


Five Examples for Comparison 
An Exception that Proves the
Rule: Foveon X3 and Optional Prefilter 
Rcam = RCohen(rgbSens)
CamTemp = Rcam*OrthoBasis
GramSchmidt(CamTemp, CamOmega)
rgbSens is a matrix whose
columns are the 3 camera sensor functions (in this case the Foveon
functions) .
Rcam
is the projection
matrix based on the camera functions.
OrthoBasis
is the 3
orthonormal
vectors for human, often called
Ω . CamTemp
is then the best fit to OrthoBasis
using a linear combination of the camera sensitivities. In general, the
columns of CamTemp
will not be an orthonormal set, so the GramSchmidt procedure is used
to orthonormalize them. The orthonormal basis for the camera sensors is
then CamOmega
.
That's the main result, and the camera's locus of unit monochromats is
a parametric plot of the 3 columns of CamOmega
.Foveon X3 Sensor without Prefilter 
Human Eye 
Foveon
3Color Camera Sensor 
Native
Orthonormal Basis of Foveon X3 
Fit to
Human
Orthonormal Basis by Foveon X3 functions 
Red dashed =
human LUM projected into v2v1 Black solid = same projection of Foveon X3's LUM Heads of green arrows = fit to human by Foveon X3 functions, same projection. 
Red dashed = human LUM projected
into v2v3 Black solid = same projection of Foveon X3's LUM Heads of green arrows = fit to human by Foveon X3 functions, same projection. 
Click to see the LUM for Foveon X3 (without prefilter) graphed in 3 dimensions! 
Foveon X3 Sensor with Prefilter 
Same Foveon
X3 Sensors
as Before 
This
Prefilter^{3} Will Narrow the Functions and Reduce Overall Sensitivity in the BlueGreen Region 
Foveon X3
Sensors Multiplied by the Prefilter Function^{3} 
Cone
Sensitivities Consistent with 2º Observer 
The thicker curves are the
orthonormal basis for the Foveon X3 sensors with prefilter. The "fit
first" method acts here to give a good alignment of the camera LUM with
human LUM. 
Fit to Human Orthonormal Basis by Prefiltered Foveon X3 functions. The best fit was found from the orthonormal basis at left. The best fit should come out the same whether the orthonormal basis is derived by the "fit first" method or not. In fact, the fit first orthonormal basis was used. 
Red dashed =
human LUM projected into v2v1 Black solid = same projection of Prefiltered Foveon X3's LUM, found by fit first method. Heads of green arrows = fit to human by Prefiltered Foveon X3 functions, same projection. 
Red dashed =
human LUM projected into v2v3 Black solid = same projection of Prefiltered Foveon X3's LUM, found by fit first method. Heads of green arrows = fit to human by Prefiltered Foveon X3 functions, same projection. 
Click to see the LUM for Foveon X3 WITH prefilter, graphed in 3 dimensions! 
Foveon X3 Sensor with and without Prefilter 
Click to see the LUM for Foveon X3 (without prefilter) graphed in 3 dimensions! 

Click to see the LUM for Foveon X3 with prefilter, graphed in 3 dimensions! 
2°
observer himself 
Foveon X3,
no filter 
Prefiltered
Foveon X3 

Y = inv(OrthoBasis'*rgbbar) =

Y = inv(CamOmega'*rgbSens) =

Y = inv(CamOmega'*rgbSens) =


Column amplitudes = 0.0852 0.409 0.153 
Column amplitudes = 2.71 9.06 8.40 
Column amplitudes = 5.89 16.5 11.5 
Prime
Color λs 
red 
green 
blue 
2° observer  603 
538 
446 
Foveon X3 
587 
510 
430 
Foveon X3, Prefiltered 
591 
541 
442 
. 
