Abstract
We present linear filters for image processing in the case that the image data is given on the sphere rather than on a plane. Such spherical images occur in various situations in computer vision and computer graphics. The class of filters we present is derived from the spherical Gaussian kernel defined as the Green’s function of the spherical diffusion equation. The derived filters include Laplacian of Gaussian, directional Gaussian derivatives, and their Hilbert transform. All computations are directly performed on the sphere without ever switching to a planar domain. These filters allow spherical image processing on multiple scales. We present results on images obtained from an omnidirectional camera.
This work was supported by the German Research Association (Deutsche Forschungsgemeinschaft — DFG) under the grant Bu 1259/2-1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
J. Antoine and P. Vandergheynst. Wavelets on the 2-sphere: A group-theoretical approach. Appl. Comput. Harmon. Anal., 7, 1999.
Th. Bülow. Spherical diffusion for surface smoothing. In First International Symposium on 3D Data Processing, Visualization, and Transmission, 2002.
G.S. Chirikjian and A.B. Kyatkin. Engineering Applications of Noncommutative Harmonic Analysis. CRC Press, 2001.
K. Daniilidis, editor. IEEE Workshop on Omnidirectional Vision, Hilton Head Island, SC, June 12, 2000.
L. Demanet and P. P. Vandergheynst. Directional wavelets on the sphere. Technical Report R-2001-2, Signal Processing Laboratory (LTS), EPFL, Lausanne, 2001.
J.R. Driscoll and D.M. Healy. Computing fourier transforms and convolutions on the 2-sphere. Advances in Applied Mathematics, 15:202–250, 1994.
G. H. Granlund and H. Knutsson. Signal Processing for Computer Vision. Kluwer Academic Publishers, 1995.
B.K.P. Horn. Robot Vision. MIT Press, 1986.
J.J. Koenderink and A. von Dorn. Representation of local geometry in the visual system. Biological Cybernetics, 55(6):367–375, 198u.
J. Sporring, et al. editor. Gaussian scale-space theory. Kluwer, Dordrecht, 1997.
B.D. Wandelt and K.M. Gorski. Fast convolution on the sphere. Phys Rev D63, 123002/1-6, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bülow, T. (2002). Multiscale Image Processing on the Sphere. In: Van Gool, L. (eds) Pattern Recognition. DAGM 2002. Lecture Notes in Computer Science, vol 2449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45783-6_73
Download citation
DOI: https://doi.org/10.1007/3-540-45783-6_73
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44209-7
Online ISBN: 978-3-540-45783-1
eBook Packages: Springer Book Archive