Stratified Self-Calibration with the Modulus Constraint

In computer vision and especially for 3D reconstruction, one of the key issues is the retrieval of the calibration parameters of the camera. These are needed to obtain metric information about the scene from the camera. Often these parameters are obtained through cumbersome calibration procedures. There is a way to avoid explicit calibration of the camera. Self-calibration is based on finding the set of calibration parameters which satisfy some constraints (e.g., constant calibration parameters). Several techniques have been proposed but it often proved difficult to reach a metric calibration at once. Therefore, in the paper, a stratified approach is proposed, which goes from projective through affine to metric. The key concept to achieve this is the modulus constraint. It allows retrieval of the affine calibration for constant intrinsic parameters. It is also suited for use in conjunction with scene knowledge. In addition, if the affine calibration is known, it can also be used to cope with a changing focal length.

[1]  Olivier D. Faugeras,et al.  Oriented Projective Geometry for Computer Vision , 1996, ECCV.

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

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

[4]  Peter F. Sturm.  Vision 3D non calibrée : contributions à la reconstruction projective et étude des mouvements critiques pour l'auto-calibrage. (Uncalibrated 3D Vision: Contributions to Projective Reconstruction and Study of the Critical Motions for Self-Calibration) , 1997 .

[5]  Long Quan,et al.  Affine stereo calibration , 1995, CAIP.

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

[7]  L. Gool,et al.  Affine reconstruction from perspective image pairs , 1993 .

[8]  A. Heyden,et al.  Euclidean reconstruction from constant intrinsic parameters , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[9]  Bill Triggs,et al.  Autocalibration and the absolute quadric , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[10]  Luc Van Gool,et al.  Euclidean 3D Reconstruction from Image Sequences with Variable Focal Lenghts , 1996, ECCV.

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

[12]  Thierry Viéville,et al.  Canonic Representations for the Geometries of Multiple Projective Views , 1994, ECCV.

[13]  Peter F. Sturm,et al.  A Factorization Based Algorithm for Multi-Image Projective Structure and Motion , 1996, ECCV.

[14]  Peter F. Sturm,et al.  Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  Luc Van Gool,et al.  A stratified approach to metric self-calibration , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[16]  O. Faugeras,et al.  Camera Self-Calibration from Video Sequences: the Kruppa Equations Revisited , 1996 .

[17]  Paul A. Beardsley,et al.  Euclidean Structure from Uncalibrated Images , 1994, BMVC.

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

[19]  Luc Van Gool,et al.  Euclidean 3D Reconstruction from Stereo Sequences with Variable Focal Lengths , 1995, ACCV.

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

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

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

[23]  Radu Horaud,et al.  Self-calibration and Euclidean reconstruction using motions of a stereo rig , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[24]  Reinhard Koch,et al.  3-D surface reconstruction from stereoscopic image sequences , 1995, Proceedings of IEEE International Conference on Computer Vision.

[25]  Richard I. Hartley,et al.  In Defense of the Eight-Point Algorithm , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[26]  Anders Heyden,et al.  Euclidean reconstruction from image sequences with varying and unknown focal length and principal point , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[27]  Richard I. Hartley,et al.  Euclidean Reconstruction from Uncalibrated Views , 1993, Applications of Invariance in Computer Vision.

[28]  Luc Van Gool,et al.  The modulus constraint: a new constraint self-calibration , 1996, Proceedings of 13th International Conference on Pattern Recognition.

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

[30]  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).

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

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

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

[34]  L. Falkenhagen.  Depth Estimation from Stereoscopic Image Pairs Assuming Piecewise Continuos Surfaces , 1995 .

[35]  Long Quan,et al.  Relative 3D Reconstruction Using Multiple Uncalibrated Images , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[36]  Luc Van Gool,et al.  Self-Calibration from the Absolute Conic on the Plane at Infinity , 1997, CAIP.

[37]  Luc Van Gool,et al.  The Cascaded Hough Transform as Support for Grouping and Finding Vanishing Points and Lines , 1997, AFPAC.

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

[39]  Richard Szeliski,et al.  Recovering 3D shape and motion from image streams using nonlinear least squares , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[40]  A. Morgan.  Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems , 1987 .

[41]  Luc Van Gool,et al.  Affine Reconstruction from Perspective Image Pairs Obtained by a Translating Camera , 1993, Applications of Invariance in Computer Vision.

[42]  Luc Van Gool,et al.  Determination of Optical Flow and its Discontinuities using Non-Linear Diffusion , 1994, ECCV.