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So what would be the shortest explanation using concepts from linear algebra?

by 3rd3 13y ago

alok-g 13y ago
The stimulus is a spectrum. Discretizing wavelengths for simplicity of explanation, the stimulus is a vector where each element specifies the amplitude at each wavelength. The color bar of rainbow colors is a sub-sampling of this spectrum where only one element is taken at a time. In other words, those are monochromatic colors. Alternatively, each point in the rainbow is obtained by multiplying a delta function with the stimulus and integrating over the wavelengths. This sub-sampling cannot possibly cover the entire color space. In fact, the majority are missing, including magenta which is not a monochromatic color. The human eyes also sub-samples this space. However, it does not use delta functions. Each cone has its own vector (or more precisely a function of wavelength) and the sensed amplitude is integral of this vector multiplied by the stimulus. This is very much a dimensionality reduction problem where given the spectrums of natural objects around us, nature chose a smaller space that allows distinguishing the objects as much as possible. Quite obviously, the sub-sampling done by the human eye also leads to loss of information. There would be spectrums which are different but would map to the same perceived color. See metamerism: http://en.wikipedia.org/wiki/Metamerism_%28color%29 http://en.wikipedia.org/wiki/Metamerism_%28color%29 Electronic-displays use RGB because those three colors then cover a good percentage of the colors human eyes can perceive. When more than three primary colors are used in the display technology to enhance color gamut, etc., avoiding metamerism issues becomes an interesting concern as we need to make sure colors which should appear the same do not appear different given that the cone response curves varies somewhat between humans, varies with age, and also surrounding illumination can impact the two rendered colors in different ways. See also my older related comment on the topic: https://news.ycombinator.com/item?id=5931005 https://news.ycombinator.com/item?id=5931005
- pionar 13y ago
  That's not as helpful as the original article. It's all in science terms (delta functions, vectors, stimulus, discretizing wavelengths), without really explaining them.
  - ithkuil 13y ago
    it was a reply to somebody kindly asking an explanation using linear algebra concepts.

So what would be the shortest explanation using concepts from linear algebra?

by 3rd3 13y ago

So what would be the shortest explanation using concepts from linear algebra?

The stimulus is a spectrum. Discretizing wavelengths for simplicity of explanation, the stimulus is a vector where each element specifies the amplitude at each wavelength. The color bar of rainbow colors is a sub-sampling of this spectrum where only one element is taken at a time. In other words, those are monochromatic colors. Alternatively, each point in the rainbow is obtained by multiplying a delta function with the stimulus and integrating over the wavelengths. This sub-sampling cannot possibly cover the entire color space. In fact, the majority are missing, including magenta which is not a monochromatic color. The human eyes also sub-samples this space. However, it does not use delta functions. Each cone has its own vector (or more precisely a function of wavelength) and the sensed amplitude is integral of this vector multiplied by the stimulus. This is very much a dimensionality reduction problem where given the spectrums of natural objects around us, nature chose a smaller space that allows distinguishing the objects as much as possible. Quite obviously, the sub-sampling done by the human eye also leads to loss of information. There would be spectrums which are different but would map to the same perceived color. See metamerism: http://en.wikipedia.org/wiki/Metamerism_%28color%29 http://en.wikipedia.org/wiki/Metamerism_%28color%29 Electronic-displays use RGB because those three colors then cover a good percentage of the colors human eyes can perceive. When more than three primary colors are used in the display technology to enhance color gamut, etc., avoiding metamerism issues becomes an interesting concern as we need to make sure colors which should appear the same do not appear different given that the cone response curves varies somewhat between humans, varies with age, and also surrounding illumination can impact the two rendered colors in different ways. See also my older related comment on the topic: https://news.ycombinator.com/item?id=5931005 https://news.ycombinator.com/item?id=5931005

pionar 13y ago
That's not as helpful as the original article. It's all in science terms (delta functions, vectors, stimulus, discretizing wavelengths), without really explaining them.
- ithkuil 13y ago
  it was a reply to somebody kindly asking an explanation using linear algebra concepts.