Abstract
We introduce a short time kernel for the Beltrami image enhancing flow. The flow is implemented by ‘convolving’ the image with a space dependent kernel in a similar fashion to the implementation of the heat equation by a convolution with a gaussian kernel. The expression for the kernel shows, yet again, the connection between the Beltrami flow and the Bilateral filter. The kernel is calculated by measuring distances on the image manifold by an efficient variation of the fast marching method. The kernel, thus obtained, can be used for arbitrary large time steps in order to produce adaptive smoothing and/or a new scale-space. We apply it to gray scale and color images to demonstrate its flow like behavior.
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References
http://www.cs.technion.ac.il/~ron/.
D. Barash. Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(6):844–847, June 2002.
M. Elad. On the bilateral filter and ways to improve it. IEEE Transactions on Image Processing, 11(10):1141–1151, October 2002.
R. Kimmel, R. Malladi, and N. Sochen. Image processing via the beltrami operator. In Proc. of 3-rd Asian Conf. on Computer Vision, Hong Kong, January 1998.
R. Kimmel and J. Sethian. Computing geodesic paths on manifolds. Proceedings of National Academy of Sciences, 95(15):8431–8435, July 1998.
F. Mémoli and G. Sapiro. Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces. Journal of Computational Physics, 173(2):730–764, 2001.
J. Sethian. A fast marching level set method for monotonically advancing fronts. Proceedings of National Academy of Sciences, 93(4):1591–1595, 1996.
J. Sethian and A. Vladimirsky. Ordered upwind methods for static hamilton-jacobi equations: theory and applications. Technical Report PAM-792(UCB), Center for Pure and Applied Mathematics, May 2001. submitted for publication to SIAM Journal on Numerical Analysis in July 2001.
N. Sochen. Stochastic processes in vision: From langevin to beltrami. In Proc. of International Conference on Computer Vision, Vancouver, Canada, July 2001.
N. Sochen, R. Kimmel, and A. Bruckstein. Diffusions and confusions in signal and image processing. Journal of Mathematical Imaging and Vision, 14(3):195–209, 2001.
N. Sochen, R. Kimmel, and R. Malladi. From high energy physics to low level vision. LBNL report LBNL-39243, UC Berkeley, August 1996.
N. Sochen, R. Kimmel, and R. Malladi. A general framework for low level vision. IEEE Trans. on Image Processing, 7(3):310–318, 1998.
N. Sochen and Y. Y. Zeevi. Representation of colored images by manifolds embedded in higher dimensional non-euclidean space. In Proc. of ICIP98, pages 166–170, Chicago, IL, January 1998.
A. Spira and R. Kimmel. An efficient solution to the eikonal equation on parametric manifolds. Submitted for publication, March 2003.
C. Tomasi and R. Manduchi. Bilateral filtering for gray and color images. In Sixth International Conference on Computer Vision, Bombay, India, January 1998.
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Spira, A., Kimmel, R., Sochen, N. (2003). Efficient Beltrami Flow Using a Short Time Kernel. In: Griffin, L.D., Lillholm, M. (eds) Scale Space Methods in Computer Vision. Scale-Space 2003. Lecture Notes in Computer Science, vol 2695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44935-3_35
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DOI: https://doi.org/10.1007/3-540-44935-3_35
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