arXiv subjects

Kunal N. Chaudhury

Publications and source records attributed to Kunal N. Chaudhury.

39 records · Page 3Linked to original sources

arXiv2012

Non-Local Euclidean Medians

In this letter, we note that the denoising performance of Non-Local Means (NLM) at large noise levels can be improved by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.

cs.CV↗

arXiv2012

Acceleration of the shiftable O(1) algorithm for bilateral filtering and non-local means

A direct implementation of the bilateral filter [1] requires O(σ_s^2) operations per pixel, where σ_s is the (effective) width of the spatial kernel. A fast implementation of the bilateral filter was recently proposed in [2] that required O(1) operations per pixel with respect to σ_s. This was done by using trigonometric functions for the range kernel of the bilateral filter, and by exploiting their so-called shiftability property. In particular, a fast implementation of the Gaussian bilateral filter was realized by approximating the Gaussian range kernel using raised cosines. Later, it was demonstrated in [3] that this idea could be extended to a larger class of filters, including the popular non-local means filter [4]. As already observed in [2], a flip side of this approach was that the run time depended on the width σ_r of the range kernel. For an image with (local) intensity variations in the range [0,T], the run time scaled as O(T^2/σ^2_r) with σ_r. This made it difficult to implement narrow range kernels, particularly for images with large dynamic range. We discuss this problem in this note, and propose some simple steps to accelerate the implementation in general, and for small σ_r in particular. [1] C. Tomasi and R. Manduchi, "Bilateral filtering for gray and color images", Proc. IEEE International Conference on Computer Vision, 1998. [2] K.N. Chaudhury, Daniel Sage, and M. Unser, "Fast O(1) bilateral filtering using trigonometric range kernels", IEEE Transactions on Image Processing, 2011. [3] K.N. Chaudhury, "Constant-time filtering using shiftable kernels", IEEE Signal Processing Letters, 2011. [4] A. Buades, B. Coll, and J.M. Morel, "A review of image denoising algorithms, with a new one", Multiscale Modeling and Simulation, 2005.

cs.CV↗

arXiv2012

Improvements on "Fast space-variant elliptical filtering using box splines"

It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. By generalizing this idea and by combining it with a non-standard variant of the Central Limit Theorem, a constant-time or O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform space-variant filtering using Gaussian-like kernels. The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size (covariance) of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, offered a limited control on the covariance and accuracy of the Gaussian approximation. In this work, we propose some improvements by appropriately modifying the algorithm in [Chaudhury2010].

cs.CV↗