基于弹性变形的曲面重建和平滑
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摘要
随着计算机辅助几何设计的不断发展,曲线曲面造型方法的研究热点经历了从表达方式到控制变形再到仿真变形的演变。经典的弹性变形方法以其简单、仿真效果好、直观、快速等特点,成为沟通几何变形与物理变形的桥梁,在各领域内得到了广泛应用。根据应用条件的不同,弹性变形方法对于外部数据的刻画、处理和交互都有不同的要求,因而需要进行具有针对性的改进。本文以弹性变形方法为基础,在空间曲线曲面立体重建和网格平滑及增强方面进行了研究；另外,给出了一种处理工业生产中复杂区域标注问题的快速方法。本文的主要工作包括：
1.本文基于弹性变形方法的思想来处理空间曲线曲面的立体重建问题。在立体重建中,我们以变形方法为基础,采用具有透视不变性的NURBS表达方式,从反向优化的角度来演化曲线曲面进行重建。这样可以更好地利用投影曲线曲面的局部性质,降低对不同像平面中图像曲线曲面数据的匹配需求,同时提高重建精度。考虑到重建二维图像数据存在不可避免的误差,我们讨论了其对立体重建的影响。最后使用所提立体重建方法对理想数据和真实数据进行了实验,得到了令人满意的重建效果。此外,重建二维图像数据中,提出了一种将图像目标边界信息和区域信息相结合的新的变分水平集图像分割方法。它有效利用了图像信息且不需重新初始化水平集函数,能够对多种类型图像进行有效分割。
2.定义弹性变形所使用的曲面基本形式描述了曲面的局部微分特征,从网格信号处理角度对这种特征进行处理则可以得到具有真实造型效果的优质网格。本文基于线性弹性变形方法对局部微分特征的描述,对网格曲面的基本形式特征进行调整,然后在约束最小二乘意义下重建网格,并使用快速的线性系统求解器,达到了实时响应的平滑、增强效果。实验结果表明本文方法简单快速并可有效防止体积收缩和形状畸变。
3.对复杂区域标注问题进行了研究,给出了一种快速的基于链码的复杂区域标注方法FCBL (Fast Code-Based Labeler)使用指定标注字符尺寸对复杂区域进行离散,然后通过编码技术对区域信息进行处理以减少存储量并根据具体情况对链码加以增强。采用基于链码的搜索机制并针对各种约束进行了扩展,进一步使用最小二乘估计最优方向来提高速度和精度。基于大量工业数据的实验验证了FCBL的可行性和稳定性。
With the development of Computer Aided Geometric Design, the research focus of curve and surface modeling methods has changed from representation to controllable de-formation, and then to simulation deformation. The classic elastic deformation methods become the bridge of communication between geometric deformation and physical defor-mation, and illuminate extensive applications in various fields, due to their advantages in simplicity, effective simulation, intuition and speed. According to different applica-tion conditions, elastic deformation methods require distinct representations, processing schemes and interactions with respect to exterior data, and hence they need to be im-proved contrapuntally. In this dissertation, elastic deformation methods are employed as the base of studying space curve/surface stereo reconstruction and mesh smoothing together with enhancement. In addition, a fast approach dealing with industrial prob-lems of labeling in complex irregular regions is proposed as well. The main work can be summarized as follows:
1. The idea of elastic deformation methods is first used to handle space curve/surface stereo reconstruction problem. In the step of stereo reconstruction, based on deformation method and perspective invariant NURBS representation, we evolute the curve/surface from the view of inverse optimization to finish reconstruction. This manner can obtain more effective use of local properties from projected curve/surface, reduce the need of matching curve/surface data in multiview images, meanwhile improve the reconstruction precision. Considering the 2D data reconstruction inevitably exists error, a discussion on its influence to stereo reconstruction is given next. Finally, the proposed approach is ex-perimented with ideal and real data, and gains a satisfying reconstruction effect. Besides, in the step of image data reconstruction, a variational level set segmentation approach which integrates the image information from both boundary gradient and region is pre-sented. It effectively utilizes the image information and does not need re-initialization. Experiments illustrate its abilities in segmenting different kinds of images.
2. Surface fundamental forms which are used to define elastic deformation describe the local differential features of surface. From the perspective of mesh signal processing, high quality mesh with real modeling effect can be obtained by processing this type of features. Based on the description of local differential features given by elastic deformation methods, we modify the fundamental form features of mesh surface. The new mesh is reconstructed in the least square sense with proper constraints added. With the help of fast linear system solver, the algorithm can achieve real-time smoothing and enhancement effect. Experimental results demonstrate that the proposed method is simple, fast and able to prevent volume shrinkage and shape distortion to some extent.
