COLOR BILATERAL FILTERING USING STRATIFIED FOURIER SAMPLING

Ghosh, Sanjay and Chaudhury, Kunal N (2018) COLOR BILATERAL FILTERING USING STRATIFIED FOURIER SAMPLING. In: Global Conference on Signal and Information Processing (GlobalSIP), 26-29 Nov. 2018, Anaheim, CA, USA, pp. 26-30.

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Abstract

Brute force implementation of the bilateral filter is known to be prohibitively slow. Several fast approximations have been proposed in the literature that are able to accelerate the filtering without perceptible loss of filtering quality. In particular, it has been shown that by replacing the range kernel (usually Gaussian) of the bilateral filter with its Fourier approximation, the filtering can be performed using fast convolutions. While an accurate Fourier approximation of a one-dimensional Gaussian (for grayscale filtering) can be obtained using N similar to 10 terms, a comparable approximation in three dimensions (for color filtering) requires N-3 Fourier terms, and proportionate number of convolutions. As shown in prior work, we can overcome this problem using Monte Carlo (MC) sampling. In this paper, we demonstrate that the variance of MC sampling can be reduced using stratified sampling, i.e., by conditionally sampling the low and high frequency terms. Importantly, we are able to cut down the pixelwise fluctuation of the filtered output as a result. We analytically compute the variances of MC and stratified sampling, whereby the variance reduction is evident. The PSNR fluctuation of our approximation is also shown to be smaller than existing Monte-Carlo algorithms.

Item Type:	Conference Proceedings
Publication:	2018 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP 2018)
Publisher:	IEEE
Additional Information:	Copyright for this article belongs to IEEE
Keywords:	color bilateral filter; Monte Carlo sampling; variance reduction; stratified sampling; fast algorithm
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	29 May 2019 10:55
Last Modified:	31 May 2019 07:08
URI:	http://eprints.iisc.ac.in/id/eprint/62349

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