1 Light and the EM spectrum The H.V.S. and Color Perception

2 What is an Image ? An image is a projection of a 3D scene into a 2D projection plane. An image can be defined as a 2 variable function I(x,y), where for each position (x,y) in the projection plane, I(x,y) defines the light intensity at this point.

3 Camera trial #1 scene film Put a piece of film in front of an object. source: Yung-Yu Chuang

4 Pinhole camera scene film Add a barrier to block off most of the rays. It reduces blurring The pinhole is known as the aperture The image is inverted barrier pinhole camera source: Yung-Yu Chuang

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6 X Y (x,y,z) ( x,y ) center of projection (pinhole) d d – focal length The Pinhole Camera Model (where) Z d

7 The Shading Model (what) Shading Model: Given the illumination incident at a point on a surface, what is reflected?

8 Shading Model Parameters The factors determining the shading effects are: –The light source properties: Positions, Electromagnetic Spectrum, Shape. –The surface properties: Position, orientation, Reflectance properties. –The eye (camera) properties: Position, orientation, Sensor spectrum sensitivities.

9 Newton’s Experiment, 1665 Cambridge. Discovering the fundamental spectral components of light. (from Foundations of Vision: Brian Wandell, The Light Properties

10 A prism

11 Electromagnetic Radiation - Spectrum Wavelength in nanometers (nm)

12 Electromagnetic Wave

13 Monochromators Monochromators measure the power or energy at different wavelengths

14 The Spectral Power Distribution (SPD) of a light is a function e( ) which defines the relative energy at each wavelength. Wavelength ( ) Relative Power Spectral Power Distribution (SPD)

15 Examples of Spectral Power Distributions Blue SkylightTungsten bulb Red monitor phosphorMonochromatic light

Interactions between light and matter depends on the physical characteristics of light as well as the matter. Three types of interactions: –Reflection –Absorption –Transmittance 16 The Surface Properties Incoming Light Transmitted Light Reflected Light

17 The Bidirectional Reflectance Distribution Function (BRDF) A BRDF describes how much light is reflected when light makes contact with a certain material Spectral radiance: quantity of light reflected in direction (  e,  e ) Spectral irradiance: quantity of light arriving from direction (  i,  i )

18 Specular reflection mirror like reflection at the surface Diffuse (lambertian) reflection Reflected randomly between color particles reflection is equal in all directions. Incident light Specular reflection Diffuse reflection normal Simplified Model 

19 Different Types of Surfaces

Simplified rendering models: reflectance Often are more interested in relative spectral composition than in overall intensity, so the spectral BRDF computation simplifies a wavelength-by-wavelength multiplication of relative energies..* = B. Freeman, and Foundations of Vision, by Brian Wandell,

21 Surface Body Reflectances (albedo) YellowRed BlueGray Wavelength (nm) Spectral Property of Lambertian Surfaces

Forsyth, 2002 Some reflectance spectra

23 Optic Nerve Fovea Vitreous Optic Disc Lens Pupil Cornea Ocular Muscle Retina Humor Iris The Eye Properties  Cornea - קרנית  Pupil - אישון  Iris - קשתית  Retina - רשתית

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25 The Visual Pathway Retina Optic Nerve Optic Chiasm Lateral Geniculate Nucleus (LGN) Visual Cortex

26 Eye v.s. Camera Yaho Wang’s slides

27 light rods cones horizontal amacrine bipolar ganglion The Human Retina

28 Retina contains 2 types of photo-receptors –Cones: Day vision, can perceive color tone – Rods: Night vision, perceive brightness only

29 Cones: High illumination levels (Photopic vision) Sensitive to color (there are three cone types: L,M,S) Produces high-resolution vision 6-7 million cone receptors, located primarily in the central portion of the retina Wavelength (nm) Relative sensitivity Cone Spectral Sensitivity M L S M A side note: Humans and some monkeys have three types of cones (trichromatic vision); most other mammals have two types of cones (dichromatic vision). Marine mammals have one type of cone. Most birds and fish have four types. Lacking one or more type of cones result in color blindness.

30 Rods: Low illumination levels (Scotopic vision). Highly sensitive (respond to a single photon). Produces lower-resolution vision 100 million rods in each eye. No rods in fovea. Wavelength (nm) Relative sensitivity Rod Spectral Sensitivity

31 rods S - Cones L/M - Cones Foveal Periphery photoreceptors Photoreceptor Distribution

32 Cone Receptor Mosaic (Roorda and Williams, 1999) L-conesM-conesS-cones

33 Distribution of rod and cone photoreceptors Degrees of Visual Angle Receptors per square mm x 10 4 rods cones Cone’s Distribution: L-cones (Red) occur at about ~65% of the cones throughout the retina. M-cones (green) occur at about ~30% of the cones. S-cones (blue) occur at about ~2-5% of the cones (Why so few?). fovea

34 The Cone Responses Assuming Lambertian Surfaces Illuminant Sensors Surface e( ) – Fixed, point source illuminant k( ) –surface’s reflectance l( ),m( ),s( ) – Cone responsivities Output

35 Metamer - two lights that appear the same visually. They might have different SPDs (spectral power distributions) Wavelength (nm) Power The phosphors of the monitor were set to match the tungsten light. Tungsten lightMonitor emission

36 The Trichromatic Color Theory Thomas Young ( ) - A few different retinal receptors operating with different wavelength sensitivities will allow humans to perceive the number of colors that they do. Suggested 3 receptors. Helmholtz & Maxwell (1850) - Color matching with 3 primaries. Trichromatic: “tri”=three “chroma”=color color vision is based on three primaries (i.e., it is 3D).

