Fast Isotropic Median Filtering

Fast Isotropic Median Filtering BEN WEISS, Google Research, USA Fig. 1. Top row: Original photo, median-filtered with a radius-48 square kernel (with hand-applied matte), and with an equivalent-area circular kernel. Bottom row: square vs. circular filtered image quality for binary noise, as well as for two swatches from the image, unsharp-masked 200% to emphasize the high-frequency artifacts. Across a wide range of parameters, our circular median filter is dramatically faster and higher quality than the state of the art.

Median filtering is a cornerstone of computational image processing. It provides an effective means of image smoothing, with minimal blurring or softening of edges, invariance to monotonic transformations such as gamma adjustment, and robustness to noise and outliers. However, known algorithms have all suffered from practical limitations: the bit depth of the image data, the size of the filter kernel, or the kernel shape itself. Squarekernel implementations tend to produce streaky cross-hatching artifacts, and nearly all known efficient algorithms are in practice limited to square kernels. We present for the first time a method that overcomes all of these limitations. Our method operates efficiently on arbitrary bit-depth data, arbitrary kernel sizes, and arbitrary convex kernel shapes, including circular shapes.