一起。通过极小化如下公式， 求解出一个 既能极小化相邻切片的相对形变又能保证拟合点云数据的广义圆柱。
argmin{Ci) + aEm (cit ci+1) + βΕ3 {οί_ί, cit ci+1)) 在该公式中， 将扫掠路径上的所有 NURBS切片曲线 {cj都放到一起求解， 其中： Et^DEm与外插公式中一致； Es为光滑项， 用来保证相邻三个 NURBS切 片曲线的控制点连接成的夹角尽可能小； β为一个常数参数， 本实施例一般取 0. 01作为 β的值。
歩骤 S405 , 将上述重建得到的多个广义圆柱合并为一个曲面， 并对所述 广义圆柱的相交处进行平滑操作， 从而重建点云曲面。
本实施例将沿用户指定的扫掠路径计算得到的广义圆柱转换为距离场，使 用 CSG并操作将所述距离场合并到一起， 然后根据该距离场生成曲面， 再用拉 普拉斯平滑操作对不同广义圆柱的接合处进行平滑操作，从而得到一个最终的 曲面。
歩骤 S406 , 对上述重建的点云曲面进行交互操作， 从而提高所述重建的 点云曲面的质量。 所述的交互操作主要包括： 指定尖锐特征及修改重建曲面。 具体如下：
指定尖锐特征： 允许用户在二维屏幕上画一笔， 然后求出广义圆柱上与之 相交的 NURBS曲线，通过修改 NURBS控制点的权重使重建出的曲面具有与用户 要求一致的尖锐特征。
修改重建曲面： 有时自动计算出的点云曲面不一定符合用户要求， 此时， 用户可以选中广义圆柱上的任意一条 NURBS曲线，通过编辑其控制点对最终曲 面进行修改。
参阅图 3所示， 是本发明点云曲面重建系统的硬件架构图。该系统包括提 取模块、 编辑模块、 拟合模块、 重建模块及交互模块。
所述提取模块用于自动提取输入点云的骨架曲线。具体而言， 本实施例采 用 "L1-中值"算法提取所述输入点云的骨架曲线。
所述编辑模块用于交互式地编辑所述提取的骨架曲线， 并指定扫掠路径。 具体如下：
如图 2所示，本实施例采用五种基本操作对所述输入点云的骨架曲线进行 编辑。 以下对所述五种基本操作进行逐一介绍：
( 1 ) 切断： 从表示点云的骨架曲线图中删除一条边， 以切断骨架曲线的 一条分支； 或者从表示点云的骨架曲线图中删除一个度数大于 2的顶点， 从而 删除一个结合点。
( 2 ) 连接： 连接表示点云的骨架曲线图上的两个终端结点， 从而将两条 分支连接为一条。
( 3 ) 修剪： 删除点云的骨架曲线图中一个骨架分支的末端部分。
(4 ) 延长： 从点云的骨架曲线图中骨架分支的端点处沿着末端切向继续 向前生长；
( 5 ) 变形： 用户通过拖动点云的骨架曲线图中骨架上的一个点， 对骨架 实施形变。 本实施例采用移动最小二乘变形算法实现。
所述拟合模块用于沿着所述编辑后的骨架曲线获取质量较高的点云切片， 利用所述点云切片拟合出 NURBS闭合曲线， 如果拟合效果不好， 则允许用户交 互式地对所述 NURBS闭合曲线进行修正。 具体歩骤如下：
根据所述编辑后的骨架曲线选取质量较高的点云切片，来拟合 NURBS闭合 曲线。 本实施例采用基于曲率的平方距离极小化方法从二维点云切片中拟合 NURBS闭合曲线。
若拟合效果不精确，则允许用户交互式地拖动所述 NURBS闭合曲线控制点 对其修正。
所述重建模块用于沿着上述指定的扫掠路径，结合拟合出的 NURBS闭合曲 线， 对点云进行重建得到多个广义圆柱。 具体如下：
本实施例沿着用户指定的扫掠路径对上述获取的点云切片进行扫掠，同时 保证获得的新点云切片曲线和输入的点云相匹配。
在上述获取的二维点云切片和从二维点云切片拟合的 NURBS 闭合曲线的 基础上，对每个 NURBS闭合曲线向外插值， 使外插之后的 NURBS曲面在边界处 相遇， 从而可以检测不同切片曲线的控制点的对应关系。通过极小化如下公式 来实现外插：
argminc . (£'£i (c/ ) + aEm ci, Cj))
其中， 为原始 NURBS曲线， Cj为外插得到的一条 NURBS曲线， Ed(Cj)表示 Cj与相应二维点云切片之间的误差， Em (Ci, Cj )表示 Ci和 Cj之间的相对变形程度， α为一个常数参数， 本实施例一般取 0. 1 作为 α的值。 从 开始， 不断向外， 逐个求出相邻的切片曲线。
在检测到不同切片曲线的控制点的对应关系之后，将所述扫掠路径上上一 歩拟合的所有 NURBS闭合曲线结合到一起。通过极小化如下公式， 求解出一个 既能极小化相邻切片的相对形变又能保证拟合点云数据的广义圆柱。
argmin{Ci) + aEm (cit ci+1) + βΕ3 {οί_ί, cit ci+1)) 在该公式中， 将扫掠路径上的所有 NURBS切片曲线 {cj都放到一起求解， 其中： Et^DEm与外插公式中一致； Es为光滑项， 用来保证相邻三个 NURBS切 片曲线的控制点连接成的夹角尽可能小； β为一个常数参数， 本实施例一般取 0. 01作为 β的值。
所述重建模块还用于将上述重建得到的多个广义圆柱合并为一个曲面，并 对所述广义圆柱的相交处进行平滑操作， 从而重建点云曲面。
本实施例将沿用户指定的扫掠路径计算得到的广义圆柱转换为距离场，使 用 CSG并操作将所述距离场合并到一起， 然后根据该距离场生成曲面， 再用拉 普拉斯平滑操作对不同广义圆柱的接合处进行平滑操作，从而得到一个最终的 曲面。
所述交互模块用于对上述重建的点云曲面进行交互操作，从而提高所述重 建的点云曲面的质量。所述的交互操作主要包括： 指定尖锐特征及修改重建曲 面。 具体如下：
指定尖锐特征： 允许用户在二维屏幕上画一笔， 然后求出广义圆柱上与之 相交的 NURBS曲线，通过修改 NURBS控制点的权重使重建出的曲面具有与用户 要求一致的尖锐特征。
修改重建曲面： 有时自动计算出的点云曲面不一定符合用户要求， 此时， 用户可以选中广义圆柱上的任意一条 NURBS曲线，通过编辑其控制点对最终曲 面进行修改。
虽然本发明参照当前的较佳实施方式进行了描述，但本领域的技术人员应 能理解， 上述较佳实施方式仅用来说明本发明， 并非用来限定本发明的保护范 围， 任何在本发明的精神和原则范围之内， 所做的任何修饰、 等效替换、 改进 等， 均应包含在本发明的权利保护范围之内。

