Image Formation. Camera trial #1. Pinhole camera. What is an Image? Light and the EM spectrum The H.V.S. and Color Perception

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1 Image Formation Light and the EM spectrum The H.V.S. and Color Perception 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. 2 Camera trial # Pinhole camera pinhole camera scene film scene barrier film 3 source: Yung-Yu Chuang Put a piece of film in front of an object. 4 source: Yung-Yu Chuang Add a barrier to block off most of the rays. It reduces blurring The pinhole is known as the aperture The image is inverted

2 The Pinhole Camera Model (where) (x,y) (x,y,z) d focal length d Y center of projection (pinhole) X Z 5 6 x y = w d X Y Z The Shading Model (what) 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: 7 Shading Model: Given the illumination incident at a point on a surface, what is reflected? 8 Position, orientation, Sensor spectrum sensitivities. 2

3 Light and the Visible Spectrum The light Spectrum Electromagnetic Radiation - Spectrum Ultraviolet Short- Gamma X rays Infrared Radar FM TV wave AM AC electricity Wavelength in meters (m) Visible light 9 Newton s Experiment, 665 Cambridge. Discovering the fundamental spectral components of light. 4 nm 5 nm 6 nm 7 nm Wavelength in nanometers (nm) Monochromators Spectral Power Distribution Monochromators measure the power or energy at different wavelengths The Spectral Power Distribution (SPD) of a light is a function e(λ) which defines the energy at each wavelength. Relative Power Wavelength (λ) 2 3

4 Examples of Spectral Power Distributions Surface Parameters normal Incident light Specular reflection.5.5 Diffuse reflection Blue Skylight Tungsten bulb.5.5 Diffuse (lambertian) reflection reflected randomly between color particles reflection is equal in all directions Red monitor phosphor Monochromatic light 4 Specular reflection mirror like reflection at the surface Spectral Property of Lambertian Surfaces.8 Yellow.8 Red Blue Gray Different Types of Surfaces Wavelength (nm) 5 6 Surface Body Reflectances (albedo) 4

5 R V N θ L R V N θ L Surface properties Light properties Ambient reflection: I amb = K(λ) e a (λ) geometry Ambient reflection: I amb = K(λ) e a (λ) Diffuse reflection: I diff = K(λ) e p (λ) (N L) Diffuse reflection: I diff = K(λ) e p (λ) (N L) Specular reflection: I spec = K s (λ)e p (λ) (R V) n Specular reflection: I spec = K s (λ)e p (λ) (R V) n e p e a - the ambient and point light intensities. K, K s [,] - the surface ambient / diffuse / specular reflectivity. 7 N - the surface normal, L - the light direction, V viewing direction e p e a - the ambient and point light intensities. K, K s [,] - the surface ambient / diffuse / specular reflectivity. 8 N - the surface normal, L - the light direction, V viewing direction The final illumination equation: I(λ) = I amb +I diff +I spec If several light sources are placed in the scene: I(λ)= I amb +Σ k (I k diff +Ik spec ) Ambient surface Diffuse surface Diffuse + Specular 9 2 5

6 Composition of Light Sources The Human Visual System Lens Cornea Pupil Iris Fovea Vitreous Humor Optic Disc Optic Nerve 2 קרנית - Cornea אישון - Pupil קשתית - Iris רשתית - Retina 22 Ocular Muscle Retina The Visual Pathway Retina Optic Nerve Optic Chiasm Lateral Geniculate Nucleus (LGN) Visual Cortex

7 Eye v.s. Camera Color Representation 25 Yaho Wang s slides 26 The Human Retina rods cones Retina contains 2 types of photo-receptors Cones: Day vision, can perceive color tone Rods: Night vision, perceive brightness only bipolar ganglion horizontal amacrine light

8 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 Relative sensitivity Cone Spectral Sensitivity L S M Wavelength (nm) 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. Rods: Low illumination levels (Scotopic vision). Highly sensitive (respond to a single photon). Produces lower-resolution vision million rods in each eye. No rods in fovea. 3 Relative sensitivity Rod Spectral Sensitivity Wavelength (nm) Photoreceptor Distribution Foveal Periphery photoreceptors Cone Receptor Mosaic (Roorda and Williams, 999) 3 rods S - Cones L/M - Cones 32 L-cones M-cones S-cones 8

