ECE 638: Principles of Digital Color Imaging Systems Lecture 2: Foundations of Color Science

Synopsis l Briefly trace development of our knowledge of color and vision; so that we can “discover” it in a logical manner. l Explore concepts of color matching that form basis for trichromatic theory of color and colorimetry l Develop mathematical framework for trichromatic theory

Early concepts of vision l Anatomy of eye l Emanation theory l Pinhole camera l The lens l Spectrum of white light l Trichromacy Source: Robert M. Boynton, Human Color Vision, Optical Society of America, 1992, pp. 1-18

Anatomy of the human eye Early Greeks practiced dissection

Emanation theory l Empedocles (5th century BC) – the “eye is like a lantern” l Galen ( AD) –physiologist –the brain is “an organ where all sensations arrive, and where all mental images, and all intelligent ideas arise. –rays are discharged in the direction of the object, interact with the object, and return to the eye –His views remained influential for about 1500 years

Pinhole camera l Abu Ali Mohammed Ibn Al Hazen ( AD) –Experimented with simple pinhole camera –Concluded that eye contained an “image” with a point-to-point correspondence with scene under observation l Leonardo da Vinci ( ) –Developed notions of perspective –Proposed ray tracing –Hampered by hypothesis that image within eye must be right- side up

The lens l Spectacles discovered by 1285 l Used to improve pinhole camera by G. B. Della Porta in 1589 l Johannes Kepler –Astronomer –Constructed and understood lenses –Concluded that image within eye formed on retina l Aranzi cut a hole in back of animal’s eye to observe retinal image in 1595

Spectrum of white light l Newton’s experiment with prism (1730) l Concluded that white light is a mixture of colored lights l Removed color from perceived object and placed it in rays reflected from the object

Trichromacy l Color mixtures –Artisans and scientists experimented with them from ancient times –Are properties due to materials or due to perception? l Thomas Young proposed trichromatic theory in 1801 –“As it is almost impossible to conceive each sensitive point of the retina to contain an infinite number of particles, each capable of vibrating in perfect unison with every possible undulation, it becomes necessary to suppose the number limited; for instance to the three principal colours, red, yellow, and blue, that each of the particles is capable of being put in motion more or less forcibly by undulations differing less or more from perfect unison.”

Trichromacy (cont.) l Young’s ideas were ignored for over 50 years l Helmholtz revived them in his Handbook of Physiological Optics first published from 1856 to 1866

Helmholtz’s three spectral sensivity curves (1924)

Simulated retinal mosaic

Trichromacy (cont.) l “It is still impossible to the present day to show clear anatomical differences between the three cone types that are believed to exist in primates, or to extract their photo-pigments, which are believed responsible for absorption of light.” – Robert M. Boynton, Human Color Vision, 1992

If we cannot conclusively establish physiological properties of the human eye, how can we quantitatively work with color? Answer: we treat the human visual system (HVS) as a block box, and characterize it by its response to color stimuli.

Input-output characterization of HVS l Present subject with specially designed visual stimuli under precisely controlled conditions l Physiology –Measure chemical, electrical, or magnetic changes –Examples: neural probes, functional magnetic resonance l Psychophysics –Measure cognitive response: “I can see A” “A matches B” “A looks brighter than B”

Trichromatic theory of color l Follows directly from simple model for interaction of stimulus and three different types of receptors in the human eye. l Can be described in terms of linear vector spaces l Forms basis for colorimetry and design of many aspects of color imaging systems l Does not predict all visual phenomena

Sources l G. Wyszecki and W. S. Stiles, Color Science: Concepts, and Methods, Quantitative Data and Formulae, Wiley, 1982, pp

Development of trichromatic theory l Color matching experiment l Grassman’s laws for color matching l Spectral models for color l Surface-illuminant interaction model l Sensor model l Reinterpretation of conditions for color match

Color matching experiment – setup

Color matching experiment - procedure l Test stimulus is fixed l Observer individually adjusts strengths of the three match stimuli to achieve a visual match between the two sides of the split field l Mixture is assumed to be additive, i.e. radiant power of mixture in any wavelength interval is sum of radiant powers of the three match stimuli in the same interval l To achieve a match with some test stimuli, it may be necessary to move one or two of the match stimuli over to the side where the test stimulus is located

Trichromatic generalization “…over a wide range of conditions of observation, many color stimuli can be matched in color completely by additive mixtures of three fixed primary stimuli whose radiant powers have been suitably adjusted” l This statement is subject to a number of qualifications. See reference below for details Source: G. Wyszecki and W. S. Stiles, p. 117.

Colorimetry l “The branch of color science concerned … with specifying numerically the color of a physically defined visual stimulus in such a manner that: –when viewed by an observer with normal color vision, under the same observing conditions, stimuli with the same specification look alike,… –stimuli that look alike have the same specification –The numbers comprising the specifications are continuous functions of the physical parameters defining the spectral radiant power distribution of the stimulus” l Source: G. Wyszecki and W. S. Stiles, p. 117.

Grassman’s laws of color matching (1853) l Definitions: means “ matches ” is an additive mixture of and l Symmetry: l Transitivity:

Grassman’s laws (cont.) l Proportionality: where is a positive factor that scales the radiant power without changing relative spectral distribution l Additivity: Any two of implies that

Limitations of Grassman’s laws l Grassman’s laws provide a basic description of the results of color matching experiments l But they don’t provide: –general basis for understanding why the laws hold –a theory that can easily describe a wider range of situations

Trichromatic model l Assume simple characterizations for –illuminant –optical properties of surfaces –interaction of illuminant with surface –response of HVS to visual stimulus l All are based on spectral representations

Spectral representation of color

Interaction of illuminant and surface l At each wavelength, characterize surface by ratio of power in reflected light to that incident on surface l Reflectance l Absorptance –Absorptance includes any light that is not reflected from front surface

Limitations of interaction model – angular dependence l Does not account for dependence of spectral reflectance on –angle between incident light and surface normal –angle between reflected light and surface normal l More general model includes both specular and body reflectance terms l Complete characterization requires bi-directional reflectance function

Limitations of interaction model – scattering l Model is only valid for: –bulk (macroscopic) behavior –Microscopic behavior in which there is no lateral scattering l More complex scattering models exist

Scattering example – Yule-Nielsen effect l Lateral scattering of light within paper causes light rays that enter white paper substrate to be trapped under colorant dots l Print appears darker than predicted by fractional area coverage of colorant Ray is trapped under colorant dot

Limitations of interaction model – fluorescence l Model assumes that reflected light at any wavelength depends only on light incident at that wavelength l Does not describe interaction of light with surfaces that fluoresce –papers and fabrics containing whiteners or brighteners –human teeth