Claims

权 利 要 求
1.一种点云曲面重建方法， 其特征在于， 该方法包括如下步骤：
a.提取输入点云的骨架曲线；
b.编辑所述提取的骨架曲线， 并指定扫掠路径；
c.沿着所述编辑后的骨架曲线获取点云切片， 利用所述点云切片拟合出 NURBS闭合曲线；
d.沿着上述指定的扫掠路径， 结合拟合出的 NURBS闭合曲线， 对点云重 建得到多个广义圆柱；
e.将上述重建得到的多个广义圆柱合并为一个曲面， 并对所述广义圆柱的 相交处进行平滑操作重建点云曲面。
2.如权利要求 1所述的方法， 其特征在于， 该方法还包括步骤：
对上述重建的点云曲面进行交互操作，从而提高所述重建的点云曲面的质
3.如权利要求 1或 2所述的方法， 其特征在于， 所述的编辑包括： 切断、 连接、 修剪、 延长、 变形。
4.如权利要求 3所述的方法， 其特征在于， 所述的步骤 c包括：
采用基于曲率的平方距离极小化方法拟合 NURBS闭合曲线，对拟合效果 不满意时允许用户对所述 NURBS闭合曲线进行修正。
5.如权利要求 4所述的方法， 其特征在于， 所述的步骤 d包括：
沿着指定的扫掠路径对获取的点云切片进行扫掠，同时保证获得的新点云 切片曲线和输入的点云相匹配；
对每个 NURBS闭合曲线向外插值， 使外插之后的 NURBS曲面在边界处 相遇， 从而检测不同切片曲线的控制点的对应关系；
在检测不同切片曲线的控制点的对应关系之后，将所述扫掠路径上拟合的 所有 NURBS闭合曲线结合到一起。
6.—种点云曲面重建系统，其特征在于，该系统包括提取模块、编辑模块、 拟合模块及重建模块， 其中：
所述提取模块用于提取输入点云的骨架曲线； 所述编辑模块用于编辑所述提取的骨架曲线， 并指定扫掠路径； 所述拟合模块用于沿着所述编辑后的骨架曲线获取点云切片，利用所述点 云切片拟合出 NURBS闭合曲线；
所述重建模块用于沿着上述指定的扫掠路径，结合拟合出的 NURBS闭合 曲线， 对点云重建得到多个广义圆柱；
所述重建模块还用于将上述重建得到的多个广义圆柱合并为一个曲面，并 对所述广义圆柱的相交处进行平滑操作重建点云曲面。
7.如权利要求 6所述的系统， 其特征在于， 该系统还包括交互模块用于： 对上述重建的点云曲面进行交互操作，从而提高所述重建的点云曲面的质
8.如权利要求 6或 7所述的系统， 其特征在于， 所述的编辑包括： 切断、 连接、 修剪、 延长、 变形。
9.如权利要求 8所述的系统， 其特征在于， 所述的拟合模块具体用于： 采用基于曲率的平方距离极小化方法拟合 NURBS闭合曲线，对拟合效果 不满意时允许用户对所述 NURBS闭合曲线进行修正。
10.如权利要求 9所述的系统， 其特征在于， 所述的重建模块具体用于： 沿着指定的扫掠路径对获取的点云切片进行扫掠，同时保证获得的新点云 切片曲线和输入的点云相匹配；
对每个 NURBS闭合曲线向外插值， 使外插之后的 NURBS曲面在边界处 相遇， 从而检测不同切片曲线的控制点的对应关系；
在检测不同切片曲线的控制点的对应关系之后，将所述扫掠路径上拟合的 所有 NURBS闭合曲线结合到一起。
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CN104050720B (zh) 2017-02-15

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