Administrivia Assignment 2 available now - back to programming - - PowerPoint PPT Presentation

C OMPUTATIONAL A SPECTS OF D IGITAL P HOTOGRAPHY Light & Color (continued) Wojciech Jarosz wojciech.k.jarosz@dartmouth.edu

Administrivia Assignment 2 available now - back to programming - due next Wednesday CS 89/189: Computational Photography, Fall 2015 2

Last time… Light & Color - Physics background - Color perception & measurement - Color reproduction - Color spaces CS 89/189: Computational Photography, Fall 2015 3

What is light? CS 89/189: Computational Photography, Fall 2015 4

Spectral distribution function (SPD) Light can be a mixture of many wavelengths - SPD: intensity as a function of wavelength over enter spectrum CS 89/189: Computational Photography, Fall 2015 5

Light-matter interaction × = CS 89/189: Computational Photography, Fall 2015 After a slide by Frédo Durand Foundations of Vision , by Wandell 6

Physical light to perceptual color ? Physical Perceptual CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 7

The eye as a measurement device near fovea away from fovea CS 89/189: Computational Photography, Fall 2015 8

A simple light detector model n ( λ ) p ( λ ) Z X = n ( λ ) p ( λ ) d λ CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 9

Light detection math Z X = s ( λ ) r ( λ ) d λ detector’s sensitivity measured signal input spectrum Z S = r S ( λ ) s ( λ ) d λ Z M = r M ( λ ) s ( λ ) d λ Z L = r L ( λ ) s ( λ ) d λ CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 10

Start with infinite Stimulus 
 number of values 
 (arbitrary spectrum) (one per wavelength) Response curves Multiply End up with 3 values Integrate (one per cone type) 1 number 1 number 1 number

Linear algebra interpretation L M S Input CS 89/189: Computational Photography, Fall 2015 After a slide by Matthias Zwicker 12

Linear algebra interpretation L M S Input cone sensitivities CS 89/189: Computational Photography, Fall 2015 After a slide by Matthias Zwicker 13

Linear algebra interpretation L M S Input * cone sensitivities input spectrum CS 89/189: Computational Photography, Fall 2015 After a slide by Matthias Zwicker 14

Linear algebra interpretation L M S Input Tristimulus response is a = * matrix-vector multiplication tristimulus 
 response cone sensitivities input spectrum CS 89/189: Computational Photography, Fall 2015 After a slide by Matthias Zwicker 15

Cone responses to a spectrum s Integral notation: Matrix notation: Z S = r S ( λ ) s ( λ ) d λ = r S · s       | S r S Z M = r M ( λ ) s ( λ ) d λ = r M · s M r M s  =      | L r L Z L = r L ( λ ) s ( λ ) d λ = r L · s r S , r M and r L are N -dimensional vectors, where N ¡= ¡∞ CS 89/189: Computational Photography, Fall 2015 16

Physical light to perceptual color       | S r S M r M s  =      | L r L Physical Perceptual CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 17

Basic fact of colorimetry Take a spectrum (which is an infinity of numbers) Eye produces three numbers (a projection to 3D) This throws away a lot of information! - many spectra can produce same S, M, L tristimulus values! - metamers - affected by illuminant CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 18

Warning: tricky thing with color Cone responses overlap & are not orthogonal! Basis functions for analysis - eyes, cameras are different than for synthesis - lights, monitors The RGB in your camera is different than 
 the RGB in your monitor! CS 89/189: Computational Photography, Fall 2015 After a slide by Frédo Durand 19

Color reproduction (the right way) We want to compute the combination of R, G, B that will project to the same visual response as s CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 20

Color reproduction as linear algebra What color do we see when we look at the display? - Feed C to display B C CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 21

Color reproduction as linear algebra What color do we see when we look at the display? - Feed C to display - Display produces s a L M RGB C CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 22

Color reproduction as linear algebra What color do we see when we look at the display? - Feed C to display - Display produces s a - Eye looks at s a and produces E E = M SML M RGB C       S r S · s R r S · s G r S · s B R M r M · s R r M · s G r M · s B G  =      L r L · s R r L · s G r L · s B B CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 23

