When QOI meets XZ

QOI, the Quite OK Image format, has been gaining in popularity. Chris Wellons offers a great analysis.

QOI's key advantages is its simplicity. Being a byte-oriented format without entropy encoding, it can be further compressed with generic data compression programs like LZ4, XZ, and zstd. PNG, on the other hand, uses DEFLATE compression internally and is typically resistant to further compression. By applying a stronger compression algorithm on QOI output, you can often achieve a smaller file size compared to PNG.

XZ

Lasse Collin has shared some effective options for compressing uncompressed BMP/TIFF files. I tested them on the QOI benchmark images.

When the color table (palette) is used, a delta filter would increase the compressed size and should be disabled.

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% cat ~/tmp/b.sh
#!/bin/zsh -ue
f() {
  pngcrush -fix -m 1 -l 0 $1 ${1/.png/.uncompressed.png}
  [[ -f ${1/.png/.uncompressed.png} ]] || cp $1 ${1/.png/.uncompressed.png}
  /tmp/p/qoi/qoiconv $1 ${1/.png/.qoi}
  convert $1 ${1/.png/.bmp}
  convert $1 -compress none ${1/.png/.tiff}
  xz --lzma2=pb=0 -fk ${1/.png/.qoi}
  if [[ $(file $1) =~ RGBA ]]; then
    pnm=${1/.png/.pam}
    convert $1 $pnm
    xz --delta=dist=4 --lzma2=lc=4 -fk $pnm
    xz --delta=dist=4 --lzma2=lc=4 -fk ${1/.png/.bmp}
    xz --delta=dist=4 --lzma2=lc=4 -fk ${1/.png/.tiff}
  elif [[ $(file $1) =~ 'colormap' ]]; then
    pnm=${1/.png/.ppm}
    convert $1 $pnm
    xz --lzma2=pb=0 -fk $pnm
    xz --lzma2=pb=0 -fk ${1/.png/.bmp}
    xz --lzma2=pb=0 -fk ${1/.png/.tiff}
  else
    pnm=${1/.png/.ppm}
    convert $1 $pnm
    xz --delta=dist=3 --lzma2=pb=0 -fk $pnm
    xz --delta=dist=3 --lzma2=pb=0 -fk ${1/.png/.bmp}
    xz --delta=dist=3 --lzma2=pb=0 -fk ${1/.png/.tiff}
  fi
  stat -c '%n %s' $1 ${1/.png/.qoi.xz} $pnm.xz ${1/.png/.bmp.xz} ${1/.png/.tiff.xz}
}

f $1
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cd /tmp/dc-img/images/
ls -1 **/*.png | rush ~/tmp/b.sh '"{}"'
ls -1 **/*.uncompressed.png | rush 'xz -fk --lzma2=pb=0 "{}"'

ruby -e 'puts "directory\t.png\t.png.xz\t.qoi.xz\t.bmp.xz\t.tiff.xz\t.p[ap]m.xz"; Dir.glob("*").each{|dir| next unless File.directory? dir;
  png=pngxz=qoi=bmp=pnm=tiff=0; Dir.glob("#{dir}/*.qoi.xz").each{|f|
  png+=File.size(f.sub(/\.qoi.xz/,".png"));
  pngxz+=File.size(f.sub(/\.qoi.xz/,".uncompressed.png.xz"));
  qoi+=File.size(f); bmp+=File.size(f.sub(/\.qoi/,".bmp")); ppm=f.sub(/\.qoi/,".ppm");  pnm+=File.exists?(ppm) ? File.size(ppm) : File.size(f.sub(/\.qoi/,".pam")); tiff+=File.size(f.sub(/\.qoi/,".tiff"));
};
  puts "#{dir}\t#{png}\t#{pngxz}\t#{qoi}\t#{bmp}\t#{tiff}\t#{pnm}"
}'

While DEFLATE-compressed PNG files can hardly be further compressed, we can convert these PNG files to uncompressed ones then apply xz. The .png.xz results below do not apply a filter, and the files are generally larger than .qoi.xz.

