# Four features from three dimensions?

• physical101
In summary, a person is asking for ideas on how to distinguish four signals in three-dimensional space. They provide more information about the signals being in different planes and in the Beer-Lambert color space. Other members suggest using certain methods and the person expresses excitement about finding a solution.

#### physical101

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

Cheers

Duane

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.

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.

Cheers

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?

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?

physical101 said:

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?
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.

physical101 said:
I have an image that is composed of four different colours.
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.

think again

http://www.researchgate.net/publication/227540537_Blind_decomposition_of_lowdimensional_multispectral_image_by_sparse_component_analysis [Broken]

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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?

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.

## 1. What are the four features in three dimensions?

The four features in three dimensions are length, width, height, and depth. These four features make up the three-dimensional space that we live in.

## 2. How do the four features in three dimensions differ from two dimensions?

In two dimensions, there are only two features - length and width. Three dimensions add an additional feature, height, which allows for objects to have depth and volume.

## 3. What is the significance of understanding four features in three dimensions?

Understanding the four features in three dimensions is important in many fields, including mathematics, physics, and engineering. It allows us to accurately describe and measure objects and phenomena in our three-dimensional world.

## 4. Can the four features in three dimensions be applied in other dimensions?

Yes, the concept of four features in three dimensions can be extended to higher dimensions. For example, in four dimensions, there would be an additional feature of time, making up the four-dimensional space-time continuum.

## 5. How can understanding four features in three dimensions be useful in everyday life?

Understanding the four features in three dimensions can help us navigate and interact with the world around us. It allows us to visualize and manipulate objects, and also plays a crucial role in fields such as architecture, design, and computer graphics.