Fast global image smoothing based on weighted least squares

Area of Science:

• Computer Vision
• Image Processing
• Numerical Analysis

Background:

• Image smoothing is crucial for various applications.
• Existing edge-preserving filters have limitations.
• Optimization-based methods offer global solutions but are computationally intensive.

Purpose of the Study:

• To develop an efficient and effective edge-preserving image smoothing technique.
• To overcome the limitations of local filtering and the computational cost of optimization-based methods.
• To introduce generalized algorithms for flexible smoothing objectives.

Main Methods:

• A fast global smoother (FGS) is proposed.
• The method approximates solutions to large linear systems by solving sequential 1D subsystems.
• A separable implementation utilizes linear-time tridiagonal matrix algorithms for iterative solving.

Main Results:

• The FGS achieves comparable runtime to fast edge-preserving filters.
• It overcomes limitations of local filtering through global optimization.
• Results are high-quality, achieving state-of-the-art performance at 10-30x faster speeds.
• Generalized algorithms support Lγ norm smoothing and robust data terms.

Conclusions:

• The proposed fast global smoother offers an efficient and effective solution for spatially inhomogeneous edge-preserving image smoothing.
• The technique combines the benefits of fast filtering and robust global optimization.
• It demonstrates significant speed improvements over existing optimization-based methods while maintaining high-quality results.