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JPPalus dc0b3c03aa maj 3 years ago
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Slim down your color space

Octrees are used in color quantization to divide the image color space into nested clusters. The deepest clusters are the leaves and they represent only one color. Upper nodes represent the average color of their children, taking into account the pixel count of each color. The octree is pruned until the desired number of color is reached, the remaining leaves forming the palette colors.

The method used to decide where to reduce the octree is roughly the one described in this imagemagick document. An error value is assigned to each node, and using heap sort, nodes with higher error values are folded in priority. The error value of a node is the sum of the differences between its average color and the color of its children (themselves also being average colors unless they are leaves). The difference between two colors is evaluated to the sum of squared differences between each channel, weighted by rough YUV-ish coefficients.


Dithering uses an error-diffusion Floyd Steinberg matrix. When applied, instead of browsing the pruned octree to find the palette color matching an original color, the original color must be compared to each color in the palette in order to find the closest match, using the same color difference formula described previously. This is because error diffusion will create new pixel values not included in the original image, therefore new colors that may not belong to any of the clusters in the octree.

Note that even without using dither, looking for the closest palette color yields better results than browsing the octree. The downside of this method is a major slowdown, as what was before a 8-step operation (the maximum depth of the octree) performed on each pixel becomes a 256-step operation.


Click for full-scale image

Photographic image:

Original 256 colors 256 colors dithered ImageMagick
859 kB 231 kB 287 kB 336 kB

Synthesized image:

Original 256 colors 256 colors dithered ImageMagick
454 kB 89 kB 130 kB 195 kB

ImageMagick command: convert in.png -colors 256 png8:out.png

Sample images from


Reducing an octree node means folding all its leaves onto itself. It is not possible to "partially" fold a node and preserve some of its leaves. As a consequence, it may not be possible to fill the palette with the exact number of colors wanted. This becomes obvious when setting a maximum number of colors lower than 8, which will always yield a palette of only 1 color: the average color of the image.

Limiting the octree depth can provide a performance gain (negligible when using dither), but also impact the chosen palette color. On some images (such as our second sample image), setting a lower depth may give results that are more visually pleasing.