ECE 638: Principles of Digital Color Imaging Systems Lecture 12: Characterization of Illuminants and Nonlinear Response of Human Visual System

Synopsis Characterization of illuminants Review of model for HVS and light interaction with surfaces Development of black body radiator concept Correlated color temperature Artificial sources and CIE standard illuminants Nonlinear Response of Human Visual System Weber’s law Gamma correction CIE uniform color spaces

Review of HVS color model Trichromatic Stage Opponent Color Stage Wandell’s Model Equivalent Representation for Trichromatic Stage: CIE XYZ (standard space for Colorimetry)

Review of Stimulus Model Seeking a more compact parameterization of Stimulus Model:

Development of black-body radiator* Imagine an experiment in which you heat up various structures made of different materials to a fixed temperature to see which combination radiates the most energy. Example: Most efficient possible absorber is a small aperture in a hollow cylinder When heated, this becomes a black body radiator (BBR) with spectral power distribution Planck’s law describes power for a BBR at any given temperature (see W&S, p13) * This material is taken from Wyzecki and Stiles

Spectral power distribution for black body radiator text

Relative spectral power distribution of black body radiator text

Example (cont.) -- Chromaticity for a BBR at some temperature T. How to relate BBR to real-world stimulus? For each temperature T, compute the CIE XYZ coordinates of a BBR emitting light when heated to temperature T. -- Chromaticity for a BBR at some temperature T. --Chromaticity for a phase of daylight. Hypothetical arrangement of chromaticity points for BBR and daylight. The next slide shows what it actually looks like. “Phases of daylight” refer to different conditions of sky (i.e. cloudy or not, shading of observer from direct sun, and time of day

Daylight locus text

Spectral power distribution of daylight text These curves are based on a principal components expansion of a family of actual daylight power spectra. Two such power spectra are shown on next slide.

Two phases of real daylight

Spectral power distribution of tungsten text

Relative spectral power distribution of fluorescent sources text

Summary of Daylight Characteristics Daylight behaves a lot like a BBR Each phase of daylight can be correlated with a BBR operating at unique temperature. More generally, this can be done for any illuminant. examples: 1) sun+total sky (clear overcast) 5000k7000k 2) daylight from north sky >7000k 3) daylight from sun disk only <5000k

Artificial Sources and CIE Standard Illuminants 1) tungsten behaves like a BBR at lower T than daylight 2) flourescent only somewhat (See W&S) CIE Standard Illuminants Older A,B,C (not used much today)

Synopsis Characterization of illuminants Review of model for HVS and light interaction with surfaces Development of black body radiator concept Correlated color temperature Artificial sources and CIE standard illuminants Nonlinear Response of Human Visual System Weber’s law Gamma correction CIE uniform color spaces

Probit Analysis Overall HVS model thus far is linear Psychometric function Question: Does Bag in right hand weigh more than Bag in left hand? Yes or No? Probit Analysis 0.5 Threshold level stimulus Slope measure of sensitivity # of books in right hand when # of books in left hand is fixed

Weber’s Law Weber’s Law: Vision Stimulus Increment Total Stimulus constant Weber’s Law: Vision Source: D.E. Pearson, Transmission of Pictorial Information Threshold for a difference is ~ Subject adjusts until they see a difference Luminance:

Weber’s Law Application Quantization – space quantization levels non-uniformly as a function of luminance What does Weber’s law suggest: Integrating, we get Suggests that we should quantize L so that levels are farther apart as L increases Just perceivable difference in brightness constant

Weber’s Law Application (cont.) Two possible implementations: 1) non-uniform quantization directly 2) process with a non-uniform mapping then quantize uniformly How does this get used? 1) Gamma 2) CRT (Cathode Ray Tube) D/A Digital Value DV Voltage V Electron Gun Y DV~V Phosphor

Gamma Correction and Limitations of Weber’s Law DV = captured luminance Limitations of Weber’s Law “Happy Coincidence”

Summary of impact of gamma in imaging systems and image processing According to trichromatic model for HVS, cone responses are linearly related to incident photon count: This model is also applicable to image capture devices – scanners, cameras. However, the output from these devices is generally gamma-corrected to account for Weber’s Law and in anticipation of the power-law behavior of output devices – displays and printers.

Gamma Correction Typical value (sRGB): RGB captured image in linear space (linear RGB) Gamma-corrected output from cameras and scanners (assuming 8 bits/channel) (This is the default.) Typical value (sRGB):

Gamma Uncorrection What displays and printers do (generally hidden from user) Similar relationships hold for CIE X and CIE Z components So gamma correction means raise to power Gamma uncorrection* means raise to power *This is also called degamma-ing the image

Implications for Image Processing If you want to convert an image to CIE XYZ, and thence to a uniform color space, such as CIE L*a*b*, you must first gamma uncorrect it. If you want to halftone an image, you must first gamma uncorrect it. If you want to display or print an image that you have processed in a linear space (pixel values proportional to photon count), you must first gamma correct it. Note that a binary halftone image would have values 0 or 255 only; so gamma correction of the halftone image has no effect.