Color reproduction as linear algebra Goal of reproduction: visual response to s and s a is the same: M SML s = M SML s a Substitute in expression for s a ¡ , M SML s = M SML M RGB C C = ( M SML M RGB ) − 1 M SML s color matching matrix for RGB CS 89/189: Computational Photography, Fall 2015 After a slide by Steve Marschner 24

Meaning of these curves/rows Monochromatic wavelength λ can be reproduced with: 
 b ( λ ) amount of the 435.8nm primary, 
 + ¡ g ( λ ) amount of the 546.1 primary, 
 + ¡ r ( λ ) amount of the 700 nm primary Negative light required? CS 89/189: Computational Photography, Fall 2015 25

CIE XYZ color space Linear algebra to the rescue! Purely positive basis functions Linear transformation of CIE RGB Non-physical primaries CIE XYZ CIE RGB       X 0.49 0.31 0.20 R 1 Y G 0.17697 0.81240 0.01063  =      0.17697 Z 0.00 0.01 0.99 B CS 89/189: Computational Photography, Fall 2015 26

CIE XYZ color cone 3D spaces can be hard to visualize Chrominance is our notion of color, as opposed to brightness/luminance Recall that our eyes correct for 
 multiplicative scale factors - discount light intensity CS 89/189: Computational Photography, Fall 2015 27

Chromaticity Diagram

The CIE xyY Color Space Chromaticity (x,y) can be derived by normalizing the XYZ color components: X Y x = y = X + Y + Z X + Y + Z - (x,y) characterize color - Y characterizes brightness Combining xy with Y allows us to represent any color Plotting on xy plane allows us to see all colors of a single brightness CS 89/189: Computational Photography, Fall 2015 29

CIE Chromaticity Chart Spectral colors along curved boundary Linear combination of two colors: line connecting two points Linear combination of 3 colors span a triangle (color gamut) CS 89/189: Computational Photography, Fall 2015 30

CIE RGB Color Space Color primaries at: 
 435.8, 546.1, 700.0 nm CS 89/189: Computational Photography, Fall 2015 31

Color Gamuts values ce ut CS 89/189: Computational Photography, Fall 2015 32

CIE Chromaticity Chart Features White Point Dominant wavelength Inverse color A’ A B CS 89/189: Computational Photography, Fall 2015 33

Perceptually-Uniform Color Spaces All these color spaces so far are perceptually non- uniform: - two colors close together in space are not necessarily visually similar - two colors far apart are not necessarily very different! Measuring “perceptual distance” in color spaces important for many industries Experiments by MacAdams CS 89/189: Computational Photography, Fall 2015 34

MacAdams Color Ellipses Test patches CS 89/189: Computational Photography, Fall 2015 35

CIELab and CIELuv Color Spaces Two attempts to make a perceptually-uniform color space MacAdams ellipses become nearly (but not perfectly) circular CS 89/189: Computational Photography, Fall 2015 36

Higher-level color perception

Higher-level color perception Color perception is much more complicated than response of SML cones… Visual pathway - A lot happens after the cones - But: cone responses are input to further processing CS 89/189: Computational Photography, Fall 2015 38

Color constancy Also known as chromatic adaptation Color of object is perceived as the same even under varying illumination For example: - A white sheet of paper under green illumination is still perceived as white, even though the reflected light is green! The human brain infers the white color from the context, which is “green-ish“ too because of the green illumination. CS 89/189: Computational Photography, Fall 2015 39

Color constancy CS 89/189: Computational Photography, Fall 2015 40

blue and black? or white and gold?

Color constancy failure http://xkcd.com/1492/

Hering’s opponent process theory (1874) After sensing by cones, colors are encoded as red versus green, blue versus yellow, and black versus white Physiological evidence found in the 1950s + + + 0 0 0 - - - Red/Green 
 Blue/Yellow 
 Black/White 
 Receptors Receptors Receptors CS 89/189: Computational Photography, Fall 2015 43