37 Color Matching Experiment testmatch Primaries Given a set of 3 primaries, one can determine for every spectral distribution, the intensity of the guns required to match the color of that spectral distribution. The 3 numbers can serve as a color representation. R( ) G( ) B( ) T( )

38 Color matching experiment 1 from: Bill Freeman

39 Color matching experiment 1 p 1 p 2 p 3 from: Bill Freeman

40 Color matching experiment 1 p 1 p 2 p 3 from: Bill Freeman

41 Color matching experiment 1 p 1 p 2 p 3 The primary color amounts needed for a match from: Bill Freeman

42 Color matching experiment 2 from: Bill Freeman

43 Color matching experiment 2 p 1 p 2 p 3 from: Bill Freeman

44 Color matching experiment 2 p 1 p 2 p 3 from: Bill Freeman

45 Color matching experiment 2 p 1 p 2 p 3 We say a “negative” amount of p 2 was needed to make the match, because we added it to the test color’s side. The primary color amounts needed for a match: p 1 p 2 p 3 from: Bill Freeman

46 Color matching experiment for Monochromatic lights Primary Intensities

47 r( ) g( ) b( ) Wavelength (nm) Primary Intensity Stiles & Burch (1959) Color matching functions. Primaries are: and Problems: Some perceived colors cannot be generated. This is true for any choice of visible primaries. The Color Matching Functions (CMF)

48 Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 from: Bill Freeman The superposition principle

49 Observation - Color matching is linear: –if (S  P) then (S+N  P+N) –if (S  P) then (  S   P) Let T( )=c  ( - 0 )+d  ( - 1 ) a double chromatic color: How should we adjust the 3 primaries? 0 1 c d

50 Outcome 1: Any T( ) can be matched: Outcome 2: CMF can be calculated for any chosen primaries U( ), V( ), W( ):

51 The CIE (Commission Internationale d’Eclairage) defined in 1931 three hypothetical lights X, Y, and Z whose matching functions are positive everywhere: The CIE Color Standard

52 Tristimulus Let X, Y, and Z be the tri-stimulus values. A color can be specified by its trichromatic coefficients, defined as X ratio Y ratio Z ratio Two trichromatic coefficients are enough to specify a color (x + y + z = 1). From: Bahadir Gunturk

53 Input light spectrum x y From: Bahadir Gunturk CIE Chromaticity Diagram

54 Input light spectrum x y From: Bahadir Gunturk CIE Chromaticity Diagram

55 Input light spectrum x y From: Bahadir Gunturk CIE Chromaticity Diagram

56 Input light spectrum Boundary x y 380nm 700nm From: Bahadir Gunturk CIE Chromaticity Diagram

57 Input light spectrum Boundary From: Bahadir Gunturk CIE Chromaticity Diagram

58 Light composition From: Bahadir Gunturk CIE Chromaticity Diagram

59 CIE Chromaticity Diagram Light composition From: Bahadir Gunturk

60 The sRGB is a device-independent color space. It was created in 1996 by HP and Microsoft for use on monitors and printers. It is the most commonly used color space. It is defined by a transformation from the xyz color space. The sRGB Color Standard

61 Color matching predicts matches, not appearance

62 Color Appearance

63 Color Appearance

64 Color Appearance

65 Color Spaces

66 RGB Color Space (additive) Define colors with (r, g, b) ; amounts of red, green, and blue

67 CMY Color Space (subtractive) Cyan, magenta, and yellow are the complements of red, green, and blue –We can use them as filters to subtract from white –The space is the same as RGB except the origin is white instead of black

Color names for cartoon spectra nm red green blue nm cyan magenta yellow nm From: B. Freeman

Additive color mixing nm red green Red and green make… nm yellow Yellow! When colors combine by adding the color spectra. Example color displays that follow this mixing rule: CRT phosphors, multiple projectors aimed at a screen, Polachrome slide film.

Subtractive color mixing When colors combine by multiplying the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons nm cyan yellow nm Cyan and yellow (in crayons, called “blue” and yellow) make… nm Green! green

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72 Red Green Blue Magenta Cyan Yellow

73 HSV color space Hue - the chroma we see (red, green, purple). Saturation - how pure is the color (how far the color from gray ). Value (brightness) - how bright is the color.

74 HSV color space Value Saturation Hue

75 T H E E N D