交互式空间物体三维测量方法的研究与实现
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摘要
三维测量技术在机器视觉、实物仿形及生物医学等众多领域都具有广泛的工程应用前景。但利用传统的测量方法，许多三维测量工作仅能依靠一些简单的手工操作进行估算，如在医学领域需要完成的二尖瓣面积、正常眼眶实际形状、大小以及肿瘤体积等复杂三维测量工作都是如此。计算机图形学技术的发展使我们可以在计算机中观察复杂物体，这为在计算机中完成三维测量提供了前提条件。在计算机中完成三维物体的测量，可以实现许多传统方法无法完成的复杂测量工作或使原来极为繁琐的测量工作变得简洁。生物组织的形态在三维物体中最为复杂，而对其进行三维测量在医学领域有着极为重要的现实意义，因此本文重点研究了利用计算机技术进行生物组织三维测量的方法。
本文使用图像恢复、图像校正、图像分割技术对二维CT断层图像的质量进行改善；使用边缘提取、三角剖分技术完成被测物体的三维建模；最后结合OpenGL图形库实现了被测物体的三维可视化。
本文详细研究了三维观察的具体过程，推导了三维物体世界坐标系和设备(屏幕)坐标系之间的转换关系，为三维交互技术的实现和三维测量结果的真实化奠定了基础。本文使用三维跟踪球技术实现对被测物体的交互旋转功能，使用平行透视下的拾取机制实现被测物体上特征点的选取，完成了三维交互设计。
三维测量主要包括空间两点间距离的测量和空间不规则物体表面积、体积的测量。空间两点间距离测量又可分为空间任意两点间直、曲线距离的测量和三维空间的深度测量。
本文提出了一种沿法线方向的三维深度测量方法，将其应用于面部软组织厚度信息的测量，与原来的方法相比提高了测量精度。并在计算过程中提出了一种基于坐标旋转的方法，将计算中所涉及的三维信息转化为二维信息，降低了计算复杂度。
本文在实现空间两点间曲线距离的测量时，设计了一种新的数据存贮结构，解决了杂乱交点的排序这一难题，提高了测量速度。并在具体计算时，采用三次样条曲线代替轮廓线，提高了曲线长度的计算精度。
最后，结合本研究所进行的颅骨面貌复原、颅像重合、三维立体适形放
疗计划等研究课题，采用面向对象的软件开发方法建立了一个数字化颅面三
维测量系统，完成了面部软组织厚度、面部距离特征和肿瘤表面积及体积的
测量工作，取得了良好的效果。
3-D measurement has capacious applications in engineering, such as its uses in machine vision, profile modeling and biomedical industry. But many 3-D measurements only can be estimated by handiwork now, for example, the area of mitral valve, the shape and size of eyepit and the volume of tumour in medicine field. With the development of computer graphics, complex objects can be observed on the computer screen, it's the foundation of computer aided 3-D measurement. Computer aided 3-D measurement can realize many complex measurements which cannot be done now, or reduce the complexity of many 3-D measurements. Biologic organ is one of the most complex 3-D objects, and the 3-D measurement of it play very important role in medicine field, so the method of biologic organ's 3-D measurement is studied in this thesis.
Techniques of image recovery, image geometric correction and image segmentation are applied in this thesis to improve the quality of images, which are got from CT devices. Edge extraction and triangulation are used to complete the 3-D modeling of measuring objects. Then OpenGL graphic libraries are introduced to realize the 3-D visualization.
The process of 3-D observation is detailedly studied and the transformation formulation of world coordination system and screen coordination system is listed. It's the foundation of 3-D interaction and actualization of 3-D measurement results. 3-D virtual sphere technique is used to realize the function of interactive rotation and picking method based on parallel perspective is used to realize the special characteristic points picking, so the design of 3-D interaction is completed.
3-D measurement mainly includes the distance measurement between two points, and the area and volume measurement of 3-D objects. The distance measurement can be divided into linear or curvilinear distance measurement and 3-D depth measurement.
A method of 3-D depth measurement following normal direction is proposed in this thesis. With the use of this method to get thickness information of facial parenchyma, the precision is increased compared with former methods. And a coordinates transformation method is proposed in calculation to simplify the 3-D calculations to 2-D calculations. This method reduces calculation complexity.
