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Four features from three dimensions?

  1. Sep 25, 2013 #1
    Hi math fans,

    Only me, I have been asked to do the seemingly impossible and find away of distinguishing four signals from three dimensional space.

    Any ideas guys - left me stumped.

    Thanks for thinking about it anyway


  2. jcsd
  3. Sep 25, 2013 #2


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    You are going to have to be more specific. For example if each of your signals is just a random vector lying in different subspaces of R3 then this is a fairly easy problem.
  4. Sep 25, 2013 #3
    Apologies for the quick post.

    I have an image that contains four different components - with two lying in one plane and the other two lying in the opposite direction.

    I can quite easily separate the two planes but can separate within plane so easily and I was hoping that someone might have a bright idea.

  5. Sep 25, 2013 #4


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    I have no idea what you mean by "other two lying in the opposite direction". "Opposite direction" to what? To the first two "components"? Are you assuming the planes are parallel? And what are these "components" that they have a "direction" or can lie in a plane?
  6. Sep 25, 2013 #5
    Thank you for your reply.

    I have an image that is composed of four different colours.

    In the beer lambert colour space, two of the features of interest lie next to one another and the two remaining colours share a similar relationship but in a different direction to the first two.

    This almost makes a v in the feature space (not a perfect v).

    Does this help?
  7. Sep 25, 2013 #6


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    Not very much. I don't know what "lie next to one another" means, nor do I know what "share a similar relationship but in a different direction" means. If you can be more specific in your description, that would be helpful.

    I know a little about color schemes as used in computers, but Beer-Lambert is a new one to me. One scheme is RGB, in which the color for a pixel is represented by a vector whose components are the red value, the green value, and the blue value. There are different arrangements, with different numbers of bits used for the colors.

    Another scheme is aRGB, which can be thought of as a vector in four dimensions. IIRC, there are 8 bits each for alpha (transparency), red, green, and blue.

    I did a quick search for "Beer-Lambert color space" and didn't get anything specific to that, but a lot of hits on Beer-Lambert law, and variations of that name.
  8. Sep 25, 2013 #7


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    What do you want to do with the image? Finding the regions of those colors looks trivial, if you really just have four colors in the whole image.

    If every color in the image is a mixture of those four colors, there is (in general) no way to recover the mixture information without ambiguity if your color space is three-dimensional.
  9. Sep 25, 2013 #8
    think again

    http://www.researchgate.net/publication/227540537_Blind_decomposition_of_lowdimensional_multispectral_image_by_sparse_component_analysis [Broken]
    Last edited by a moderator: May 6, 2017
  10. Sep 25, 2013 #9


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    As far as I can see, that method uses additional assumptions about the image (like correlations between pixels in an image and so on). Assumptions you did not specify here.

    Why don't you use the method described there?
  11. Sep 26, 2013 #10
    Sorry, I just read back my post. It was quite abrupt - I apologise about that, I was just excited that I found a paper that seemed to do something that I have been trying todo. I will have ago at implementing the paper and if successful I will put something on the Matlab file exchange as I believe this multimixing problem might be applicable to a large variety of things.

    Thank you for your help
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