Journal of Real-Time Image Processing

, Volume 15, Issue 4, pp 725–738 | Cite as

Real-time correction of panoramic images using hyperbolic Möbius transformations

  • Luis PeñarandaEmail author
  • Luiz Velho
  • Leonardo Sacht
Original Research Paper


Wide-angle images gained a huge popularity in the last years due to the development of computational photography and imaging technological advances. They present the information of a scene in a way which is more natural for the human eye but, on the other hand, they introduce artifacts such as bent lines. These artifacts become more and more unnatural as the field of view increases. In this work, we present a technique aimed to improve the perceptual quality of panorama visualization. The main ingredients of our approach are, on one hand, considering the viewing sphere as a Riemann sphere, what makes natural the application of Möbius (complex) transformations to the input image, and, on the other hand, a projection scheme which changes in function of the field of view used. We also introduce an implementation of our method, compare it against images produced with other methods and show that the transformations can be done in real time, which makes our technique very appealing for new settings, as well as for existing interactive panorama applications.


Panorama Perspective projection Möbius transformation Real time Implementation 



The authors thank the Flickr and Wikimedia Commons users who made available their equirectangular images under the Creative Commons license, used to obtain some figures of the paper: Gadl (Figs. 6, 10, 11, 12), Luca Biada (Fig. 7), DXR (Fig. 8) and HamburgerJung (Fig. 9). L. Sacht acknowledges the doctoral scholarship from CNPq. L. Peñaranda acknowledges financial support from IMPA during years 2012 to 2014.

Supplementary material

Supplementary material 1 (mp4 23413 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil
  2. 2.Universidade Federal do Rio de Janeiro (UFRJ)Rio de JaneiroBrazil
  3. 3.Universidade Federal de Santa Catarina (UFSC)FlorianópolisBrazil

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