directory .png .png.xz .qoi.xz .bmp.xz .tiff.xz .p[ap]m.xz
icon_512 11154424 7861652 7476640 8042032 8064476 8039192
icon_64 828119 750836 708480 730472 757760 735296
photo_kodak 15394305 14464504 12902852 13612440 13616140 13610844
photo_tecnick 237834256 254803292 213268188 210591724 210508596 210468412
photo_wikipedia 88339751 100449996 86679696 86380124 86274480 86241296
pngimg 229608249 134233476 193382668 186389368 186654256 186420564
screenshot_game 266238855 237976536 218915316 216626004 216847500 216765748
screenshot_web 40272678 24690360 21321460 21458496 21532360 21533432
textures_photo 37854634 36393340 28967008 30054968 30064236 30059784
textures_pk 43523493 40868036 54117600 41990596 40632916 46695172
textures_pk01 18946769 15734348 14950836 14835648 14853420 14839312
textures_pk02 102962935 86037000 82279000 79374112 79348768 79336276
textures_plants 51765329 53044044 43681548 44913260 45021996 45048652

While compressing QOI with XZ (.qoi.xz) can achieve good results, using a delta filter directly on the uncompressed BMP format (.bmp.xz) can sometimes lead to even smaller files. (TIFF and PPM/PAM, when compressed, can achieve similar file sizes to .bmp.xz.) This suggests that QOI is probably not better than a plain delta filter.

It's important to note that uncompressed BMP/TIFF files are huge. This can be problematic if the decompressed data can't be streamed directly into the program's internal structures. In such cases, a large temporary buffer would be needed, wasting memory.

Drop LZ match finders

QOI_OP_INDEX essentially does length-1 LZ77 using a conceptual window that contains 64 unique pixels. When further compressed, another match finder seems to help very little.

Lasse Collin mentioned that the LZ layer cannot be disabled but it can be made really weak using xz --lzma2=dict=4KiB,mode=fast,nice=2,mf=hc3,depth=1. Let's try it.

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% =time -f '%e' xz -fk Prune_video_game_screenshot_2.qoi && stat -c %s Prune_video_game_screenshot_2.qoi.xz
0.76
2462360
% =time -f '%e' xz --lzma2=dict=4KiB,mode=fast,nice=2,mf=hc3,depth=1 -fk Prune_video_game_screenshot_2.qoi && stat -c %s Prune_video_game_screenshot_2.qoi.xz
0.27
2526664

Indeed, weakening the LZ layer improves compression speed signicantly. Now, let's test all benchmark images.

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% cat ~/tmp/qoi-weak-xz.sh
#!/bin/zsh
/tmp/p/qoi/qoiconv $1 ${1/.png/.qoi}
xz --lzma2=pb=0 -fk ${1/.png/.qoi}
xz --lzma2=dict=4KiB,mode=fast,nice=2,mf=hc3,depth=1 -c ${1/.png/.qoi} > ${1/.png/.qoi.weak-lz.xz}
% cd /tmp/dc-img/images
% ls -1 **/*.png | rush ~/tmp/qoi-weak-xz.sh '"{}"'

ruby -e 'puts "directory\tstrong\tweak\tincrease"; Dir.glob("*").each{|dir| next unless File.directory? dir;
  strong=weak=0; Dir.glob("#{dir}/*.qoi.weak-lz.xz").each{|f| weak+=File.size(f); strong+=File.size(f.sub(/\.weak-lz/,""));};
  puts "#{dir}\t#{strong}\t#{weak}\t#{(100.0*weak/strong-100).round(2)}%"
}'
directory strong weak increase
icon_512 7476640 8629900 15.42%
icon_64 708480 735036 3.75%
photo_kodak 12902852 13464072 4.35%
photo_tecnick 213268188 217460392 1.97%
photo_wikipedia 86679696 88609716 2.23%
pngimg 193382668 206679224 6.88%
screenshot_game 218915316 234889060 7.3%
screenshot_web 21321460 24820020 16.41%
textures_photo 28967008 31249492 7.88%
textures_pk 54117600 57956168 7.09%
textures_pk01 14950836 15749556 5.34%
textures_pk02 82279000 87747576 6.65%
textures_plants 43681548 45494084 4.15%

This size increase is small for certain directories but quite large for the others. For the directories with small size increases, relying purely on delta coding and a fast entropy encoder will give a strong competitor.

The Dark Horse of the Image Codec World: Near-Lossless Image Formats Using Ultra-Fast LZ Codecs remarks that fast LZ can make strong contenders.

PNG

The PNG International Standard defines the compression method 0 as DEFLATE with a sliding window of at most 32768 bytes. Technically new compression methods can be defined, but that would break compatibility of existing decoders and stakeholders would just resort to new image formats. However, it would be a nice experiment to check that after the compression part is improved, how PNG compares with newer image formats.