James Bigler: CS6650 Homework 3

Using this function L(x,y,lambda) = (y/yres) delta(lambda - (420 * (x/xres) + 380)) plotted over the domain of x:[0,512], y:[0,512]. The next question is what is lambda and how do we get RGB from these values.

Using the formulas for the CIE Tristimus values (X,Y,Z) we can eliminate lambda for the tilda functions.

X = 683 integral from lambda0 to lambda1 of (x-tilda(lambda) * L(lambda) d(lambda)
Y = 683 integral from lambda0 to lambda1 of (y-tilda(lambda) * L(lambda) d(lambda)
Z = 683 integral from lambda0 to lambda1 of (z-tilda(lambda) * L(lambda) d(lambda)

We can substitute our L above and using the dirac-delta identity (integral of x0 to x1 (f(x)delta(x-a)) = f(a) when x0 < x < x1, 0 otherwise) we get: X = 683y/yres * x-tilda (420x/xres + 380)
We look up the values of the tilta functions, and we can get X,Y,Z. We can use a simple matrix transfer to get RGB

The problem with the image now is that RGB range from [-473.816, -159.435, -144.455] to [1374.53, 1084.51, 1446.64]. Below is a list of methods of getting these values between 0 and 1, while trying to preseve most of the qualities of the function

Just Clamping

This isn't the right solution, as the colors are to vivid.

Scaling

This picks too much of the residue color around and looks washed out.

Clamp minimum to 0

Got this idea from Shaun Ramsey's page on this. It's nice, but it lacks some of the yellow, cyan, and magenta that comes from the overlap of the red, green and blue.

Maximum of 1 - Scale

Note we can see some traces of yellow, cyan, and magenta. However there is a lot of noise(white stuff) around. We will have to get these color from something else.

Min 0 - Gamma 2 - Scale

Whoa! Let's scale back on the gamma.

Min 0 - Gamma 2 - Scale

This is more like it! I think I'll take it.

Others

Max of 200 Scaled
Min of 0 Max of 500 Gamma 1.2 Scale
Min of 0 Gamma 1.5 Scale
Min of 0 Ln(x) Min of 0 Scale
Min of 0 Scale Sqrt(x)
Min of 0 Sqrt(x)
Min of 0 Sqrt(x) Scale
Ln(x)
Ln(x) Min of 0 Scale
Ln(x) Ln(x)
Ln(x) Ln(x) Ln(x)
Scale Sqrt

// this is sample code