RECORD
Fast Adaptive Bilateral Filtering
Computer Vision and Pattern Recognition · Submitted 6 Nov 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our algorithm can accelerate the brute-force implementation by at least $20 \times$, without perceptible distortions in the visual quality.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
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 so-called 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 $20 \times$, without perceptible distortions in the visual quality. We demonstrate the effectiveness of our algorithm for sharpening, JPEG deblocking, and texture filtering.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the classical bilateral filter, a fixed Gaussian range kernel is used along with a spatial kernel for edge-preserving smoothing. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | We consider a generalization of this filter, the so-called adaptive bilateral filter, where the center and width of the Gaussian range kernel is allowed to change from pixel to pixel. | background 0.81 | 0.17 | 0.03 | asserted 0.99 |
| s2 | 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. | background 0.99 | 0.10 | 0.02 | hedged possibility 0.57 |
| s3 | Similar to the bilateral filter, the brute-force implementation of its adaptive counterpart requires intense computations. | background 0.95 | 0.08 | 0.02 | asserted 1.00 |
| s4 | While several fast algorithms have been proposed in the literature for bilateral filtering, most of them work only with a fixed range kernel. | gap 0.85 | 0.04 | 0.03 | asserted 0.99 |
| s5 | In this paper, we propose a fast algorithm for adaptive bilateral filtering, whose complexity does not scale with the spatial filter width. | contribution 1.00 | 0.93 | 0.62 | asserted 1.00 |
| s6 | This is based on the observation that the concerned filtering can be performed purely in range space using an appropriately defined local histogram. | method 0.92 | 0.73 | 0.09 | asserted 0.99 |
| s7 | 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. | method 0.93 | 0.90 | 0.08 | asserted 0.98 |
| s8 | 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. | method 0.98 | 0.93 | 0.07 | asserted 1.00 |
| s9 | Our algorithm can accelerate the brute-force implementation by at least $20 \times$, without perceptible distortions in the visual quality. | result 1.00 | 0.96 | 0.53 | asserted 0.99 |
| s10 | We demonstrate the effectiveness of our algorithm for sharpening, JPEG deblocking, and texture filtering. | result 0.89 | 0.94 | 0.15 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original 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 so-called 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 $20 \times$, without perceptible distortions in the visual quality. We demonstrate the effectiveness of our algorithm for sharpening, JPEG deblocking, and texture filtering.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.