Color Spaces and Distances

13 important questions on Color Spaces and Distances

What is the challenge that a color space aims to tackle?

To represent colors in a datastructure.
And additionally as well attempt to describe it in such a way to describe similarity between pixels, thus colors. And this is something more subjective to the human mind.

How does light correspond to visual interpretation?

Wavelength corresponds to color and amplitude corresponds to intensity.

Describe the RGB color space format

Red, Green, Blue, three colors three dimensions
Additive color space
Intensity relies on all three dimensions
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Describe the HSV color space format

Hue, Saturation, Value
Hue describes color
Saturation grayness
Value the intensity

Saturation doesnt carry much information and can therefore oftentimes be neglected

Why is the CIELAB color space an effective data format to use in consideration of color correction?

We can easily describe a color in two dimensional space.
Its like HSV on steriods

Describe the single channel color value distance between two respective pixels A and B

D = | A - B |

Describe the formula to compute the distance between two pixel colors with the L1 Manhatten distance function

Sum the three single-channel distances

Describe the formula to compute the distance between two 3-channel pixel values with the L2 Euclidean distance function

First, per channel, compute the single-channel distance.
Then, sum the results of the three channels
Last, take the squared root

How can we decide on whether there is similarity between a single pixel in consideration of a group of pixels?

By first computing the Gaussian distribution for the group of pixels, we obtain the mean and the the standard deviation.
Then we can compute the distance of the single pixel to the mean pixel color, and we see if its appearance is within the threshold (of similarity).

In the comparison of a pixel to a group of pixels, what does a low variance in the Gaussian distribution imply for the acceptance rate?

Decreasing variance implies the similarity within the dataset is higher. In consideration of a different pixel it will have a higher tendency to deviate, and the chance of getting rejected increases, also the threshold of acceptance is more strict.

Describe the Mahalanobis distance function in order to compute the distance of a three-channel pixel color value to the Gaussian distribution of a pixel set.

Per pixel color channel, we take the one-channel distance of the pixel and the mean for that channel. This we square and divide by the standard deviation of that color channel. We sum the results on the three channels and take the square root of this.

What does the standard deviation describe about a Gaussian distribution?

It describes in combination with the mean value, the range of the distribution in which 2/3 of the data set is present.
Twice the standard deviation describes where 19/20 of the data recides.
Triple the standard deviation describes where 997/1000 of the data recides.

Name a few approaches to play with the color distance computation.

  • Omit channels from the distance
  • Scale distances differently per channel, or apply different thresholds in the case of the Mahalanobis distance function
  • Adapt threshold based on HSV intensity

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