Paeth

Paeth is the name of a predictive filter used in the Portable Network Graphics (PNG) image compression format. It is one of the five filters designed to reduce redundancy by predicting pixel values from neighboring pixels, thereby producing smaller residuals that are easier to compress.

The Paeth predictor estimates the current pixel value from three already decoded neighbors: a, the left pixel; b, the pixel above; and c, the pixel above and to the left. It computes p = a + b − c, then selects among a, b, and c the value closest to p. The chosen neighbor becomes the predicted value for the current pixel, and the residual (the difference between the real pixel and the predicted value) is then compressed. During decoding, the residual is added back to the predicted value to recover the original pixel.

In PNG, Paeth is used as Filter Type 4. Each scanline can be encoded with a different filter, and the PNG encoder typically tests all filters to determine which produces the smallest encoded data. The first pixel of a row has only the left neighbor unavailable, so its left value is treated as zero for the purposes of prediction.

The Paeth predictor is particularly effective on natural images with smooth gradients or repeating patterns, where pixel values tend to correlate with their neighbors. Its performance varies with image content, and as with the other PNG filters, it is most beneficial when paired with an effective compression stage. The predictor contributes to PNG’s lossless compression efficiency by reducing entropy prior to entropy coding.