Movatterモバイル変換

Abstract

Median filtering is a cornerstone of modern image processing, and is used extensively in smoothing and de-noising applications. The fastest commercial implementations (e.g. in Adobe Photoshop CS2) exhibitO(r) runtime in the radius of the filter, which limits their usefulness in realtime or resolution-independent contexts. We introduce a CPU-based, vectorizableO(logr) algorithm for median filtering, to our knowledge the most efficient yet developed. Our algorithm extends to images of any bit-depth, and can also be adapted to perform bilateral filtering. On 8-bit data [shown at right], our median filter outperforms Photoshop’s implementation by up to a factor of fifty.

PreprintSlideshow

Median filterBilateral filter

Median Filter Variations. Top row: original; sharpened with Gaussian; sharpened with median (note fewer halo artifacts.)
Middle row: Filtered at 20th; 50th [median]; and 80th percentiles.
Bottom row: “High Pass” using median; bilateral smoothing filter; logarithmic bilateral filter.

16-bit Median Filter Performance.

The Bilateral Filter. From left: 8-Bit Source Image; Linear-Intensity Bilateral; Logarithmic-Intensity Bilateral.
Center matches Photoshop's Surface Blur; at right is our enhanced algorithm. Note improved lip color and hair detail.

Bilateral Filter Performance. (Comparison based on Surface Blur at threshold 16.)

"String Theory." A creative algorithm by Kai Krause, based on the Weiss Median with realtime-controllable parameters.