Perspective and Non-perspective Camera Models in Underwater Imaging – Overview and Error Analysis

  • Anne Sedlazeck
  • Reinhard Koch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7474)


When capturing images underwater, image formation is affected in two major ways. First, the light rays traveling underwater are absorbed and scattered depending on their wavelength, creating effects on the image colors. Secondly, the glass interface between air and water refracts the ray entering the camera housing because of a different index of refraction of water, hence the ray is also affected in a geometrical way.

This paper examines different camera models and their capabilities to deal with geometrical effects caused by refraction. Using imprecise camera models leads to systematic errors when computing 3D reconstructions or otherwise exploiting geometrical properties of images. In the literature, many authors have published work on underwater imaging by using the perspective pinhole camera model (single viewpoint model - SVP) with a different effective focal length and distortion to compensate for the error induced by refraction at the camera housing. On the other hand, methods were proposed, where refraction is modeled explicitly or where generic, non-single-view-point camera models are used. In addition to discussing all three model categories, an accuracy analysis of using the perspective model on underwater images is given and shows that the perspective model leads to systematic errors that compromise measurement accuracy.


Autonomous Underwater Vehicle Camera Model Perspective Model Radial Distortion Reprojection Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aggarwal, M., Ahuja, N.: A pupil-centric model of image formation. International Journal of Computer Vision 48(3), 195–214 (2002)zbMATHCrossRefGoogle Scholar
  2. 2.
    Bouguet, J.Y.: Visual methods for three-dimensional modelling. Ph.D. thesis, California Institute of Technology Pasadena, CA, USA (1999),
  3. 3.
    Brandou, V., Allais, A., Perrier, M., Malis, E., Rives, P., Sarrazin, J., Sarradin, P.: 3d reconstruction of natural underwater scenes using the stereovision system iris. In: Proc. OCEANS 2007- Europe, pp. 1–6 (2007)Google Scholar
  4. 4.
    Bryant, M., Wettergreen, D., Abdallah, S., Zelinsky, A.: Robust camera calibration for an autonomous underwater vehicle. In: Australian Conference on Robotics and Automation (ACRA 2000) (August 2000)Google Scholar
  5. 5.
    Carreras, M., Ridao, P., Garcia, R., Nicosevici, T.: Vision-based localization of an underwater robot in a structured environment. In: Proceedings of the International Conference on Robotics and Automation, ICRA 2003, vol. 1, pp. 971–976 (Sepember 2003)Google Scholar
  6. 6.
    Chang, Y.J., Chen, T.: Multi-view 3d reconstruction for scenes under the refractive plane with known vertical direction. In: IEEE International Conference on Computer Vision, ICCV (2011)Google Scholar
  7. 7.
    Chari, V., Sturm, P.: Multiple-view geometry of the refractive plane. In: Proceedings of the 20th British Machine Vision Conference, London, UK (September 2009),
  8. 8.
    Costa, C., Loy, A., Cataudella, S., Davis, D., Scardi, M.: Extracting fish size using dual underwater cameras. Aquacultural Engineering 35(3), 218–227 (2006), CrossRefGoogle Scholar
  9. 9.
    Eustice, R., Singh, H., Howland, J.: Image registration underwater for fluid flow measurements and mosaicking. In: OCEANS 2000 MTS/IEEE Conference and Exhibition, vol. 3, pp. 1529–1534 (2000)Google Scholar
  10. 10.
    Ferreira, R., Costeira, J.P., Santos, J.A.: Stereo Reconstruction of a Submerged Scene. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3522, pp. 102–109. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Foerstner, W., Wolff, K.: Exploiting the multi view geometry for automatic surfaces reconstruction using feature based matching in multi media photogrammetry. In: Proceedings of the 19th ISPRS Congress, pp. 5B 900–907 (2000)Google Scholar
  12. 12.
    Fryer, J.G., Fraser, C.S.: On the calibration of underwater cameras. The Photogrammetric Record 12 (1986)Google Scholar
  13. 13.
    Garcia, R., Batlle, J., Cufi, X., Amat, J.: Positioning an underwater vehicle through image mosaicking. In: Proceedings of the International Conference on Robotics and Automation, ICRA 2001, vol. 3, pp. 2779–2784 (2001)Google Scholar
  14. 14.
