# Defining more than routine 3-axis "Color Space" from a camera imaging system..

#### Asher Kelman

##### OPF Owner/Editor-in-Chief
Defining more than routine 3-axis "Color Space" from a camera imaging system..

Does the color map have to be in 3D space? Is it possible one could use other transforms that would allow more complete representations. IOW, is it possible that one can add more axes, even though we couldn't view them in mathematical models?

Asher

#### Doug Kerr

##### Well-known member
Hi, Asher,

Does the color map have to be in 3D space? Is it possible one could use other transforms that would allow more complete representations.

It is generally accepted that, for homo sapiens (certainly not for many other species), the sensation of color is three-dimensional (in the mathematical sense): three values are sufficient to specify a color, and thus we can "plot" color in a three-axis space. And no space with more than three dimensions can do a better job of "specifying" a color - can give a "more-complete representation".

Bu that is not to say that other transforms (mathematically-redundant) cannot help us to better grasp the significance of color, or the working of color-handling chains.

A parallel in another realm is this. If we have a vessel that is a closed cylindrical cylinder, we can completely describe it (physically) in terms of two parameters, perhaps length and diameter. But, in a catalog of cylindrical air tanks, it is certainly useful to state perhaps length, diameter, and volume (and in a setting where this would be of any consequence, perhaps surface area as well).

In engineering, this is spoken of as "over-specifying" the vessel: we dare not, in specifying the construction of one, give length, diameter, and volume, not just because it is not needed, but because our values may conflict.

But when our purpose is to describe, rather than specify, this can in fact be very useful.

Another parallel is this. We can completely define the location of a point on the earth's surface in terms of its latitude and longitude. But it may be very useful, in describing the location of a radio tower, to not only describes its location in terms of latitude and longitude, but also in terms of coordinates in a mapping system, and also in terms of its location as a certain distance off the the side of the centerline of a particular highway at a certain milepost.

Now, can we think of a six-dimensional space in which the axes are:
• Latitude and longitude
• Easting and Northing on a grid
• Milepost and offset distance on some stated highway.

Yes, we can. But not all points in such a space are valid - only those whose latitude and longitude coordinates are consistent with their Easting and Northing coordinates and with their milepost and offset coordinates. That's actually only a tiny fraction of all the points in the space.

Since a six-dimensional space has no physical realization, I cannot describe this "sparse" space as comprising, for example, only a bunch of little threads. But it is conceptually much like that.

To get back to something we can better visualize, let's return to our universe of air tanks, for which we can have a length, a diameter, and (not independently) a volume. If we imagine a three dimensional space on which we will plot all available (or even all possible) air tanks, we find that they all must lie on a surface - the surface the satisfies the mathematical relationship between diameter, length, and volume. So it is really only a "two dimensional plot on a non-flat surface". But it could still be very useful to the connoisseur of air tanks.

Now as to what kind of "over-specified" color model might be valuable to us, we would first have to be able to articulate its objectives. In what way could we better visualize something about a color, and what, than in any three-dimensional description? What is it that we need to improve our appreciation of?

It is an interesting challenge.

Best regards,

Doug

#### Asher Kelman

##### OPF Owner/Editor-in-Chief
Hi, Asher,

......... Now as to what kind of "over-specified" color model might be valuable to us, we would first have to be able to articulate its objectives. In what way could we better visualize something about a color, and what, than in any three-dimensional description? What is it that we need to improve our appreciation of?

It is an interesting challenge.

Best regards,

Doug

What about descriptors of image quality of an actual output of a camera such as

• accuracy

• transitions between colors

• uniformity

• bias

of an image of a giant standard perfect color wheel in lights of different spectral makeup.

Asher

#### Doug Kerr

##### Well-known member
Hi, Asher,

What about descriptors of image quality of an actual output of a camera such as

• accuracy

• transitions between colors

• uniformity

• bias

of an image of a giant standard perfect color wheel in lights of different spectral makeup.
What you are speaking of is not a set of criteria for an enhanced color space but rather the matter of how to present, in a report, a gigantic, multidimensional body of data taken from an extensive series of tests on one or more cameras - quite a different matter.

Regarding a "color wheel" as the test target, note that no two-dimensional target can represent all colors - even all colors within some restricted gamut.

You can make a color wheel that exhibits, for example, all hues over some range of saturations (perhaps different by hue) at a uniform luminance, or some other two-dimensional subset of the color space.

Best regards,

Doug

#### Asher Kelman

##### OPF Owner/Editor-in-Chief
Hi, Asher,

What you are speaking of is not a set of criteria for an enhanced color space but rather the matter of how to present, in a report, a gigantic, multidimensional body of data taken from an extensive series of tests on one or more cameras - quite a different matter.

