Fast Adaptive Bilateral Filtering

Abstract

In the classical bilateral filter, a fixed Gaussian range kernel is used along with a spatial kernel for edge-preserving smoothing. We consider a generalization of this filter, the socalled adaptive bilateral filter, where the center and width of the Gaussian range kernel is allowed to change from pixel to pixel. Though this variant was originally proposed for sharpening and noise removal, it can also be used for other applications such as artifact removal and texture filtering. Similar to the bilateral filter, the brute-force implementation of its adaptive counterpart requires intense computations. While several fast algorithms have been proposed in the literature for bilateral filtering, most of them work only with a fixed range kernel. In this paper, we propose a fast algorithm for adaptive bilateral filtering, whose complexity does not scale with the spatial filter width. This is based on the observation that the concerned filtering can be performed purely in range space using an appropriately defined local histogram. We show that by replacing the histogram with a polynomial and the finite range-space sum with an integral, we can approximate the filter using analytic functions. In particular, an efficient algorithm is derived using the following innovations: the polynomial is fitted by matching its moments to those of the target histogram (this is done using fast convolutions), and the analytic functions are recursively computed using integration-by-parts. Our algorithm can accelerate the brute-force implementation by at least 20×, without perceptible distortions in the visual quality. We demonstrate the effectiveness of our algorithm for sharpening, JPEG deblocking, and texture filtering.

Impulse Noise Removal in Mammograms using Bi-Dimensional Empirical Mode Decomposition and Fast Adaptive Bilateral Filter

“…The representing centre in equation 1 and denoting the width in equation 3 are meant to be spatially varying one. The Gaussian spatial kernel is denoted as (4) In equation 1 and 3, and are needs to be vary for each pixels in an image; this makes the bilateral filter as an adaptive bilateral filter [15]. By acclimating the values of at each pixel, the sharp edges are preserved in the images.…”

Evaluation of Deblocking Methods for Chang’e-4 Descent Images

“…Fast adaptive bilateral filtering (FABF) (Gavaskar and Chaudhury, 2018) is a fast algorithm for adaptive bilateral filtering, whose complexity does not scale with the spatial filter width. In addition, the concerned filtering can be performed purely in range space using an appropriately defined local histogram.…”

“…The deblocking algorithms mainly include image enhancement and image restoration. The methods based on image enhancement smooth the block effect by filtering the image (Foi et al, 2007;Yoo et al, 2014;Li et al, 2014;Gavaskar et Chaudhury, 2018). Costella (2006) proposed the UnBlock algorithm without requiring the encoded JPEG or MPEG source file and any tunable parameters.…”

“…Li et al (2014) proposed a structure-texture enhancing method, which decomposes the input image into a structure layer and texture (high-frequency) layer, and contrast enhancement is then used for structural layer data. Gavaskar and Chaudhury (2018) proposed an efficient algorithm for adaptive bilateral filtering based on the observation that the concerned filtering can be performed purely in range space using an appropriately defined local histogram. In general, image enhancement approach aims at smoothing visible artifacts instead of restoring original pixel values, and it is somewhat heuristic in the sense that no objective criterion is optimized.…”

“…Due to the lack of texture in lunar surface images, especially the Chang'e-4 descent images captured at high solar elevation angle, the performance of the deblocking method should be particularly considered. Therefore, in this paper, unblock (Costella, 2006), adaptive fast bilateral filtering (Gavaskar and Chaudhury, 2018), structure-texture enhancement (Li et al, 2014), and high-order Markov random field (Sun et al, 2007) are chosen to remove the block effects in the images, and the performances of these methods are compared.…”