Accurate Visual Metrology from Single and Multiple Uncalibrated Images

Introduction: Accurate Measurements from Images. Why use Vision? Why is Visual Metrology Hard? Applications and Examples. Summary.- Related Work: Introduction. Using Images for Measuring and Reconstruction.- Background Geometry and Notation: Introduction. Notation. Camera Models and Perspective Mappings. Radial Distortion Correction. Vanishing Points and Vanishing Lines. Uncertainty Analysis.- Metrology on Planes: Estimating the Homography. Uncertainty Analysis. Application - A Plane Measuring Device. Duality and Homologies. Single View Metrology: Introduction. Geometry. Algebraic Representation. Uncertainty Analysis. Three-Dimensional Metrology from a Single View. Applications. Missing Base Point.- Metrology from Planar Parallax: Introduction. Background. Geometry and Duality. Scene Reconstruction. Uncertainty Analysis.- Gallery of Examples: Introduction. Reconstruction from Photographs. Reconstruction from Paintings. Discussion.- Conclusion: Summary. Discussion. Future Work.- Metrology on Planes, Computing Homography Uncertainty.- Maximum Likelehood Estimation of End Points for Isotropic Uncertainties.- Single View Metrology, Variance of Distance Between Planes.- Single View Metrology, Variance of the Affine Parameter alpha.- Metrology form Planar Parallax, Derivations.- Metrology form Planar Parallax, Variance of Distances.- Index.

[1]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[2]  J. Canny.  Finding Edges and Lines in Images , 1983 .

[3]  H. Cramér.  Mathematical methods of statistics , 1947 .

[4]  Olivier D. Faugeras,et al.  From projective to Euclidean reconstruction , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]  Roberto Cipolla,et al.  The visual motion of curves and surfaces , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  G. F. McLean,et al.  Vanishing Point Detection by Line Clustering , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[8]  Yongduek Seo,et al.  Physics-based 3D position analysis of a soccer ball from monocular image sequences , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[9]  Andrew Zisserman,et al.  Self-Calibration from Image Triplets , 1996, ECCV.

[10]  Roberto Cipolla,et al.  Active Visual Inference of Surface Shape , 1995, Lecture Notes in Computer Science.

[11]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[12]  Reinhard Koch,et al.  Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[13]  Roger Y. Tsai,et al.  A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses , 1987, IEEE J. Robotics Autom..

[14]  J J Koenderink,et al.  Affine structure from motion. , 1991, Journal of the Optical Society of America. A, Optics and image science.

[15]  H. Maas.  Robust Automatic Surface Reconstruction with Structured Light , 1992 .

[16]  A. Shashua,et al.  Shape tensors for efficient and learnable indexing , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[17]  F. Figueroa,et al.  A Robust Method to Determine the Coordinates of a Wave Source for 3-D Position Sensing , 1994 .

[18]  Andrew Zisserman,et al.  Metric rectification for perspective images of planes , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[19]  Olivier D. Faugeras,et al.  What can two images tell us about a third one? , 1994, ECCV.

[20]  Roberto Cipolla,et al.  Camera Calibration from Vanishing Points in Image of Architectural Scenes , 1999, BMVC.

[21]  Richard I. Hartley.  Self-Calibration from Multiple Views with a Rotating Camera , 1994, ECCV.

[22]  Luc Van Gool,et al.  Reading between the lines-a method for extracting dynamic 3D with texture , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[23]  Stefan Carlsson,et al.  Duality of reconstruction and positioning from projective views , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[24]  Narendra Ahuja,et al.  Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  K. A. Stroud,et al.  Engineering Mathematics , 2020, Nature.

[26]  Ray A. Jarvis,et al.  A Perspective on Range Finding Techniques for Computer Vision , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Roberto Cipolla,et al.  Epipole Estimation Using Affine Motion Parallax , 1993, BMVC.

[28]  Rachid Deriche,et al.  A Robust Technique for Matching two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry , 1995, Artif. Intell..

[29]  P. Anandan,et al.  Parallax Geometry of Pairs of Points for 3D Scene Analysis , 1996, ECCV.

[30]  J. Clarke.  Modelling uncertainty: A primer , 1998 .

[31]  Michal Irani,et al.  Representation of scenes from collections of images , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[32]  Christopher G. Harris,et al.  A Combined Corner and Edge Detector , 1988, Alvey Vision Conference.

[33]  Ian D. Reid,et al.  Duality, Rigidity and Planar Parallax , 1998, ECCV.

[34]  Allen R. Hanson,et al.  Robust methods for estimating pose and a sensitivity analysis , 1994 .

[35]  Antonio Criminisi,et al.  Shape from Texture: Homogeneity Revisited , 2000, BMVC.

[36]  Amnon Shashua,et al.  Trilinearity in Visual Recognition by Alignment , 1994, ECCV.

[37]  Ken-ichi Anjyo,et al.  Tour into the picture: using a spidery mesh interface to make animation from a single image , 1997, SIGGRAPH.

[38]  Robert T. Collins,et al.  Vanishing point calculation as a statistical inference on the unit sphere , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[39]  Ian D. Reid,et al.  A plane measuring device , 1999, Image Vis. Comput..

[40]  J. Gibson.  The perception of the visual world , 1951 .

[41]  Andrew Zisserman,et al.  Automated mosaicing with super-resolution zoom , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[42]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[43]  A. H.,et al.  The Science of Art , 1897, Nature.

[44]  Roger Mohr,et al.  Projective Geometry and Computer Vision , 1993, Handbook of Pattern Recognition and Computer Vision.

[45]  Olivier D. Faugeras,et al.  Motion of an uncalibrated stereo rig: self-calibration and metric reconstruction , 1996, IEEE Trans. Robotics Autom..

