计算机辅助文物复原中的若干问题 研究

1. 计算机辅助文物复原中的若干问题研究 潘荣江 panrj@sdu.edu.cn 山东大学计算机科学与技术学院 2005 年 11 月

2. 基础知识 1 图形学的研究内容 2 3D data types 3 2½-D Data 4 Reconstruction 5 Range Acquisition Methods

4. Main Themes • Imaging • Representing 2D images • Modeling • Representing 3D objects • Rendering • Constructing 2D images from 3D models • Animation • Simulating changes over time

5. Modeling--Design • Graphics for Engineering and Architectural System AutoCAD 2002 Interior Design

6. Modeling--Reconstruction

7. 3D Data Types • Point Data • “Point clouds” • Advantage: simplest data type • Disadvantage: no information on adjacency / connectivity • Volumetric Data • Regularly-spaced grid in (x,y,z): “voxels” • For each grid cell, store • Occupancy (binary: occupied / empty) • Density • Other properties • Popular in medical imaging • CAT scans • MRI

8. 3D Data Types • Advantages: • Can “see inside” an object • Uniform sampling: simpler algorithms • Disadvantages: • Lots of data • Wastes space if only storing a surface • Most “vision” sensors / algorithms returnpoint or surface data

9. 3D Data Types • Surface Data • Polyhedral • Piecewise planar • Polygons connected together • Most popular: “triangle meshes” • Smooth • Higher-order (quadratic, cubic, etc.) curves • Bézier patches, splines, NURBS, subdivision surfaces, etc.

10. 3D Data Types • Advantages: • Usually corresponds to what we see • Usually returned by vision sensors / algorithms • Disadvantages: • How to find “surface” for translucent objects? • Parameterization often non-uniform • Non-topology-preserving algorithms difficult • Implicit surfaces (cf. parametric) • Zero set of a 3D function • Usually regularly sampled (voxel grid) • Advantage: easy to write algorithms that change topology • Disadvantage: wasted space, time

11. 2½-D Data • Image • stores an intensity / color alongeach of a set of regularly-spaced rays in space • Range image • stores a depth along each of a set of regularly-spaced rays in space • Not a complete 3D description • does not store objects occluded (from some viewpoint) • View-dependent scene description

12. 2½-D Data • This is what most sensors / algorithmsreally return • Advantages • Uniform parameterization • Adjacency / connectivity information • Disadvantages • Does not represent entire object • View dependent

13. 2½-D Data • Range images • Range surfaces • Depth images • Depth maps • Height fields • 2½-D images • Surface profiles • xyz maps • …

14. Related Fields • Computer Vision • Passive range sensing • Rarely construct complete, accurate models • Application: recognition • Metrology • Main goal: absolute accuracy • High precision, provable errors more important than scanning speed, complete coverage • Applications: industrial inspection, quality control, modeling

15. Related Fields • Computer Graphics • Often want complete model • Low noise, geometrically consistent model more important than absolute accuracy • Application: animated CG characters

16. Terminology • Range acquisition, shape acquisition, rangefinding, range scanning, 3D scanning • Alignment, registration • Surface reconstruction, 3D scan merging, scan integration, surface extraction • 3D model acquisition

17. Range Acquisition Taxonomy Mechanical (CMM, jointed arm) Inertial (gyroscope, accelerometer) Contact Ultrasonic trackers Magnetic trackers Industrial CT Rangeacquisition Transmissive Ultrasound MRI Radar Non-optical Sonar Reflective Optical

18. Range Acquisition Taxonomy Shape from X: stereo motion shading texture focus defocus Passive Opticalmethods Active variants of passive methods Stereo w. projected texture Active depth from defocus Photometric stereo Active Time of flight Triangulation

19. Touch Probes • Jointed arms with angular encoders • Return position, orientation of tip Faro Arm – Faro Technologies, Inc.

20. Optical Range Acquisition Methods • Advantages: • Non-contact • Safe • Usually inexpensive • Usually fast • Disadvantages: • Sensitive to transparency • Confused by specularity and interreflection • Texture (helps some methods, hurts others)

21. Stereo • Find feature in one image, search along epipolar line in other image for correspondence

22. Stereo • Advantages: • Passive • Cheap hardware (2 cameras) • Easy to accommodate motion • Intuitive analogue to human vision • Disadvantages: • Only acquire good data at “features” • Sparse, relatively noisy data (correspondence is hard) • Bad around silhouettes • Confused by non-diffuse surfaces • Variant: multibaseline stereo to reduce ambiguity

23. Active Optical Methods • Advantages: • Usually can get dense data • Usually much more robust and accurate than passive techniques • Disadvantages: • Introduces light into scene (distracting, etc.) • Not motivated by human vision

24. Pulsed Time of Flight • Basic idea: send out pulse of light (usually laser), time how long it takes to return

25. Pulsed Time of Flight • Advantages: • Large working volume (up to 100 m.) • Disadvantages: • Not-so-great accuracy (at best ~5 mm.) • Requires getting timing to ~30 picoseconds • Does not scale with working volume • Often used for scanning buildings, rooms, archeological sites, etc.