3. Labeling in complex irregular regions is studied and a fast code-based labeler (FCBL) is proposed to accomplish this objective. The region is discretized by specified labeling character size, and then encoded by the Freeman encoding technique for decreas-ing the storage. We enhance the encoding scheme to make it more suitable for our complex problem. Based on the codes, searching algorithms are designed and can be extended with customized constraints. In addition, by introducing a smart optimal direction estimation, the labeling speed and accuracy of FCBL are significantly improved. Experiments with a large range of real data gained from industrial factories demonstrate the feasibility and stability of FCBL.
1.本文基于弹性变形方法的思想来处理空间曲线曲面的立体重建问题。在立体重建中,我们以变形方法为基础,采用具有透视不变性的NURBS表达方式,从反向优化的角度来演化曲线曲面进行重建。这样可以更好地利用投影曲线曲面的局部性质,降低对不同像平面中图像曲线曲面数据的匹配需求,同时提高重建精度。考虑到重建二维图像数据存在不可避免的误差,我们讨论了其对立体重建的影响。最后使用所提立体重建方法对理想数据和真实数据进行了实验,得到了令人满意的重建效果。此外,重建二维图像数据中,提出了一种将图像目标边界信息和区域信息相结合的新的变分水平集图像分割方法。它有效利用了图像信息且不需重新初始化水平集函数,能够对多种类型图像进行有效分割。
2.定义弹性变形所使用的曲面基本形式描述了曲面的局部微分特征,从网格信号处理角度对这种特征进行处理则可以得到具有真实造型效果的优质网格。本文基于线性弹性变形方法对局部微分特征的描述,对网格曲面的基本形式特征进行调整,然后在约束最小二乘意义下重建网格,并使用快速的线性系统求解器,达到了实时响应的平滑、增强效果。实验结果表明本文方法简单快速并可有效防止体积收缩和形状畸变。
3.对复杂区域标注问题进行了研究,给出了一种快速的基于链码的复杂区域标注方法FCBL (Fast Code-Based Labeler)使用指定标注字符尺寸对复杂区域进行离散,然后通过编码技术对区域信息进行处理以减少存储量并根据具体情况对链码加以增强。采用基于链码的搜索机制并针对各种约束进行了扩展,进一步使用最小二乘估计最优方向来提高速度和精度。基于大量工业数据的实验验证了FCBL的可行性和稳定性。
With the development of Computer Aided Geometric Design, the research focus of curve and surface modeling methods has changed from representation to controllable de-formation, and then to simulation deformation. The classic elastic deformation methods become the bridge of communication between geometric deformation and physical defor-mation, and illuminate extensive applications in various fields, due to their advantages in simplicity, effective simulation, intuition and speed. According to different applica-tion conditions, elastic deformation methods require distinct representations, processing schemes and interactions with respect to exterior data, and hence they need to be im-proved contrapuntally. In this dissertation, elastic deformation methods are employed as the base of studying space curve/surface stereo reconstruction and mesh smoothing together with enhancement. In addition, a fast approach dealing with industrial prob-lems of labeling in complex irregular regions is proposed as well. The main work can be summarized as follows:
1. The idea of elastic deformation methods is first used to handle space curve/surface stereo reconstruction problem. In the step of stereo reconstruction, based on deformation method and perspective invariant NURBS representation, we evolute the curve/surface from the view of inverse optimization to finish reconstruction. This manner can obtain more effective use of local properties from projected curve/surface, reduce the need of matching curve/surface data in multiview images, meanwhile improve the reconstruction precision. Considering the 2D data reconstruction inevitably exists error, a discussion on its influence to stereo reconstruction is given next. Finally, the proposed approach is ex-perimented with ideal and real data, and gains a satisfying reconstruction effect. Besides, in the step of image data reconstruction, a variational level set segmentation approach which integrates the image information from both boundary gradient and region is pre-sented. It effectively utilizes the image information and does not need re-initialization. Experiments illustrate its abilities in segmenting different kinds of images.
2. Surface fundamental forms which are used to define elastic deformation describe the local differential features of surface. From the perspective of mesh signal processing, high quality mesh with real modeling effect can be obtained by processing this type of features. Based on the description of local differential features given by elastic deformation methods, we modify the fundamental form features of mesh surface. The new mesh is reconstructed in the least square sense with proper constraints added. With the help of fast linear system solver, the algorithm can achieve real-time smoothing and enhancement effect. Experimental results demonstrate that the proposed method is simple, fast and able to prevent volume shrinkage and shape distortion to some extent.
3. Labeling in complex irregular regions is studied and a fast code-based labeler (FCBL) is proposed to accomplish this objective. The region is discretized by specified labeling character size, and then encoded by the Freeman encoding technique for decreas-ing the storage. We enhance the encoding scheme to make it more suitable for our complex problem. Based on the codes, searching algorithms are designed and can be extended with customized constraints. In addition, by introducing a smart optimal direction estimation, the labeling speed and accuracy of FCBL are significantly improved. Experiments with a large range of real data gained from industrial factories demonstrate the feasibility and stability of FCBL.
引文
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