[46]  Amnon Shashua,et al.  Novel view synthesis in tensor space , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[47]  R. Y. Tsai,et al.  An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision , 1986, CVPR 1986.

[48]  Roberto Cipolla,et al.  Robust structure from motion using motion parallax , 1993, 1993 (4th) International Conference on Computer Vision.

[49]  Amnon Shashua,et al.  On Geomatric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views , 1993, Applications of Invariance in Computer Vision.

[50]  Harry Shum,et al.  What can be determined from a full and a weak perspective image? , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[51]  Paul A. Beardsley,et al.  3D Model Acquisition from Extended Image Sequences , 1996, ECCV.

[52]  Richard I. Hartley,et al.  Estimation of Relative Camera Positions for Uncalibrated Cameras , 1992, ECCV.

[53]  Amnon Shashua.  Multiple-View Geometry and Photometry , 1995, ACCV.

[54]  Michael Werman,et al.  Duality of Multi-Point and Multi-Frame Geometry: Fundamental Shape Matrices and Tensors , 1996, ECCV.

[55]  William H. Press,et al.  Numerical recipes in C , 2002 .

[56]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[57]  Frank P. Ferrie,et al.  Active recognition: using uncertainty to reduce ambiguity , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[58]  Richard Szeliski,et al.  Vision Algorithms: Theory and Practice , 2002, Lecture Notes in Computer Science.

[59]  Jitendra Malik,et al.  Modeling and Rendering Architecture from Photographs: A hybrid geometry- and image-based approach , 1996, SIGGRAPH.

[60]  S. Zietz,et al.  Bioengineering approach to non-invasive measurement of body composition. , 1994, Biomedical sciences instrumentation.

[61]  Olivier D. Faugeras,et al.  Characterizing the Uncertainty of the Fundamental Matrix , 1997, Comput. Vis. Image Underst..

[62]  Marc Levoy.  The Digital Michelangelo Project , 1999, Comput. Graph. Forum.

[63]  Jefferey A. Shufelt,et al.  Performance Evaluation and Analysis of Vanishing Point Detection Techniques , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[64]  O. Faugeras,et al.  3-D Reconstruction of Urban Scenes from Sequences of Images , 1995 .

[65]  Olivier D. Faugeras,et al.  Relative 3D positioning and 3D convex hull computation from a weakly calibrated stereo pair , 1993, 1993 (4th) International Conference on Computer Vision.

[66]  Roger Mohr,et al.  Accurate Projective Reconstruction , 1993, Applications of Invariance in Computer Vision.

[67]  O. Faugeras.  Stratification of three-dimensional vision: projective, affine, and metric representations , 1995 .

[68]  Antonio Criminisi,et al.  Creating Architectural Models from Images , 1999, Comput. Graph. Forum.

[69]  Roberto Cipolla,et al.  Robust Egomotion Estimation from Affine Motion Parallax , 1994, ECCV.

[70]  Gene H. Golub,et al.  Matrix computations , 1983 .

[71]  Ian D. Reid,et al.  Goal-directed Video Metrology , 1996, ECCV.

[72]  Olivier D. Faugeras,et al.  What can be seen in three dimensions with an uncalibrated stereo rig , 1992, ECCV.

[73]  O. D. Faugeras,et al.  Camera Self-Calibration: Theory and Experiments , 1992, ECCV.

[74]  M. Brady,et al.  Rejecting outliers and estimating errors in an orthogonal-regression framework , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[75]  Andrew Zisserman,et al.  Robust parameterization and computation of the trifocal tensor , 1997, Image Vis. Comput..

[76]  Ian D. Reid,et al.  3D Trajectories from a Single Viewpoint using Shadows , 1998, BMVC.

[77]  Daphna Weinshall,et al.  From Ordinal to Euclidean Reconstruction with Partial Scene Calibration , 1998, SMILE.

[78]  David A. Forsyth,et al.  Extracting projective structure from single perspective views of 3D point sets , 1993, 1993 (4th) International Conference on Computer Vision.

[79]  Andrew P. Witkin,et al.  Analyzing Oriented Patterns , 1985, IJCAI.

[80]  Richard I. Hartley,et al.  A linear method for reconstruction from lines and points , 1995, Proceedings of IEEE International Conference on Computer Vision.

[81]  S Pollard,et al.  Identifying correspondences in binocular stereo. , 1985 .

[82]  Harpreet S. Sawhney.  Simplifying motion and structure analysis using planar parallax and image warping , 1994, Proceedings of 12th International Conference on Pattern Recognition.

[83]  Luc Van Gool,et al.  Planar homologies as a basis for grouping and recognition , 1998, Image Vis. Comput..

[84]  J. Rice.  Mathematical Statistics and Data Analysis , 1988 .

[85]  I. Reid,et al.  Metric calibration of a stereo rig , 1995, Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95).

[86]  Kenichi Kanatani,et al.  Statistical optimization for geometric computation - theory and practice , 1996, Machine intelligence and pattern recognition.

[87]  Harry Edwin Burton,et al.  The Optics of Euclid1 , 1945 .

[88]  Olivier Faugeras,et al.  Automatic calibration and removal of distortion from scenes of structured environments , 1995, Optics & Photonics.

[89]  C. E. Springer,et al.  Geometry and Analysis of Projective Spaces , 1967 .

[90]  Du Q. Huynh,et al.  Affine reconstruction from monocular vision in the presence of a symmetry plane , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[91]  Antonio Criminisi,et al.  New approach to obtain height measurements from video , 1999, Other Conferences.

[92]  Shree K. Nayar,et al.  Vision in bad weather , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[93]  della Francesca Piero,et al.  De prospectiva pingendi , 1984 .