Complex Plane Transformations for Manipulation and Visualization of Panoramas

Leonardo Sacht, Luiz Velho

Abstract

We present a method for manipulation and visualization of wide-angle images using transformations defined on the complex plane C. We map the unit sphere S2 to C using the stereographic projection, multiply the complex plane by a given complex number, and map the result back to the sphere using the inverse of the stereographic projection. Since all these transformations preserve angle, we obtain a result containing only distortions due to the latitude/longitude representation of the sphere, which were already present in the input image. We then explore the possibility given by our technique of mapping wide fields of view to narrower ones. This makes possible to apply perspective projection to wider fields of view, leading to a natural generalization of the perspective projection in the context of panoramic images. Our results are generated in real-time and compare competitively with state-of-the-art methods used to project the viewing sphere to the image plane.

References

  1. Carroll, R., Agrawal, M., and Agarwala, A. (2009). Optimizing content-preserving projections for wide-angle images. In ACM SIGGRAPH 2009 papers, SIGGRAPH 7809, pages 43:1-43:9, New York, NY, USA. ACM.
  2. Conway, J. B. (1978). Functions of One Complex Variable. Springer-Verlag, New York.
  3. Crane, K., Pinkall, U., and Schrö der, P. (2011). Spin transformations of discrete surfaces. ACM Trans. Graph., 40.
  4. fieldOfView (2012). Interactive panoramas - fieldofview. http:// fieldofview.com/panoramas.
  5. Flickr (2012). Flickr: Equirectangular. http:// www.flickr.com/groups/equirectangular/.
  6. German, D. M., Burchill, L., Duret-Lutz, A., Prez-Duarte, S., Prez-Duarte, E., and Sommers, J. (2007). Flattening the viewable sphere. In Cunningham, D. W., Meyer, G. W., Neumann, L., Dunning, A., and Paricio, R., editors, Computational Aesthetics, pages 23- 28. Eurographics Association.
  7. Google Street View (2012). Street view - google maps. http:// maps.google.com/streetview.
  8. Kopf, J., Lischinski, D., Deussen, O., Cohen-Or, D., and Cohen, M. F. (2009). Locally adapted projections to reduce panorama distortions. Comput. Graph. Forum, 28(4):1083-1089.
  9. Kopf, J., Uyttendaele, M., Deussen, O., and Cohen, M. F. (2007). Capturing and viewing gigapixel images. In ACM SIGGRAPH 2007 papers, SIGGRAPH 7807, New York, NY, USA. ACM.
  10. Sacht, L., Velho, L., Nehab, D., and Cicconet, M. (2011). Scalable motion-aware panoramic videos. In SIGGRAPH Asia 2011 Sketches, SA 7811, pages 37:1- 37:2, New York, NY, USA. ACM.
  11. Snyder, J. P. (1987). Map projections - a working manual. Technical Report 1395, U. S. Geological Survey.
  12. Zelnik-Manor, L., Peters, G., and Perona, P. (2005). Squaring the circles in panoramas. In Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2, ICCV 7805, pages 1292-1299, Washington, DC, USA. IEEE Computer Society.
  13. Zorin, D. and Barr, A. H. (1995). Correction of geometric perceptual distortions in pictures. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, SIGGRAPH 7895, pages 257-264, New York, NY, USA. ACM.
Download


Paper Citation


in Harvard Style

Sacht L. and Velho L. (2013). Complex Plane Transformations for Manipulation and Visualization of Panoramas . In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013) ISBN 978-989-8565-46-4, pages 179-184. DOI: 10.5220/0004197701790184


in Bibtex Style

@conference{grapp13,
author={Leonardo Sacht and Luiz Velho},
title={Complex Plane Transformations for Manipulation and Visualization of Panoramas},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)},
year={2013},
pages={179-184},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004197701790184},
isbn={978-989-8565-46-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information Visualization Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2013)
TI - Complex Plane Transformations for Manipulation and Visualization of Panoramas
SN - 978-989-8565-46-4
AU - Sacht L.
AU - Velho L.
PY - 2013
SP - 179
EP - 184
DO - 10.5220/0004197701790184