A new data storage structure is designed to resolve the difficulty in arrangement of unorderly intersection points and accelerate the measuring process during curvilinear distance between two points measuring. In calculation, cubic spline curve is used to instead contour line. This method can increase the precision of curvilinear distance measurement.
Finally, a digital skull-face 3-D computer aided measuring system is developed based on object-oriented software programming method. This system has completed the measurements of facial parenchyma thickness, facial distance characteristics and tumour's area and volume. It gets an upstanding effecting in facial reconstruction process, superposition identification between skulls and photos, and three-dimensional conformal radiotherapy technique.
本文使用图像恢复、图像校正、图像分割技术对二维CT断层图像的质量进行改善；使用边缘提取、三角剖分技术完成被测物体的三维建模；最后结合OpenGL图形库实现了被测物体的三维可视化。
本文详细研究了三维观察的具体过程，推导了三维物体世界坐标系和设备(屏幕)坐标系之间的转换关系，为三维交互技术的实现和三维测量结果的真实化奠定了基础。本文使用三维跟踪球技术实现对被测物体的交互旋转功能，使用平行透视下的拾取机制实现被测物体上特征点的选取，完成了三维交互设计。
三维测量主要包括空间两点间距离的测量和空间不规则物体表面积、体积的测量。空间两点间距离测量又可分为空间任意两点间直、曲线距离的测量和三维空间的深度测量。
本文提出了一种沿法线方向的三维深度测量方法，将其应用于面部软组织厚度信息的测量，与原来的方法相比提高了测量精度。并在计算过程中提出了一种基于坐标旋转的方法，将计算中所涉及的三维信息转化为二维信息，降低了计算复杂度。
本文在实现空间两点间曲线距离的测量时，设计了一种新的数据存贮结构，解决了杂乱交点的排序这一难题，提高了测量速度。并在具体计算时，采用三次样条曲线代替轮廓线，提高了曲线长度的计算精度。
最后，结合本研究所进行的颅骨面貌复原、颅像重合、三维立体适形放
疗计划等研究课题，采用面向对象的软件开发方法建立了一个数字化颅面三
维测量系统，完成了面部软组织厚度、面部距离特征和肿瘤表面积及体积的
测量工作，取得了良好的效果。
3-D measurement has capacious applications in engineering, such as its uses in machine vision, profile modeling and biomedical industry. But many 3-D measurements only can be estimated by handiwork now, for example, the area of mitral valve, the shape and size of eyepit and the volume of tumour in medicine field. With the development of computer graphics, complex objects can be observed on the computer screen, it's the foundation of computer aided 3-D measurement. Computer aided 3-D measurement can realize many complex measurements which cannot be done now, or reduce the complexity of many 3-D measurements. Biologic organ is one of the most complex 3-D objects, and the 3-D measurement of it play very important role in medicine field, so the method of biologic organ's 3-D measurement is studied in this thesis.
Techniques of image recovery, image geometric correction and image segmentation are applied in this thesis to improve the quality of images, which are got from CT devices. Edge extraction and triangulation are used to complete the 3-D modeling of measuring objects. Then OpenGL graphic libraries are introduced to realize the 3-D visualization.
The process of 3-D observation is detailedly studied and the transformation formulation of world coordination system and screen coordination system is listed. It's the foundation of 3-D interaction and actualization of 3-D measurement results. 3-D virtual sphere technique is used to realize the function of interactive rotation and picking method based on parallel perspective is used to realize the special characteristic points picking, so the design of 3-D interaction is completed.
3-D measurement mainly includes the distance measurement between two points, and the area and volume measurement of 3-D objects. The distance measurement can be divided into linear or curvilinear distance measurement and 3-D depth measurement.
A method of 3-D depth measurement following normal direction is proposed in this thesis. With the use of this method to get thickness information of facial parenchyma, the precision is increased compared with former methods. And a coordinates transformation method is proposed in calculation to simplify the 3-D calculations to 2-D calculations. This method reduces calculation complexity.
