How to choose the number of bins when creating HSV histogram?

Question

I was reading some documentation about HSV histogram, and in several refs the Saturation channel was quantized into 256 values. Why is that? Is there any reason behind choosing this number? I have the same questions for the Hue channel, often it is quantized into 180 values.

Answer 1

Disclaimer: Off-hand answers (i.e., not backed up by any documentation):

"256" is a popular number for a bin size because Programmers Like Round Numbers -- it fits in a single byte. And "180" because the HSB circle is "360 [degrees]", but "360" does not fit into a single byte.

For many image formats, the range of RGB values is limited to 0..255 per channel -- 3 bytes in total. To store the same amount of data (ignoring any artifacts of converting to another color model), Saturation and Brightness are often expressed in single bytes as well. The same could be done for Hue, by scaling the original range of 0..359 (as Hue is usually expressed as a value in degrees on the HSB Color Wheel) into the byte range 0..255. However, probably because it's easier to do calculations with a number close to the original 360° full circle, the range is clipped to 0..179. That way the value can be stored into a single byte (and thus "HSB" uses as much memory as "RGB") and can be converted trivially back to (close to) its original value -- multiply by 2. Obviously, sticking to the storage space wins over fidelity.

Given 256 values for both S and B, and 180 for H, you end up with a color space of 256*256*180 = 11,796,480 colors. To inspect the number of colors, you build a histogram: an array where you can read out the total amount of pixels in a certain color or color range. Using a color range here, instead of actual values, significantly cuts down the memory requirements.

For an RGB color image, with the colors fairly evenly distributed, you could shift down each channel a certain number of bits. This is how a straightforward conversion from 24-bit "true-color" RGB down to 15-bit RGB "high-color" space works: each channel gets divided by 8, reducing 256 values down to 32 (5 bits per channel). Conversion to a 16-bit high-color RGB space works the same; the bit that got left over in the 15-bit conversion is assigned to green. Thus, the range of colors for green is doubled, which is useful since the human eye is more perceptive for shades of green than for the other two primaries.

It gets more complicated when the colors in the input image are not evenly distributed. A naive solution is to create an array of [256][256][256], initialize all to zero, then fill the array with the colors of the image, and finally sort them. There are better alternatives -- let me consult my old Computer Graphics ^[1] here. Hold on.

13.4 Reproducing Color mentions the names of two different approaches from Heckbert (Color Image Quantization for Frame Buffer Display, SIGGRAPH 82): the popularity and the median-cut algorithms. (Unfortunately, that's all they say about this topic. I assume efficient code for both can be googled for.)

A rough guess:

The size for each bin (H,S,B) should be reflected by what you are trying to use it for. This older SO question, for example, uses a large bin for hue -- color is considered the most important -- and only 3 different values for both saturation and brightness. Thus, bright images with some subdued areas (say, a comic book) will give a good spread in this histogram, but a real-color photograph will not so much.

The main limit is that the bin sizes, multiplied with each other, should use a reasonably small amount of memory, yet cover enough of each component to get evenly filled. Perhaps some trial-and-error comes into play here. You could initially evenly distribute all of H, S, and B components over the available memory in your histogram and process a small part of the image; say, 1 out of 4 pixels, horizontally and vertically. If you notice one of the component bins fills up too fas where others stay untouched, adjust the ranges and restart.

If you need to do an analysis of multiple pictures, make sure they are all alike in their color gamut. You cannot expect a reasonable bin size to work on all sorts of images; you would end up with an evenly distribution, where all matches are only so-so.

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^{[1] Computer Graphics. Principles and Practices. (1997) J.D. Foley, A. van Dam, S.K. Feiner, and J.F. Hughes, 2nd ed., Reading, MA: Addison-Wesley.}