    Glaeser, G., Schröcker, H.P.: Reflections on refractions. Journal for Geometry and Graphics (JGG) 4, 1–18 (2000)zbMATHGoogle Scholar
  15. 15.
    Gracias, N., Santos Victor, J.: Underwater video mosaics as visual navigation maps. Journal of Computer Vision and Image Understanding (CVIU) 79(1), 66–91 (2000)CrossRefGoogle Scholar
  16. 16.
    Gracias, N., van der Zwaan, S., Bernardino, A., Santos-Victor, J.: Mosaic-based navigation for autonomous underwater vehicles. IEEE Journal of Oceanic Engineering 28(4), 609–624 (2003)CrossRefGoogle Scholar
  17. 17.
    Grossberg, M.D., Nayar, S.K.: The raxel imaging model and ray-based calibration. International Journal of Computer Vision 61(2), 119–137 (2005)CrossRefGoogle Scholar
  18. 18.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004),
  19. 19.
    Harvey, E.S., Shortis, M.R.: Calibration stability of an underwater stereo-video system: Implications for measurement accuracy and precision. Marine Technology Society Journal 32, 3–17 (1998)Google Scholar
  20. 20.
    Hecht, E.: Optik. Oldenburg Verlag,Muenchen Wien (2005)Google Scholar
  21. 21.
    Heikkila, J., Silven, O.: A four-step camera calibration procedure with implicit image correction. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, p. 1106 (1997)Google Scholar
  22. 22.
    Hogue, A., German, A., Jenkin, M.: Underwater environment reconstruction using stereo and inertial data. In: IEEE International Conference on Systems, Man and Cybernetics, ISIC 2007, October 7-10, pp. 2372–2377 (2007)Google Scholar
  23. 23.
    Hogue, A., German, A., Zacher, J., Jenkin, M.: Underwater 3d mapping: Experiences and lessons learned. In: The 3rd Canadian Conference on Computer and Robot Vision, June 7- 9, p. 24 (2006)Google Scholar
  24. 24.
    Jasiobedzki, P., Se, S., Bondy, M., Jakola, R.: Underwater 3d mapping and pose estimation for rov operations. In: OCEANS 2008, September 15-18, pp. 1–6 (2008)Google Scholar
  25. 25.
    Johnson-Roberson, M., Pizarro, O., Williams, S., Mahon, I.: Generation and visualization of large-scale three-dimensional reconstructions from underwater robotic surveys. Journal of Field Robotics 27 (2010)Google Scholar
  26. 26.
    Kawai, R., Yamashita, A., Kaneko, T.: Three-dimensional measurement of objects in water by using space encoding method. In: IEEE International Conference on Robotics and Automation, ICRA 2009, May 12-17, pp. 2830–2835 (2009)Google Scholar
  27. 27.
    Kunz, C., Singh, H.: Hemispherical refraction and camera calibration in underwater vision. In: OCEANS 2008, September 15-18, pp. 1–7 (2008)Google Scholar
  28. 28.
    Kwon, Y.: A camera calibration algorithm for the underwater motion analysis. In:17th International Symposium on Biomechanics in Sports, ISBS - Conference Proceedings Archive (1999)Google Scholar
  29. 29.
    Kwon, Y., Casebolt, J.: Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis. Sports Biomech. 5(1), 95–120 (2006)CrossRefGoogle Scholar
  30. 30.
    Lavest, J.-M., Rives, G., Lapresté, J.T.: Underwater Camera Calibration. In: Vernon, D. (ed.) ECCV 2000, Part II. LNCS, vol. 1843, pp. 654–668. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  31. 31.
    Li, R., Tao, C., Zou, W.: An underwater digital photogrammetric system for fishery geomatics. In: Intl. Archives of PRS, vol. XXXI, pp. 319–323 (1996)Google Scholar
  32. 32.
    Li, R., Li, H., Zou, W., Smith, R., Curran, T.: Quantitative photogrammetric analysis of digital underwater video imagery. IEEE Journal of Oceanic Engineering 22(2), 364–375 (1997)CrossRefGoogle Scholar
  33. 33.
