Flat refractive geometry

While the study of geometry has mainly concentrated on single-viewpoint (SVP) cameras, there is growing attention to more general non-SVP systems. Here we study an important class of systems that inherently have a non-SVP: a perspective camera imaging through an interface into a medium. Such systems are ubiquitous: they are common when looking into water-based environments. The paper analyzes the common flat-interface class of systems. It characterizes the locus of the viewpoints (caustic) of this class, and proves that the SVP model is invalid in it. This may explain geometrical errors encountered in prior studies. Our physics-based model is parameterized by the distance of the lens from the medium interface, beside the focal length. The physical parameters are calibrated by a simple approach that can be based on a single-frame. This directly determines the system geometry. The calibration is then used to compensate for modeled system distortion. Based on this model, geometrical measurements of objects are significantly more accurate, than if based on an SVP model. This is demonstrated in real-world experiments.

[1]  D.R. Edgington,et al.  Detecting, Tracking and Classifying Animals in Underwater Video , 2005, OCEANS 2006.

[2]  David Ryan Koes,et al.  Precise omnidirectional camera calibration , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[3]  P. Sturm,et al.  On Calibration, Structure from Motion and Multi-View Geometry for Generic Camera Models , 2006 .

[4]  Y.Y. Schechner,et al.  Recovery of underwater visibility and structure by polarization analysis , 2005, IEEE Journal of Oceanic Engineering.

[5]  Yoav Y. Schechner,et al.  Active Polarization Descattering , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Rongxin Li,et al.  Quantitative photogrammetric analysis of digital underwater video imagery , 1997 .

[7]  Young-Hoo Kwon,et al.  Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis , 2006, Sports biomechanics.

[8]  Janne Heikkilä,et al.  A four-step camera calibration procedure with implicit image correction , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9]  Stefan Schuster,et al.  Archer Fish Learn to Compensate for Complex Optical Distortions to Determine the Absolute Size of Their Aerial Prey , 2004, Current Biology.

[10]  Jean-Thierry Lapresté,et al.  Underwater Camera Calibration , 2000, ECCV.

[11]  Yael Pritch,et al.  Omnistereo: Panoramic Stereo Imaging , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Kiriakos N. Kutulakos,et al.  Dynamic Refraction Stereo , 2005, ICCV.

[13]  Marie-José Aldon,et al.  Camera Self-Calibration in Underwater Environment , 2003, WSCG.

[14]  Peter F. Sturm,et al.  Towards complete generic camera calibration , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[15]  Gábor Horváth,et al.  Underwater binocular imaging of aerial objects versus the position of eyes relative to the flat water surface. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  Nathalie Pessel,et al.  An experimental study of a robust self-calibration method for a single camera , 2003, 3rd International Symposium on Image and Signal Processing and Analysis, 2003. ISPA 2003. Proceedings of the.

[17]  K. Wolff,et al.  EXPLOITING THE MULTI VIEW GEOMETRY FOR AUTOMATIC SURFACES RECONSTRUCTION USING FEATURE BASED MATCHING IN MULTI MEDIA PHOTOGRAMMETRY , 2000 .

[18]  Marc Levoy,et al.  Synthetic aperture confocal imaging , 2004, SIGGRAPH 2004.

[19]  Mohit Gupta,et al.  On controlling light transport in poor visibility environments , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[20]  M. Levoy,et al.  Light field microscopy , 2006, SIGGRAPH 2006.

[21]  C. S. Fraser,et al.  ON THE CALIBRATION OF UNDERWATER CAMERAS , 2006 .

[22]  Zhengyou Zhang,et al.  A Flexible New Technique for Camera Calibration , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Victor Alchanatis,et al.  Real-time underwater sorting of edible fish species , 2007 .

[24]  Songde Ma,et al.  Implicit and Explicit Camera Calibration: Theory and Experiments , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  A. Ivanoff,et al.  Correcting Lenses for Underwater Use , 1960 .

[26]  Andrew Hogue,et al.  Sensorslam: an investigation into sensor parameter estimation for slam , 2009 .

[27]  Tomás Pajdla,et al.  Structure from motion with wide circular field of view cameras , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  Narendra Ahuja,et al.  A Pupil-Centric Model of Image Formation , 2002, International Journal of Computer Vision.

[29]  Shree K. Nayar,et al.  Non-Single Viewpoint Catadioptric Cameras: Geometry and Analysis , 2006, International Journal of Computer Vision.

[30]  Shree K. Nayar,et al.  A Theory of Single-Viewpoint Catadioptric Image Formation , 1999, International Journal of Computer Vision.

[31]  Hanumant Singh,et al.  Relative Pose Estimation for Instrumented, Calibrated Imaging Platforms , 2003, DICTA.

[32]  D. Burkhard,et al.  Flux density for ray propagation in geometrical optics , 1973 .

[33]  Shahriar Negahdaripour,et al.  Stereo from flickering caustics , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[34]  Georg Glaeser,et al.  Re∞ections on Refractions , 2000 .

[35]  Shree K. Nayar,et al.  The Raxel Imaging Model and Ray-Based Calibration , 2005, International Journal of Computer Vision.

[36]  Theodore S. Melis,et al.  Underwater Microscope for Measuring Spatial and Temporal Changes in Bed-Sediment Grain Size , 2007 .

[37]  H. Singh,et al.  Hemispherical refraction and camera calibration in underwater vision , 2008, OCEANS 2008.

[38]  Hans-Gerd Maas,et al.  New developments in Multimedia Photogrammetry , 2001 .

[39]  Shahriar Negahdaripour,et al.  Opti-Acoustic Stereo Imaging, System Calibration and 3-D Reconstruction , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[40]  S. Negahdaripour,et al.  Integrated System for Robust 6-DOF Positioning Utilizing New Closed-Form Visual Motion Estimation Methods in Planar Terrains , 2006, IEEE Journal of Oceanic Engineering.

[41]  Mario Fernando Montenegro Campos,et al.  Underwater stereo , 2004, Proceedings. 17th Brazilian Symposium on Computer Graphics and Image Processing.

[42]  Yoav Y. Schechner,et al.  Instant 3Descatter , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[43]  José Santos-Victor,et al.  Underwater Video Mosaics as Visual Navigation Maps , 2000, Comput. Vis. Image Underst..

[44]  Visesh Chari,et al.  Multi-View Geometry of the Refractive Plane , 2009, BMVC.