A new data storage structure is designed to resolve the difficulty in arrangement of unorderly intersection points and accelerate the measuring process during curvilinear distance between two points measuring. In calculation, cubic spline curve is used to instead contour line. This method can increase the precision of curvilinear distance measurement.
Finally, a digital skull-face 3-D computer aided measuring system is developed based on object-oriented software programming method. This system has completed the measurements of facial parenchyma thickness, facial distance characteristics and tumour's area and volume. It gets an upstanding effecting in facial reconstruction process, superposition identification between skulls and photos, and three-dimensional conformal radiotherapy technique.
引文
[1]陈道炯，覃开宇，刘昌艳．复杂曲面三维数模重建技术的应用与研究[J]．合肥工业大学(自然科学版)，1998，21(6)：52-56
[2]程祥荣，华先明，华中平等，计算机辅助全口义齿人工牙排列的研究[J]．中华口腔医学杂志，2000，35(2)：147-149
[3]Zhang Aiwu，Li Mingzhe，Hu Shaoxing et al．3D Measurement Technology Based on Computer Vision [J]．农业工程学报，2001，17(1)：32-37
[4]邓文怡，吕乃光，董明利等，数字摄影测量技术在三维测量中的应用[J]．光电子激光，2001，12(7)：697-700
[5]金国藩，李景镇．激光测量学[M]．科学出版社，1998
[6] H.Takasaki. Moiré topography [J]. Applied Optics, 1970, 9(6): 1467-1472
[7] Takeda Mitsuo, Mutoh Kazuhiro. Fourier transform profilometry for the automatic measurement of 3D object shapes [J]. Applied Optics, 1983,22(24): 3977-3992
[8] V. Srinvasan, H.C.Liu, M. Halioua. Automated phase-measuring profilometry of 3D diffuse objects [J]. Applied Optics, 1984,23(18): 3105-3108
[9]RE1000 Reverse Engineering System 产品说明，1995
[10]唐鹫华．X-CT技术进展[J]．中国医疗器械杂志，1995，19(5)：284-285，293
[11]倪培君，李旭东，彭建中．工业CT的技术特点及其应用实例[J]．电力安全技术，1996，31(5)：40-43
[12]周明全，耿国华，范江波．计算机辅助的颅骨面貌复原技术[J]．西北大学学报(自然科学版)，1997，27(5)：375-378
[13]兰玉文．颅像重合法研究与应用[M]．群众出版社，1999
[14]独晓，伯森，吴大可．三维放射治疗的进展[J]．中国医学物理学杂志，1999，16(1)：10-12
[15] Chen, M. A Study in Interactive 3D Rotation Using 2D Control Device [J]. Computer Graphics, 1988,22(4)
[16]石教英，蔡文立．科学计算可视化算法与系统[M]．科学出版社，1996
[17]胡哲雄，罗建平，陆尔奕．面部软组织的三维测量分析[J]．上海口腔医学，2001，10(2)：162-165
[18]陆堏，吴妙玲，阙绪光等．三维超声心动图测量二尖瓣狭窄口面积[J]．中华超声影像学杂志，1995，4(3)：97-99
[19]范先群，张涤生，龙公等．正常眼眶计算机三维测量方法的建立[J]．临床
眼科杂志，2000，8(1)：4-6
[20]姚森，易亚星，李忠科等．牙颌模型专用激光三维扫描分析系统的研制及应用[J]．口腔医学纵横杂志，2000，16(4)：285-287
[21]王茂春，蓝春生，孔广忠．成人脏器的CT图像计算机三维测量与分析[J]．中国体视学与图像分析，2000，5(4)：206-210
[22]Lorensen W E, Cline H E. Marching cubes: A high-resolution 3D surface construction algorithm[J]. Computer Graphics, 1987, 21(3):163-169
[23]李燕，周明全，耿国华．医学体数据三维可视化改进算法综述[J]．计算机应用与软件，2003，20(2)：75-77
[24] J.Weszka. A survey of Threshold Selection Techniques [J]. Computer Graphics and Image Processing, 1978,7:259-265
