Color halftoning of images

Suppose we have a 24-bit, so-called true color, image. We want to make a color hardcopy of it using an ink jet printer. Since the printer can only drop discrete dots of inks, the palette of the printed image is severely restricted compared to that of the original image. The original image has 2**24 colors whereas the typical printed image only has five (cyan, magenta, yellow, black, and white) colors if the printer has four ink wells. Newer printers have six ink wells. How much better are these printers?

I took an original image, that of a rose, and quantized it to different palettes

"CMYK 4-color": Cyan, Magenta, Yellow, Black, White
"CcMmYK 6-color": Cyan, cyan, Magenta, magenta, Yellow, Black, White
"Optimal 6-color": 6 colors chosen using Heckbert's median cut algorithm
"RGBK 4-color": Red, Green, Blue, Black, White

The "4-color" palette is the standard 4-color ink jet palette.

In the "6-color" palette, I duplicated the magenta and cyan colors and reduced the duplicates' intensities by half. I believe this is similar to Epson's 6-color printers, except of course I cannot be sure that their additional colors' intensities are exactly half of those of the original colors.

Suppose we can choose whatever ink colors we want to. What is the best result? Heckbert's median cut algorithm is widely considered to be the optimal method. The "optimal 6-color" palette was chosen by searching for six colors using Heckbert's algorithm. This palette uses the same number of ink wells, viz. six, as the "6-color" palette.

The "RGB 4-color" palette is simply one with the primary colors and black.

Before we see the results, here are a few cautionary notes.

I used Floyd-Steinberg halftoning to dither the quantization noise. Floyd-Steinberg's algorithm is one of only two algorithms known to me for dithering with a fixed palette.
In all likelihood, these images are shown at approximately 72 dpi on your monitor. You will see grains and individual dots. Bear in mind that typical printers have resolutions from 4 to 10 times better. You may want to step way back in your room, squint, and compare the halftone outputs. A copy of this image was printed using my 4-color, 300 dpi, HP 722C and looks just fine hanging in my office.
The images are in the JPEG format on this web page. There may be some distortion, although I used the highest quality factor when encoding them. Contact me if you want the files in other formats (Tiff, PPM, etc.).


Original "true color" image. It was digitized to 8-bits per color and contains 26,066 distinct colors.	Quantized to "RGB 4-color" palette.

Quantized to "CMYK 4-color" palette.	Quantized to "CcMmYK 6-color" palette.

Quantized to "Optimal 6-color" palette. No halftoning was performed.	Quantized to "Optimal 6-color" palette.

For this particular image, the palette chosen using Heckbert's algorithm did not perform well. The "arbitrary" palettes (CMYK, RGBK, etc.) did better.

The "6-color" palette did better than the "4-color" palette. Six colors can cover more of the color space. This can in fact translate to better spatial resolution. Consider the almost vertical left edge of the bottom-most petal. The "CcMmYK" output is better defined than the "CMYK" or "RGBK" output. The other petals, most notably the second outermost one from the left, appear sharper. Also, the faint vertical streak near the upper left corner is an out of focus banana plant trunk. The "CcMmYK" halftone rendered that better than the other two.

Henry Chu 3.II.2000