Fast and high-quality scale-aware filtering for 3D images

Scale-aware image filters are useful in graphics applications, but applying such filters to 3D images has not been well studied and introduces 3D-specific issues. This paper proposes a fast scale-aware 3D image filter that recursively applies an average-based joint filter that alternates its input and guidance images at each recursion. The joint filter transforms each voxel domain via the arc length of the guidance image manifold, and the $$L^{1}$$ Gaussian convolutions are performed efficiently and accurately on the transformed and decomposed sub-domains. Our filter employs a novel 3D half-box filter to avoid corner-missing artifacts, incorporates voxel pitches into the formulations, fixes the convolution order to reduce non-uniform convergence, and introduces a novel convolution kernel to obtain consistent results that avoid distorted edges. The new filter was numerically examined and compared to conventional filters in terms of accuracy, speed, convergence rate, and visual quality, and was found to achieve fast computations while providing high-quality results.