9 Cone s Distribution: L-cones (Red) occur at about ~65% of the cones throughout the retina. M-cones (green) occur at about ~3% of the cones. S-cones (blue) occur at about ~2-5% of the cones (Why so few?). 33 Receptors per square mm 8 x 4 rods cones Distribution of rod and cone photoreceptors Degrees of Visual Angle fovea 34 The Cone Responses Assuming Lambertian Surfaces Output Sensors Illuminant L = l( λ) e( λ) k( λ) M = m( λ) e( λ) k( λ) S = s( λ) e( λ) k( λ) e(λ) Fixed, point source illuminant k(λ) surface s reflectance l(λ),m(λ),s(λ) Cone responsivities Surface The Trichromatic Color Theory Metamer - two lights that appear the same visually. They might have different SPDs (spectral power distributions). Trichromatic: tri =three chroma =color color vision is based on three primaries (i.e., it is 3D). Power 2 Tungsten light Monitor emission Wavelength (nm) 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 (85) - Color matching with 3 primaries. 35 The phosphors of the monitor were set to match the tungsten light. 36 9

10 Color Matching Experiment 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. Color matching experiment test match + - R(λ) T(λ) + - G(λ) Primaries + - B(λ) 37 ( λ ) rr ( λ ) + gg ( λ ) bb ( λ ) T + 38 from: Bill Freeman Color matching experiment Color matching experiment p p 2 p 39 3 from: Bill Freeman p p 2 p 4 3 from: Bill Freeman

11 Color matching experiment Color matching experiment 2 The primary color amounts needed for a match p p 2 p 4 3 from: Bill Freeman 42 from: Bill Freeman Color matching experiment 2 Color matching experiment 2 p p 2 p 43 3 from: Bill Freeman p p 2 p 44 3 from: Bill Freeman

12 Color matching experiment 2 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 p 2 p 3 p p 2 p 3 p p 2 p 45 3 from: Bill Freeman Foundations of Vision, by Brian Wandell, Sinauer Assoc., from: Bill Freeman Color matching experiment for Monochromatic lights The Color Matching Functions (CMF) Primary Intensity 3 2 b(λ) g(λ) r(λ) Primary Intensities Wavelength (nm) Stiles & Burch (959) Color matching functions. Primaries are: and Problems: Some perceived colors cannot be generated. This is true for any choice of visible primaries. 2

13 Observation - Color matching is linear: 49 if (S P) then (S+N P+N) if (S P) then (α S αp) Outcome : Any T(λ) can be matched: ( λ) r( λ) dλ ; g = T ( λ) g( λ) dλ b T ( λ) b ( λ) dλ r = T ; = Outcome 2: CMF can be calculated for any chosen primaries U(λ), V(λ), W(λ): u a v = b w c a b c a3 r b3 g c 3 b The CIE (Commission Internationale d Eclairage) defined in 93 three hypothetical lights X, Y, and Z whose matching functions are positive everywhere: 5 The CIE Color Standard Tristimulus Let X, Y, and Z be the tristimulus values. CIE Chromaticity Diagram Input light spectrum A color can be specified by its trichromatic coefficients, defined as X x = X + Y + Z Y y = X + Y + Z Z z = X + Y + Z X ratio Y ratio Z ratio Two trichromatic coefficients are enough to specify a color. (x + y + z = ) y x From: Bahadir Gunturk 5 From: Bahadir Gunturk 52 3

14 CIE Chromaticity Diagram Input light spectrum CIE Chromaticity Diagram Input light spectrum y y x x From: Bahadir Gunturk 53 From: Bahadir Gunturk 54 CIE Chromaticity Diagram Input light spectrum CIE Chromaticity Diagram Input light spectrum y 7nm Boundary Boundary 38nm x From: Bahadir Gunturk 55 From: Bahadir Gunturk 56 4

15 CIE Chromaticity Diagram Light composition CIE Chromaticity Diagram Light composition Light composition From: Bahadir Gunturk 57 From: Bahadir Gunturk 58 The srgb Color Standard Color matching predicts matches, not appearance The srgb is a device-independent color space. It was created in 996 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

16 Color Appearance Color Appearance 6 62 Color Appearance Color Spaces

17 from:bill Freeman Color names for cartoon spectra from:bill Freeman Additive color mixing red green blue nm nm yellow magenta cyan nm nm red green yellow nm nm 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. Red and green make Yellow! nm nm nm 66 from:bill Freeman Subtractive color mixing RGB Color Space (additive) cyan yellow nm nm When colors combine by multiplying the color spectra. Examples that follow this mixing rule: most photographic films, paint, cascaded optical filters, crayons. Cyan and yellow (in crayons, called blue and yellow) make Define colors with (r, g, b) amounts of red, green, and blue green nm Green!

18 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 HSV color space Hue - the color we see (red, green, purple). Saturation - how pure is the color (how far the color from gray ). Value (brightness) - how bright is the color HSV - a more intuitive color space Saturation Value T H E E N D Hue