That would be the idea. A stack of wheels at reasonable intervals would be needed. Then another with the axes swopped.

Asher

#### Jeremy Waller

##### New member
Hi Asher,

Re: Does the color map have to be in 3D space?

If you have 3 primary colours thats it - 3-space. Any colour is a linear combination of the 3 primary colours.

To produce a colour picture we have 3 planes each plane being an (n x m) matrix where n and m are the size of the image in pixels.

The following are defined in the 3-space.

* accuracy

* transitions between colors

* uniformity

* bias

Eg. Transition between colours may be measured (in the physical space of the image) by considering the gradient vector but this is still in the 3D colour space. But does this have meaning? I really don't know - Iv'e not tested it!!

To represent a point in 3-space you need 3 numbers - we are use to x,y and z. OK? We may also say that this point is on the side of a cylinder - need 3 numbers in cylindrical co-ordinates !! Of course we can say that this point lies on the surface of a sphere need 3 numbers in spherical coordinates. The absolute position of the point has not changed we just find different ways of representing it.

Regards,

Jeremy,

#### Doug Kerr

##### Well-known member
Hi, Jeremy,

I'm delighted to hear of your interest in the philosophy and application of these concepts. It is an important field.

To represent a point in 3-space you need 3 numbers - we are use to x,y and z. OK? We may also say that this point is on the side of a cylinder - need 3 numbers in cylindrical co-ordinates !! Of course we can say that this point lies on the surface of a sphere need 3 numbers in spherical coordinates. The absolute position of the point has not changed we just find different ways of representing it.

Quite so, and it is in that vein that we have numerous "recognized" color models, which are different (3-dimensional) coordinate systems used to describe the "location" of a point representing a particular color.

The realm of such a coordinate system containing all colors (often said "visible colors", but of course only visible radiation has the property of color) can be, by parallel to the notion of a number space, be called the color space of the coordinate system.

But in modern times, the term color space has been hijacked to mean a fully-defined (and "recognized") three-dimensional system of describing color, revolving around a certain color model (coordinate scheme) further particularized as to the scale and nature of its coordinates (including, perhaps, nonlinear scaling of an underlying parameter), in the case of a tristimulus color model by definition of the colors of its "primaries", and so forth.

Some of these are based on a Cartesian coordinate model and some on a cylindrical coordinate model. I know of no recognized color space predicated on a spherical coordinate model.

Perhaps you have already read my extensive article, "Color and Color Spaces", available here:

http://dougkerr.net/Pumpkin#Color

Best regards,

Doug

#### Jeremy Waller

##### New member
Hi Doug,

WRT to colour in photography etc. I'm still on the learning curve - somewhere at the bottom 1/4 !!!.

Re: Some of these are based on a Cartesian coordinate model and some on a cylindrical coordinate model.

I'm sure there is a very good reason - but I don't know it. One could play games for example:

If one converts from cartesian (x,y,z) to the spherical (rho, theta, phi) the same looking colour is there but if one were to change one of the angles (theta or phi) then convert back to f(x,y,z) the colours will change in an interesting fashion - each angle will change 2 dimensions. This could make "crazy" distortions in the colours in the original picture - better than LSD lol.

Regards,

Jeremy.

#### Ted Cousins

##### Member
Hello gentlemen,

When posting about matters of color (rather than lightness or value) I prefer CIELAB a*b* or hue and saturation in HSV. I find that is about as much as most folks can take, especially those entrenched in the 3D world of RGB.

best,

Ted

#### Doug Kerr

##### Well-known member
Hi, Ted,

Hello gentlemen,

When posting about matters of color (rather than lightness or value) I prefer CIELAB a*b* or hue and saturation in HSV. . . .

It is interesting that the CIE L*a*b* color space was originally intended to be a measure of "reflective color" (that is, it would describe the color of a surface) rather than the color of light. But it was hijacked to do the latter.

HSV is a very problematical quantitative color coordinate system, but the qualitative concepts are easily understood by humans.

You might find this article of interest:

Best regards,

Doug

#### Ted Cousins

##### Member
Hi, Ted,

It is interesting that the CIE L*a*b* color space was originally intended to be a measure of "reflective color" (that is, it would describe the color of a surface) rather than the color of light. But it was hijacked to do the latter.

HSV is a very problematical quantitative color coordinate system, but the qualitative concepts are easily understood by humans.

Exactly.

You might find this article of interest:

Best regards,

Doug

Thanks, Doug, I had downloaded that one quite some time ago.

best,

Ted