26. AM Modulation Time of Flight • Modulate a laser at frequencym ,it returns with a phase shift  • Note the ambiguity in the measured phase! Range ambiguity of 1/2mn

27. AM Modulation Time of Flight • Accuracy / working volume tradeoff(e.g., noise ~ 1/500 working volume) • In practice, often used for room-sized environments (cheaper, more accurate than pulsed time of flight)

28. Triangulation • Most scanners mount camera and light source rigidly, move them as a unit • Moving the Camera and Illumination

29. Laser Camera Triangulation: Extending to 3D • Possibility #1: add another mirror (flying spot) • Possibility #2: project a stripe, not a dot Object

30. Triangulation Scanner Issues • Accuracy proportional to working volume • Scales down to small working volume(e.g. 5 cm. working volume, 50 m. accuracy) • Two-line-of-sight problem (shadowing from either camera or laser) • Triangulation angle: non-uniform resolution if too small, shadowing if too big (useful range: 15-30)

31. Triangulation Scanner Issues • Material properties (dark, specular) • Subsurface scattering • Laser speckle • Edge curl • Texture embossing

32. Multi-Stripe Triangulation • To go faster, project multiple stripes • But which stripe is which? • Answer #1: assume surface continuity • Answer #2: colored stripes (or dots)

33. Multi-Stripe Triangulation • Answer #3: time-coded stripes

34. Time-Coded Light Patterns • Assign each stripe a unique illumination codeover time [Posdamer 82] Time Space

35. InSpeck 3D-DF

36. 内容 1 绪论 2 平面碎片的拼接 3 曲面碎片边界线的提取 4 旋转型曲面碎片旋转轴和母曲线的估计 5 旋转型曲面碎片的拼接 6 总结与展望

37. 文物 • 文物是人类在历史发展过程中遗留下来的具有历史、艺术、科学价值的遗物和遗迹。 • 珍贵的文物经受了不同程度的破坏和损害。 • 每一次考古发现都会带来大量残缺、破碎的文物。

38. 文物修复 • 文物修复是指从残缺、破碎的文物碎片中清理、修复出完整的文物，还原其本来面目。 • 修复后的文物可以用于考古研究、博物馆展览、商业文化交流等活动中 • 文物修复一般经过清理、拼接、粘合、补缺、全色几道工序。

39. 文物修复的困难 • 文物修复技术性强。 • 修复任务十分繁重，全国现有2000多万件破损文物。 • 操作不当会造成珍贵文物的进一步磨损和破坏。 • 大型文物的搬运、拼接、粘合都比较困难。

40. 考古现场的文物碎片

41. 计算机辅助文物复原 • 加快文物复原的速度 • 避免修复过程对文物的损害 • 降低文物修复的难度 • 把复原文物的数字模型直接应用于数字博物馆的文物展示和检索中，实现资源共享。 • 在古生物学、事故分析、医学手术、刑事侦查、娱乐游戏、地理分析、自动装配、计算机辅助设计、化学等领域也有应用背景。

42. 辅助修复的内容 • 拼接、补缺和全色可以利用计算机辅助进行。 • 数据获取 • 二维图像: 图像配准 • 三维数据: 多视数据配准 • 缺片填补 • Image inpainting技术 • 基于样本的纹理合成 • 几何数据的空洞填充 • 碎片拼接 • 预处理、提取特征 • 局部拼接 • 整体重建

43. 国内外研究现状 • 美国stanford大学的Forma Urbis Romae项目 • 美国Brown大学的SHAPE项目 • 英国Brunel大学与欧洲十几所大学 3D Murale • Siggraph2005上Mark Pauly 的反问题 • 浙江大学潘云鹤院士敦煌壁画保护与修复 • 西北大学周明全教授兵马俑复原

44. 平面碎片拼接的研究现状 • 自动拼版游戏(jigsaw puzzle) • 拼版大小均匀，形状规则 • 边界拼版 • 完全匹配 • Andrew Glassner彩色照片碎片 • 利用了颜色信息 • 曲线匹配 • 计算碎片间连续匹配的子曲线 • 碎片之间是完全匹配吗？

45. 曲面碎片拼接的研究现状 • 多视数据配准（multiview registration） • 依据视图的重叠部分 • 空间曲线曲面匹配 • 曲线的曲率和挠率 • 曲面的特殊性质 • 如何提取碎片的边界线？ • 如何计算边界线的曲率？

46. 边界检测的研究现状 • 没有被三角形链包围的点 • 基于采样点的Voronoi图 • 递归最小二乘法 • Pearson卡方检验和遗传算法 • 最小生成树法 • 精确、整体最优的边界？

47. 旋转型曲面碎片 • 旋转型曲面碎片 • 出土最多，使用最广泛 • 最容易破碎 • 可靠的记时器 • 形制和装饰的变化反映了文化的分布和传播 • 考古学家认为陶器是历史的脊柱

48. 旋转型曲面碎片的研究现状 • 三维Hough变换估计旋转轴 • M-estimator方法估计旋转轴 • 向量枚举法估计旋转轴 • 分两步求解两个自由参数的最小化问题，实现拼接 • 陶器表面的小装饰物？ • 重叠检测？ • 最优拼接？

49. 本文的工作基础 • 山东大学考古数字博物馆 • 1万余件文物藏品的数字化 • 100多件文物精品三维数据 • 文物信息管理系统 • 网站内容采编系统 • 虚拟展馆及交互漫游系统 • 基于Web的多媒体展示系统 • 计算机辅助文物建模系统

50. 计算机辅助文物建模系统