    Maas, H.G.: Digitale Photogrammetrie in der dreidimensionalen Stroemungsmesstechnik. Ph.D. thesis, Eidgenoessische Technische Hochschule Zuerich (1992)Google Scholar
  34. 34.
    Maas, H.G.: New developments in multimedia photogrammetry. In: Optical 3-D Measurement Techniques III. Wichmann Verlag, Karlsruhe (1995)Google Scholar
  35. 35.
    McGlone, J.C. (ed.): Manual of Photogrammetry, 5th edn. ASPRS (2004),
  36. 36.
    Mobley, C.D.: Light and Water: Radiative Transfer in Natural Waters. Academic Press (1994)Google Scholar
  37. 37.
    Morris, N., Kutulakos, K.N.: Dynamic refraction stereo. In: Proc. 10th Int. Conf. Computer Vision, pp. 1573–1580 (2005)Google Scholar
  38. 38.
    Narasimhan, S.G., Nayar, S.: Structured light methods for underwater imaging: light stripe scanning and photometric stereo. In: Proceedings of 2005 MTS/IEEE OCEANS, vol. 3, pp. 2610–2617 (September 2005)Google Scholar
  39. 39.
    Nascimento, E.R., Campos, M.F.M., Barros, W.F.: Stereo based structure recovery of underwater scenes from automatically restored images. In: Nonato, L.G., Scharcanski, J. (eds.) Proceedings SIBGRAPI 2009 (Brazilian Symposium on Computer Graphics and Image Processing), October 11-14. IEEE Computer Society, Los Alamitos (2009), Google Scholar
  40. 40.
    Negahdaripour, S., Sekkati, H., Pirsiavash, H.: Opti-acoustic stereo imaging, system calibration and 3-d reconstruction. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2007, June 17-22, pp. 1–8 (2007)Google Scholar
  41. 41.
    Negahdaripour, S., Sekkati, H., Pirsiavash, H.: Opti-acoustic stereo imaging: On system calibration and 3-d target reconstruction. IEEE Transactions on Image Processing 18(6), 1203–1214 (2009)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Negahdaripour, S., Xu, X., Khamene, A., Awan, Z.: 3-d motion and depth estimation from sea-floor images for mosaic-based station-keeping and navigation of rovs/auvs and high-resolution sea-floor mapping. In: Proceedings of the 1998 Workshop on Autonomous Underwater Vehicles, AUV 1998, pp. 191–200 (August 1998)Google Scholar
  43. 43.
    Pessel, N., Opderbecke, J., Aldon, M.J.: Camera self-calibration in underwater environment. In: WSCG (2003)Google Scholar
  44. 44.
    Pessel, N.: Auto-Calibrage d’une Caméra en Milieu Sous-Marin. Ph.D. thesis, Université Montpellier II (2003)Google Scholar
  45. 45.
    Pessel, N., Opderbecke, J., Aldon, M.J.: An experimental study of a robust self-calibration method for a single camera. In: 3rd International Symposium on Image and Signal Processing and Analysis, ISPA 2003. Sponsored by IEEE and EURASIP, Rome, Italie (September 2003)Google Scholar
  46. 46.
    Pizarro, O., Eustice, R., Singh, H.: Relative pose estimation for instrumented, calibrated imaging platforms. In: DICTA, pp. 601–612 (2003)Google Scholar
  47. 47.
    Pizarro, O., Eustice, R., Singh, H.: Large area 3d reconstructions from underwater surveys. In: Proc. OCEANS 2004, MTTS/IEEE TECHNO-OCEAN 2004, vol. 2, pp. 678–687 (2004)Google Scholar
  48. 48.
    Press, W.H., Vetterling, W.T., Teukolsky, S.A., Flannery, B.P.: Numerical Recipes in C++: the art of scientific computing, 2nd edn. Cambridge University Press, New York (2002)Google Scholar
  49. 49.
    Putze, T.: Erweiterte verfahren zur mehrmedienphotogrammetrie komplexer körper. In: Beiträge der Oldenburger 3D-Tage 2008. Herbert Wichmann Verlag, Heidelberg (2008)Google Scholar
  50. 50.
