Abstract
This paper focuses on variational image analysis on a sphere. Since a sphere is a closed Riemannian manifold with the positive constant curvature and no holes, a sphere has similar geometrical properties with a plane, whose curvature is zero. Images observed through a catadioptric system with a conic-mirror and a dioptric system with fish-eye lens are transformed to images on the sphere. Therefore, in robot vision, image analysis on the sphere is an essential requirement to the application of the omni-directional imaging system with conic-mirror and fish-eye lens for navigation and control. We introduce algorithms for optical flow computation for images on a sphere.
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References
Zdunkowski, W., Bott, A.: Dynamics of the Atmosphere. Cambridge University Press, Cambridge (2003)
Morel, J.-M., Solimini, S.: Variational Methods in Image Segmentation. Rirkhaäuser (1995)
Osher, S., Paragios, N. (eds.): Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, Heidelberg (2003)
Nelson, R.C., Aloimonos, J.: Finding motion parameters from spherical flow fields (or the advantage of having eyes in the back of your head). Biological Cybernetics 58, 261–273 (1988)
Fermüller, C., Aloimonos, J.: Ambiguity in structure from motion: sphere versus plane. IJCV 28, 137–154 (1998)
Baker, S., Nayer, S.: A theory of single-viewpoint catadioptric image formation International Journal of Computer Vision 35, 175–196 (1999)
Geyer, C., Daniilidis, K.: Catadioptric projective geometry. International Journal of Computer Vision 45, 223–243 (2001)
Neumann, T.R.: Modeling insect compound eyes: Space-variant spherical vision. In: Bülthoff, H.H., Lee, S.-W., Poggio, T.A., Wallraven, C. (eds.) BMCV 2002. LNCS, vol. 2525, pp. 360–367. Springer, Heidelberg (2002)
Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–204 (1981)
Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. International Journal of Computer Vision 12, 43–77 (1994)
Imiya, A., Iwawaki, K.: Voting method for subpixel flow detection. Pattern Recognition Letters 24, 197–214 (2003)
Nagel, H.-H.: On the estimation of optical flow: Relations between different approaches and some new results. Artificial Intelligence 33, 299–324 (1987)
Xu, C., Prince, J.L.: Generalized gradient vector flow external forces for active contours. Signal Processing 71, 131–139 (1998)
Xu, C., Prince, J.L.: Gradient vector flow: A new external force for snakes. In: Proc. CVPR 1997, pp. 66–71 (1997)
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Imiya, A., Sugaya, H., Torii, A., Mochizuki, Y. (2005). Variational Analysis of Spherical Images. In: Gagalowicz, A., Philips, W. (eds) Computer Analysis of Images and Patterns. CAIP 2005. Lecture Notes in Computer Science, vol 3691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556121_14
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DOI: https://doi.org/10.1007/11556121_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28969-2
Online ISBN: 978-3-540-32011-1
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