[25] L. S. Davis. A Survey of Edge Detection Techniques [J]. CGIP, 1975, 4:248-270
[26] J. Prewitt. Object Enhancement and Extraction [M]. Picture Processing and Psychopictorics, Acdamic Press, New York, 1970
[27] R. A. Kirsch. Computer Determination of the Constituent Structure of Biological Images [J]. Computers in Biomedical Research, 1971, 4:315-328
[28] D. Marr, E. Hildreth. Theory of Edge Detection [J]. Proc. R. Soc. London, Ser. B. 1980, 207:187-217
[29]Donald Hearn，M．Pauline Baker著．蔡士杰，吴春镕，孙正兴等译．计算机图形学[M]．电子工业出版社，1998
[30] Cline H E, Lorensen W E, Ludke S et al. Two algorithms for the three-dimensional reconstruction of tomograms [J]. Medical Physics, 1988, 15(3): 320-327
[31] S. Suzuki, K. Abe. Topological Structural Analysis of Digital Binary Images by Border Following [J]. CVGIP, 1985, 30:32-46
[32] Rosenfeld and E. Johnston. Angle Detection on Digital Curves [J]. IEEE Trans. Computers, 1973, 22:875-878
[33] J. Hershberger, J. Snoeyink. An O(n log n) implementation of the Douglas-Peucker algorithm for line simplification[C]. In Proc. 10th Annu. ACM Sympos. Comput. Geom. 1994, 383-384
[34]刘力强，周明全，耿国华．一种平行透视下的三维拾取方法[J]．西北大学学报(自然科学版)，2002，32(1)：39-42
[35]唐泽圣，周嘉玉，李新友．计算机图形学基础[M]．清华大学出版社，1995
[36]耿国华，周明全．三维医学可视化平台的研究[J]．微机发展，1999，45：
55-57
[37]林海，石教英．面向应用的可视化环境ASVE [J]．计算机辅助设计与图形学学报，2000，12(10)：796-800
[38]王文义，苏士美．可视化集成软件环境VISE的研究与实现[J]．计算机工程与应用，2000，36(2)：98-99
[39]谢志鹏，陈锻生．用OpenGL开发三维交互式虚拟场景[J]．计算机应用，2000，21(8)：38-40
[40]白云，金锋，林锐等．基于OpenGL的交互式三维图形软件开发工具[J]．计算机工程，2000，26(11)：158-160
[41]邓建中，葛仁杰，程正兴．计算方法[M]．西安交通大学出版社，1985
[42]Jackie Neider, Tom Davis, Mason Woo. OpenGL programming guide: the official guide to learning OpenGL, release 1[M]. Addison-Wesley,1993
[2]程祥荣，华先明，华中平等，计算机辅助全口义齿人工牙排列的研究[J]．中华口腔医学杂志，2000，35(2)：147-149
[3]Zhang Aiwu，Li Mingzhe，Hu Shaoxing et al．3D Measurement Technology Based on Computer Vision [J]．农业工程学报，2001，17(1)：32-37
[4]邓文怡，吕乃光，董明利等，数字摄影测量技术在三维测量中的应用[J]．光电子激光，2001，12(7)：697-700
[5]金国藩，李景镇．激光测量学[M]．科学出版社，1998
[6] H.Takasaki. Moiré topography [J]. Applied Optics, 1970, 9(6): 1467-1472
[7] Takeda Mitsuo, Mutoh Kazuhiro. Fourier transform profilometry for the automatic measurement of 3D object shapes [J]. Applied Optics, 1983,22(24): 3977-3992
[8] V. Srinvasan, H.C.Liu, M. Halioua. Automated phase-measuring profilometry of 3D diffuse objects [J]. Applied Optics, 1984,23(18): 3105-3108
[9]RE1000 Reverse Engineering System 产品说明，1995
[10]唐鹫华．X-CT技术进展[J]．中国医疗器械杂志，1995，19(5)：284-285，293
[11]倪培君，李旭东，彭建中．工业CT的技术特点及其应用实例[J]．电力安全技术，1996，31(5)：40-43
[12]周明全，耿国华，范江波．计算机辅助的颅骨面貌复原技术[J]．西北大学学报(自然科学版)，1997，27(5)：375-378
