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Locally Adaptive Smoothing Method Based on B-Splines

G. Vidal-Cassanya, A. Muñoz Barrutia, M. Unser

Proceedings of the 2006 Symposium on Computational Modelling of Objects Represented in Images—Fundamentals, Methods and Applications (CompIMAGE'06), Coimbra, Portuguese Republic, October 20-21, 2006.


This paper presents a novel method for the edge-preserving smoothing of biomedical images. It is based on the convolution of the image with scaled B-splines. The size of the spline convolution kernel at each image position is adaptive and matched to the underlying image characteristics; i.e., wide splines for smooth regions and narrow ones for pixels belonging to edges. Consequently, the algorithm reduces image noise in homogeneous areas while, at the same time, preserving image structures such as edges or corners. We argue that the proposed adaptive filtering strategy provides a good balance between the improvement in the Signal to Noise Ratio (SNR) and perceptual quality. Our algorithm takes advantage of the unique convolution and factorization properties of B-splines. Specifically, the input signal is expressed in a B-spline basis; the inner product with a B-spline of arbitrary size is then computed by using an adequate combination of 1D integrations (preprocessing) and rescaled finite differences. The method is computationally efficient with a cost per pixel that is fixed and independent upon the scaling factor.

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AUTHOR="Vidal-Cassanya, G. and Mu{\~{n}}oz-Barrutia, A. and Unser, M.",
TITLE="Locally Adaptive Smoothing Method Based on \mbox{{B}-Splines}",
BOOKTITLE="Proceedings of the 2006 Symposium on Computational Modelling
	of Objects Represented in Images---{F}undamentals, Methods and
	Applications ({CompIMAGE'06})",
YEAR="2006",
editor="",
volume="",
series="",
pages="",
address="Coimbra, Portuguese Republic",
month="October 20-21,",
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© 2006 FEUP. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from FEUP. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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