1. ECE 638: Principles of Digital Color Imaging Systems
Lecture 10: Discrete Wavelength Models
Characterization of Human Visual Subspace

2. Synopsis
Review of discrete wavelength model

3. Discrete-wavelength trichomatic model
Stimulus
Sensor response
Response of the i-th channel
Define
Span(S) defines HVS subspace
Stack sensor outputs

4. Definition of projection operator
Projection operator is a linear operator that extracts the fundamental component of the stimulus , i.e.
Equivalent forms of projection operator

5. Extraction of fundamental component of stimulus: an imaging systems interpretation
A complete imaging system can be thought of as a capture device followed by a display device.
The process of extracting the fundamental component of the stimulus can be viewed in this way
Sensor
Display

6. Questions about the human visual subspace
Question 1: Are there real stimuli that are invisible?
Answer: “No”
Question 2: Are there real stimuli for which ?
Not yet answered
Question 3: What colors in the fundamental space are physically realizable with the addition of a black space component, i.e. what colors have a physically realizable metamer?
Fundamental component must be a non-negative linear combination of the columns of the projector operator

7. Orthonormal basis for R
It can be shown (see Appendix A of Wolski’s paper) that the projection operator can be expressed as
where is a 31x3 matrix whose columns form an orthonormal basis for the human visual subspace
Thus the fundamental component of any stimulus can be expressed as

8. Transformation between color matching matrix AXYZ and basis functions F

9. Orthonormal basis functions F and a realizable metamer
text
Realizable metamer to F
F spectral basis set

10. Columns of R (fundamental components of monochromatic stimuli) in F-space
Columns of R in F-space
Non-normalized
Columns of R in F-space
Normalized to unit length
Points indicate fundamental component of spectral locus
Solid arcs show octant of unit sphere. Dashed line is “purple line”

11. Elements of fundamental space realizable without a black-space component – start with cone functions
Cone functions reported by Vos and Walraven
Vos and Walraven cone functions in F-space
Since cone functions are non-negative and span human subspace by definition, they are realizable without a black-space component.
Points in convex hull of
correspond to stimuli realizable with no null-space component

12. Expansion of set of directly realizable colors by region-growing
F-space representation of all realizable colors
Spectra corresponding to labeled points on left
Colors inside inner dotted region are realizable without a black-space component. Colors outside this region, but inside outer dotted region are realizable only with a black-space component.