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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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