Fast O1 bilateral filtering using trigonometric range kernels.

Area of Science:

• Computer Vision
• Image Processing
• Computational Photography

Background:

• Spatial averaging algorithms can achieve constant-time complexity (O(1)).
• The bilateral filter, crucial for edge-preserving smoothing, is computationally intensive due to its nonlinear range kernel.
• Existing methods for fast bilateral filtering often rely on polynomial approximations.

Purpose of the Study:

• To develop a constant-time bilateral filter leveraging O(1) spatial averaging algorithms.
• To introduce and evaluate the use of trigonometric range kernels for bilateral filtering.
• To demonstrate the superior approximation quality of trigonometric kernels over polynomial kernels.

Main Methods:

• Generalizing Porikli's polynomial kernel approach to trigonometric kernels.
• Implementing O(1) averaging algorithms with trigonometric range kernels for bilateral filtering.
• Approximating the Gaussian bilateral filter using trigonometric functions.

Main Results:

• A constant-time implementation of the bilateral filter is achieved.
• Trigonometric kernels provide a rich class for approximating the bilateral filter.
• For a fixed number of terms, trigonometric kernels offer significantly better approximation quality than polynomial kernels.

Conclusions:

• The proposed method enables efficient, constant-time bilateral filtering.
• Trigonometric kernels present a powerful and effective alternative to polynomial kernels for approximating the bilateral filter.
• This work advances the field of fast image filtering with improved accuracy and efficiency.