Deringing in DCT via overshoot and clipping

From perspective of JPEG's DCT function a line of pixels represents a sampled waveform, and therefore a block with sharp black/white edges is going to be similar to a square wave composed of only minimum and maximum sample values:

Inevitably, DCT and JPEG quantization are going distort the waveform. The distortion usually has a wavy shape that increases some values, and decreases others. This is the source of "ringing" artifacts.

Because values of the input waveform were already at minimum/maximum, the distortions will make parts of the wave out of range: overshoot (marked in cyan). Other parts will have values lowered below maximum or raised above minimum: undershoot (red).

The JPEG decoder expects that some values will overshoot and clips the waveform to fit in the allowed range (0-255 in RGB output). After clipping the overshooting values are flattened (<0 replaced with 0, >255 replaced with 255), so only the undershooting half of the distortions remains visible:

Overshoot can't make white areas any brighter, but undershoot makes white areas darker. This is the reason why black-on-white text in JPEG looks "dirty" with gray square halos around it.

Here's the trick

The waveform is altered before quantization: minimum and minimum values are extended to overshoot (everything else remains unchanged):

The modified waveform will have a higher amplitude, and after JPEG compression the distortions will be more likely to remain in the overshooting range:

Clipping done by the JPEG decoder will flatten all overshooting areas, and therefore hide all of the distortions:

The image will appear to have sharp edges without any ringing artifacts and "dirty" background!

Second part of the trick

DCT breaks down the waveform into a sum of frequencies, and square waves are an edge case that's hardest to represent this way.

We can pretend that the waveform we're encoding has been clipped, and perfrom de-clipping. De-clipping only extends the waveform in the range that is clipped by the JPEG decoder, so this modification won't alter visible pixels of the image.

Instead of just blindly increasing minimum/maximum values as before, we're going to extrapolate them with splines to make them "rounder" and therefore reduce sharpness of hard-to-encode corners of the square wave:

A secondary benefit of this is that spline extrapolation won't create unwanted sharp edges around smooth borders between white and light gray. The amount of overshoot added for deringing will be roughly proportional to sharpness of edges it affects.

Random facts


Prototype. Patch for mozjpeg.

Examples and data

These images were saved with the same quality setting and have about the same file size (where they differ, version with deringing is few bytes smaller).

The graphs are dssim vs filesize (both lower=better) for all qualities between 8 and 98. "cjpeg" is libjpeg 6b, "moz" is mozjpeg 1.3, and "dering" is the proposed implementation added to mozjpeg.

Images without any hard edges with white are completely unaffected.

2014, Kornel LesiƄski