“圆形”颜色值到最近的一小组颜色 [英] "Rounding" colour values to the nearest of a small set of colours

问题描述

前置

作为项目的一部分，我正在努力提供一种方便的方法来搜索图片我们的系统。我们目前通过各种类型的用户添加的元数据（例如标题，描述，关键字）和我们提取的各种元数据（例如EXIF，IPTC，XMP等）提供搜索。

该项目使用PHP，我们可以使用Imagemagick扩展来分段并量化图像并从图像中提取最重要的颜色;我不完全确定我在这里的结果，但他们似乎相当准确，肯定比没有更好。

问题

我遇到的困难是将这些重要的颜色转换成一组代表性的颜色，例如当您查看建模空间，并使用这些算法之一计算距离。 / a>。原理与上述两种情况相同，只是算法更复杂。

Preamble

As a part of a project I'm working on I am trying to provide a convenient way to search for images in our system. We currently provide searching by various types of user added metadata (e.g. title, description, keywords) and by various metadata which we extract (e.g. EXIF, IPTC, XMP, etc). I would also like to add a "colour search" similar to what you can see in google's image search.

The project uses PHP and we can use the Imagemagick extension to segment and quantize the image and extract the most "significant" colours from the image; I'm not entirely certain of the results I'm getting here, but they seem reasonably accurate and certainly better than nothing.

The Problem

The bit that I'm having difficulty on is converting these significant colours into a set of representative colours, e.g. when you look at Google's image search there is a set of 12 colours there. I'd like to mathematically "round" my colour value to the nearest representative colour, so that I can index the image with the colours that I detect and then facet my search results that way.

Any suggestions?

解决方案

The first step would be to define the colors you want to compare to.

The second step is to find the smallest distance from your color to one of the colors you chose in the previous step. In order to be able to measure that distance you need an Euclidian space in which to model colors.

Of course the simple choice would be to the RGB space

And the distance between two colors C₁(r₁, g₁, b₁) and C₂(r₂, g₂, b₂) would be

sqrt( (r₁ - r₂)² + (g₁ - g₂)² + (b₁ - b₂)² ).

But if you need more precision it would be better to use the Hue-Chroma-Lightness bicone space, a derivative of the HSL cylinder.

In the RGB space things were straight forward as R, G and B where each on a separate axis. In HCL we need to compute the coordinates on each of the axis.

First of all we compute the chroma (which is a bit different from saturation) as:

Chroma = max(Red, Green, Blue) - min(Red, Green, Blue)

Then we normalize our H, C and L value so that H goes from 0 to 2 (to cover a circle if we multiply by PI and take radians as the unit), C goes from 0 to 1 (the radius of the trigonometric circle) and L goes from -1 (Black) to 1 (White).

Next we take z = L without any transformations as it is clear from the image that it goes along the vertical axis.

We can easily observe that for a color, Chroma is the distance from the z axis and Hue is the angle. So we get

x = C * cos(H*PI) and
y = C * sin(H*PI)

At this point x, y and z will all be in [-1, 1] and the distance between two colors will be, using the same formula as above,

sqrt( (x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)² ).

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To get even more precision and find the closest color according to human color perception you could use the CIE-L*ab modeling space and compute the distance with one of these algorithms. The principles are the same as for the two cases presented above, only the algorithms are more complex.

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