Color histogram

Characteristics of a color histogram

A color histogram focuses only on the proportion of the number of different types of colors, regardless of the spatial location of the colors. The values of a color histogram are from statistics. They show the statistical distribution of colors and the essential tone of an image.

In general, as the color distributions of the foreground and background in an image are different, there might be a bimodal distribution in the histogram.

For the luminance histogram alone, there is no perfect histogram and in general, the histogram can tell whether it is over-exposure or not, but there are times when you might think the image is over exposed by viewing the histogram; however, in reality it is not.

Principles of the formation of a color histogram

The formation of a color histogram is rather simple. From the definition above, we can simply count the number of pixels for each 256 scales in each of the 3 RGB channel, and plot them on 3 individual bar graphs.

In general, a color histogram is based on a certain color space, such as RGB or HSV. When we compute the pixels of different colors in an image, if the color space is large, then we can first divide the color space into certain numbers of small intervals. Each of the intervals is called a bin. This process is called color quantization. Then, by counting the number of pixels in each of the bins, we get the color histogram of the image.

The concrete steps of the principles can be viewed in Example 1.

Examples

Example 1

Given the following image of a cat (an original version and a version that has been reduced to 256 colors for easy histogram purposes), the following data represents a color histogram in the RGB color space, using four bins.

Bin 0 corresponds to intensities 0-63

Bin 1 is 64-127

Bin 2 is 128-191 and Bin 3 is 192-255.

Example 2

Application in camera:

Nowadays, some cameras have the ability to show the 3 color histograms when we take photos.

We can examine clips (spikes on either the black or white side of the scale) in each of the 3 RGB color histograms. If we find one or more clipping on a channel of the 3 RGB channels, then this would result in a loss of detail for that color.

To illustrate this, consider this example:

1. We know that each of the three R, G, B channels has a range of values from 0-255 (8 bit). So consider a photo that has a luminance range of 0-255.

2. Assume the photo we take is made of 4 blocks that are adjacent to each other and we set the luminance scale for each of the 4 blocks of original photo to be 10, 100, 205, 245. Thus, the image looks like the topmost figure on the right.

3. Then, we overexpose the photo a little, say, the luminance scale of each block is increased by 10. Thus, the luminance scale for each of the 4 blocks of new photo is 20, 110, 215, 255. Then, the image looks like the second figure on the right.

There is not much difference between both figures, all we can see is that the whole image becomes brighter (the contrast for each of the blocks remain the same).

4. Now, we overexpose the original photo again, this time the luminance scale of each block is increased by 50. Thus, the luminance scale for each of the 4 blocks of the new photo is 60, 150, 255, 255. The new image now looks like the third figure on the right.

Note that the scale for the last block is 255 instead of 295, for 255 is the top scale and thus the last block has clipped! When this happens, we lose the contrast of the last 2 blocks, and thus, we cannot recover the image no matter how we adjust it.

To conclude, when taking photos with a camera that displays histograms, always keep the brightest tone in the image below the largest scale 255 on the histogram in order to avoid losing details.

Drawbacks and other approaches

The main drawback of histograms for classification is that the representation is dependent on the color of the object being studied, ignoring its shape and texture. Color histograms can potentially be identical for two images with different object content which happens to share color information. Conversely, without spatial or shape information, similar objects of different color may be indistinguishable based solely on color histogram comparisons. There is no way to distinguish a red and white cup from a red and white plate. Put it another way: histogram-based algorithms have no concept of a generic 'cup', and a model of a red and white cup is no use when given an otherwise identical blue and white cup. Another problem is that color histograms have high sensitivity to noisy interference such as lighting intensity changes and quantization errors. High dimensionality (bins) color histograms are also another issue. Some color histogram feature spaces often occupy more than one hundred dimensions.

Some of the proposed solutions have been color histogram intersection, color constant indexing, cumulative color histogram, quadratic distance, and color correlograms. Although there are drawbacks of using histograms for indexing and classification, using color in a real-time system has several advantages. One is that color information is faster to compute compared to other invariants. It has been shown in some cases that color can be an efficient method for identifying objects of known location and appearance.

Further research into the relationship between color histogram data to the physical properties of the objects in an image has shown they can represent not only object color and illumination but relate to surface roughness and image geometry and provide an improved estimate of illumination and object color.

Usually, Euclidean distance, histogram intersection, or cosine or quadratic distances are used for the calculation of image similarity ratings. Any of these values do not reflect the similarity rate of two images in itself; it is useful only when used in comparison to other similar values. This is the reason that all the practical implementations of content-based image retrieval must complete computation of all images from the database, and is the main disadvantage of these implementations.

Another approach to representative color image content is two-dimensional color histogram. A two-dimensional color histogram considers the relation between the pixel pair colors (not only the lighting component). A two-dimensional color histogram is a two-dimensional array. The size of each dimension is the number of colors that were used in the phase of color quantization. These arrays are treated as matrices, each element of which stores a normalized count of pixel pairs, with each color corresponding to the index of an element in each pixel neighborhood. For comparison of two-dimensional color histograms it is suggested calculating their correlation, because constructed as described above, is a random vector (in other words, a multi-dimensional random value). While creating a set of final images, the images should be arranged in decreasing order of the correlation coefficient.

The correlation coefficient may also be used for color histogram comparison. Retrieval results with correlation coefficient are better than with other metrics.

Intensity histogram of continuous data

The idea of an intensity histogram can be generalized to continuous data, say audio signals represented by real functions or images represented by functions with two-dimensional domain.

Let ${\displaystyle f\in L^1({\mathbb{R}}^n)}$ (see Lebesgue space), then the cumulative histogram operator ${\displaystyle H}$ can be defined by:

${\displaystyle H(f)(y)=\mu \{x:f(x)\le y\}}$.

${\displaystyle \mu }$ is the Lebesgue measure of sets. ${\displaystyle H(f)}$ in turn is a real function. The (non-cumulative) histogram is defined as its derivative.

${\displaystyle h(f)=H(f{)}^{\prime }}$.