[13]兰玉文．颅像重合法研究与应用[M]．群众出版社，1999
[14]独晓，伯森，吴大可．三维放射治疗的进展[J]．中国医学物理学杂志，1999，16(1)：10-12
[15] Chen, M. A Study in Interactive 3D Rotation Using 2D Control Device [J]. Computer Graphics, 1988,22(4)
[16]石教英，蔡文立．科学计算可视化算法与系统[M]．科学出版社，1996
[17]胡哲雄，罗建平，陆尔奕．面部软组织的三维测量分析[J]．上海口腔医学，2001，10(2)：162-165
[18]陆堏，吴妙玲，阙绪光等．三维超声心动图测量二尖瓣狭窄口面积[J]．中华超声影像学杂志，1995，4(3)：97-99
[19]范先群，张涤生，龙公等．正常眼眶计算机三维测量方法的建立[J]．临床
眼科杂志，2000，8(1)：4-6
[20]姚森，易亚星，李忠科等．牙颌模型专用激光三维扫描分析系统的研制及应用[J]．口腔医学纵横杂志，2000，16(4)：285-287
[21]王茂春，蓝春生，孔广忠．成人脏器的CT图像计算机三维测量与分析[J]．中国体视学与图像分析，2000，5(4)：206-210
[22]Lorensen W E, Cline H E. Marching cubes: A high-resolution 3D surface construction algorithm[J]. Computer Graphics, 1987, 21(3):163-169
[23]李燕，周明全，耿国华．医学体数据三维可视化改进算法综述[J]．计算机应用与软件，2003，20(2)：75-77
[24] J.Weszka. A survey of Threshold Selection Techniques [J]. Computer Graphics and Image Processing, 1978,7:259-265
[25] L. S. Davis. A Survey of Edge Detection Techniques [J]. CGIP, 1975, 4:248-270
[26] J. Prewitt. Object Enhancement and Extraction [M]. Picture Processing and Psychopictorics, Acdamic Press, New York, 1970
[27] R. A. Kirsch. Computer Determination of the Constituent Structure of Biological Images [J]. Computers in Biomedical Research, 1971, 4:315-328
[28] D. Marr, E. Hildreth. Theory of Edge Detection [J]. Proc. R. Soc. London, Ser. B. 1980, 207:187-217
[29]Donald Hearn，M．Pauline Baker著．蔡士杰，吴春镕，孙正兴等译．计算机图形学[M]．电子工业出版社，1998
[30] Cline H E, Lorensen W E, Ludke S et al. Two algorithms for the three-dimensional reconstruction of tomograms [J]. Medical Physics, 1988, 15(3): 320-327
[31] S. Suzuki, K. Abe. Topological Structural Analysis of Digital Binary Images by Border Following [J]. CVGIP, 1985, 30:32-46
[32] Rosenfeld and E. Johnston. Angle Detection on Digital Curves [J]. IEEE Trans. Computers, 1973, 22:875-878
[33] J. Hershberger, J. Snoeyink. An O(n log n) implementation of the Douglas-Peucker algorithm for line simplification[C]. In Proc. 10th Annu. ACM Sympos. Comput. Geom. 1994, 383-384
[34]刘力强，周明全，耿国华．一种平行透视下的三维拾取方法[J]．西北大学学报(自然科学版)，2002，32(1)：39-42
[35]唐泽圣，周嘉玉，李新友．计算机图形学基础[M]．清华大学出版社，1995
[36]耿国华，周明全．三维医学可视化平台的研究[J]．微机发展，1999，45：
55-57
[37]林海，石教英．面向应用的可视化环境ASVE [J]．计算机辅助设计与图形学学报，2000，12(10)：796-800
[38]王文义，苏士美．可视化集成软件环境VISE的研究与实现[J]．计算机工程与应用，2000，36(2)：98-99
[39]谢志鹏，陈锻生．用OpenGL开发三维交互式虚拟场景[J]．计算机应用，2000，21(8)：38-40
[40]白云，金锋，林锐等．基于OpenGL的交互式三维图形软件开发工具[J]．计算机工程，2000，26(11)：158-160
[41]邓建中，葛仁杰，程正兴．计算方法[M]．西安交通大学出版社，1985
[42]Jackie Neider, Tom Davis, Mason Woo. OpenGL programming guide: the official guide to learning OpenGL, release 1[M]. Addison-Wesley,1993