    Putze, T.: Geometrische und stochastische Modelle zur Optimierung der Leistungsfaehigkeit des Stroemungsmessverfahrens 3D-PTV. Ph.D. thesis, Technische Universitaet Dresden (2008)Google Scholar
  51. 51.
    Queiroz-Neto, J.P., Carceroni, R., Barros, W., Campos, M.: Underwater stereo. In: Proc. 17th Brazilian Symposium on Computer Graphics and Image Processing, October 17-20, pp. 170–177 (2004)Google Scholar
  52. 52.
    Schiller, I., Beder, C., Koch, R.: Calibration of a pmd camera using a planar calibration object together with a multi-camera setup. In: The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XXI. ISPRS Congress, Beijing, China, vol. XXXVII, Part B3a, pp. 297–302 (2008),
  53. 53.
    Sedlazeck, A., Koser, K., Koch, R.: 3d reconstruction based on underwater video from rov kiel 6000 considering underwater imaging conditions. In: Proc. OCEANS 2009, OCEANS 2009-EUROPE, May 11-14, pp. 1–10 (2009)Google Scholar
  54. 54.
    Sturm, P., Ramalingam, S., Lodha, S.: On calibration, structure from motion and multi-view geometry for generic camera models. In: Daniilidis, K., Klette, R. (eds.) Imaging Beyond the Pinhole Camera, Computational Imaging and Vision, vol. 33. Springer (August 2006),
  55. 55.
    Sturm, P., Ramalingam, S.: A Generic Concept for Camera Calibration. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004, Part II. LNCS, vol. 3022, pp. 1–13. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  56. 56.
    Telem, G., Filin, S.: Calibration of consumer cameras in a multimedia environment. In: ASPERS 2006 Annual Conference (2006)Google Scholar
  57. 57.
    Telem, G., Filin, S.: Photogrammetric modeling of underwater environments. ISPRS Journal of Photogrammetry and Remote Sensing 65(5), 433–444 (2010), CrossRefGoogle Scholar
  58. 58.
    Treibitz, T., Schechner, Y., Singh, H.: Flat refractive geometry. In: Proc. IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pp. 1–8 (2008)Google Scholar
  59. 59.
    Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle Adjustment – A Modern Synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) Vision Algorithms 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  60. 60.
    Trucco, E., Doull, A., Odone, F., Fusiello, A., Lane, D.: Dynamic video mosaicing and augmented reality for subsea inspection and monitoring. In: Oceanology International, United Kingdom (2000)Google Scholar
  61. 61.
    Tsai, R.Y.: A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses, an efficient and accurate camera calibration technique. IEEE Journal of Robotics and Automation RA-3(4), 323–344 (1987)CrossRefGoogle Scholar
  62. 62.
    Wolff, K.: Zur Approximation allgemeiner optischer Abbildungsmodelle und deren Anwendung auf eine geometrisch basierte Mehrbildzuordnung am Beispiel einer Mehrmedienabbildung. Ph.D. thesis, Rheinische Friedrich-Wilhelms-Universitaet Bonn (2007)Google Scholar
  63. 63.
    Xu, X., Negahdaripour, S.: Application of extended covariance intersection principle for mosaic-based optical positioning and navigation of underwatervehicle. In: ICRA 2001, pp. 2759–2766 (2001)Google Scholar
  64. 64.
    Yamashita, A., Hayashimoto, E., Kaneko, T., Kawata, Y.: 3-d measurement of objects in a cylindrical glass water tank with a laser range finder. In: Proceedings of 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), October 27-31, vol. 2, pp. 1578–1583 (2003)Google Scholar
  65. 65.
    Yamashita, A., Fujii, A., Kaneko, T.: Three dimensional measurement of objects in liquid and estimation of refractive index of liquid by using images of water surface with a stereo vision system. In: ICRA, pp. 974–979 (2008)Google Scholar
  66. 66.
    Zhang, Z.: Flexible camera calibration by viewing a plane from unknown orientations. In: Proceedings of the International Conference on Computer Vision, Corfu, Greece, pp. 666–673 (1999),

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anne Sedlazeck
    • 1
  • Reinhard Koch
    • 1
  1. 1.Multimedia Information Processing, Institute of Computer ScienceChristian-Albrechts-University (CAU) of KielGermany

Personalised recommendations