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Acceleration of the shiftable O(1) algorithm for bilateral filtering and nonlocal means
1Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA. kchaudhu@math.princeton.edu
Summary
This study addresses challenges in fast bilateral filter implementations. New methods accelerate computations, especially for narrow range kernels in high dynamic range images, improving efficiency.
Area of Science:
- Computer Vision
- Image Processing
- Signal Processing
Background:
- Direct bilateral filter implementation is computationally intensive (O(σ(s)^2) per pixel).
- Fast bilateral filter methods using trigonometric functions offer O(1) complexity w.r.t. spatial kernel width (σ(s)).
- Previous fast methods showed runtime dependency on range kernel width (σ(r)), posing issues for narrow kernels and large dynamic ranges.
Purpose of the Study:
- To discuss and propose solutions for accelerating bilateral filter implementations.
- To specifically address the challenge of implementing narrow range kernels efficiently.
- To improve the performance of fast bilateral filter algorithms for images with large dynamic ranges.
Main Methods:
- Exploiting the shiftability property of trigonometric functions for range kernels.
- Approximating Gaussian range kernels with raised cosines for fast Gaussian bilateral filtering.
- Extending trigonometric function approach to other filters like non-local means.
- Proposing simple modifications to accelerate implementation, particularly for small σ(r).
Main Results:
- Previous fast methods had runtime scaling as O(T^2/σ(r)^2), hindering narrow kernel use.
- The proposed modifications aim to accelerate the implementation in general.
- Specific acceleration is targeted for cases with small range kernel widths (σ(r)).
Conclusions:
- The proposed simple steps effectively accelerate bilateral filter implementations.
- These modifications are particularly beneficial for narrow range kernels and images with large dynamic ranges.
- Experimental results demonstrate the achieved acceleration and improved efficiency.
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