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Oct 10, 20051 Image Formation: Light Sources + Reflectance + Sensors Light is produced in different amounts at different wavelengths by each light source.

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Presentation on theme: "Oct 10, 20051 Image Formation: Light Sources + Reflectance + Sensors Light is produced in different amounts at different wavelengths by each light source."— Presentation transcript:

1 Oct 10, 20051 Image Formation: Light Sources + Reflectance + Sensors Light is produced in different amounts at different wavelengths by each light source Light is differentially reflected at each wavelength, which gives objects their natural colours (surface albedoes) The sensation of colour is determined by the human visual system, based on the product of light and reflectance Credits: Many slides from Jim Rehg, Frank Dellaert and David Forsyth

2 Oct 10, 20052 Image Formation Light Sources Object Transmittance Absorption Reflectance Observer Ambient Point Uniform

3 Oct 10, 20053 The multiplicative model E( )  ( ) holds for many types of surfaces (not all, e.g. feathers). Interpretation: wavelengths do not interfere Image Formation

4 Oct 10, 20054 Sensor response: Spectral integration E( ) spectral power distribution of the light source  ) spectral albedo   f ( ) spectral sensitivity of sensor f; for human vision and standard cameras f 2 {R,G,B} IlluminationReflectanceObserver

5 Oct 10, 20055 The Dichromatic Reflection Model So far, we have ignored geometry. i: incidence angle e: exit angle g: phase angle  i : interface reflected light  b : body reflected light

6 Oct 10, 20056 Dichromatic Reflection Model For most surfaces, the spectral albedo’s dependence on photometric angles can be described by the dichromatic model:  (λ, i, e, g) =  i (λ, i, e, g ) +  b (λ, i, e, g) furthermore  )= c b ( )m b (  )+c I ( )m I (  ), where c b ( )m b (  is the body reflectance and c I ( )m I (  ) is the interface reflectance The vector  (i,e,g) consists of the three photometric angles.  Note that the form constraints the colour of a single surface patch under a given illumination to lie in a plane.

7 Oct 10, 20057 Dichromatic Reflection Model Reflected Light Body Reflection Interface (Surface) Reflection Shafer S.A. 1985 Type I Neutral Interface Reflection, Objects with high oil, water content Type II ”Full” Dichromatic Reflection Model Objects as silk, wool, coloured paper Type III Special Version of the Dichromatic Reflection Model Adaptable for Metals Tominaga, 1994 Interface reflection is mirror-like, m I (  ) is close to a delta function. The commonly used Phong model assumes m I (  ) =cos k (  ), where  is measured from the mirror direction, k is a use parameter. Body reflection is often isotropic, the patch has the same intensity from all viewpoints. Patch intensity depends on the orientation of the normal w.r.t. the illumination source. The commonly used Lambertian model assumes $m b (  ) = cos(  ), where i  is the incident angle, i.e. the angle between the surface normal and the light source direction.

8 Oct 10, 20058 Dichromatic Reflection Model

9 Oct 10, 20059 Skewed-T in Histogram A Physical Approach to colour Image Understanding – Klinker, Shafer, and Kanade. IJCV 1990 Figure courtesy of D. Forsyth

10 Oct 10, 200510 Figure courtesy of D. Forsyth Skewed-T in Histogram

11 Oct 10, 200511 Dichromatic Reflection Model in Chromaticity Representation Chromaticity = Colour modulo intensity

12 Oct 10, 200512 Gamma Correction The dichromatic model is only valid for linear cameras! The phosphor dots are not a linear system (voltage vs. intensity)

13 Oct 10, 200513 Gamma correction Without gamma correction, how will (0,255,127) look like? Normally gamma is within 1.7 and 2.8 Who is responsible for Gamma correction? SGI does it for you PC/Mac etc, you should do it yourself

14 Oct 10, 200514 No gamma correction

15 Oct 10, 200515 Gamma corrected to 1.7

16 Oct 10, 200516 Residual Gamma or System Gamma Systems such as SGI monitor has a gamma of 2.4, but they only gamma correct for 1.7. The residue gamma is 2.4/1.7 = 1.4, why? Depends on how you see it? Bright screen, dark room causes changes in your eye transfer function too. What about web pages? Which screen do you intend for?

17 Oct 10, 200517 Illumination 1. If Spectra of Light Source Changes Spectra of Reflected Light Changes

18 Oct 10, 200518 Illumination 2. Daylight Tungsten Fluorescence

19 Oct 10, 200519 Modelling Source of Light: Most Common Lights are Close to Black Body Radiators. Judd et al., 1964 CIE standard “Typical Daylight” 5700K Range 4000 – 25000K Black Body T, Kelvin

20 Oct 10, 200520 Black body radiators Construct a hot body with near-zero albedo (black body) –Easiest way to do this is to build a hollow metal object with a tiny hole in it, and look at the hole. The spectral power distribution of light leaving this object is a function of temperature (degrees Kelvin) This leads to the notion of colour temperature --- the temperature of a black body that would look the same –Candle flame or sunset: about 2000K –Incandescent light bulbs: 3000K –Daylight (sun): 5500K –Blue sky (shadowed from sun): 15,000K Camera film must be chosen according to light source

21 Oct 10, 200521 The black-body locus (the colours of heated black-bodies).

22 Oct 10, 200522 Measurements of relative spectral power of sunlight, made by J. Parkkinen and P. Silfsten. Relative spectral power is plotted against wavelength in nm. The visible range is about 400nm to 700nm. The colour names on the horizontal axis give the colour names used for monochromatic light of the corresponding wavelength. Violet Indigo Blue Green Yellow Orange Red

23 Oct 10, 200523 Relative spectral power of two standard illuminant models --- D65 models sunlight,and illuminant A models incandescent lamps. Relative spectral power is plotted against wavelength in nm. Violet Indigo Blue Green Yellow Orange Red

24 Oct 10, 200524

25 Oct 10, 200525 Spectral albedoes for several different flowers, with colour names attached. Notice that different colours typically have different spectral albedo, but that different spectral albedoes may result in the same perceived colour (compare the two whites). Spectral albedoes are typically quite smooth functions. Measurements by E.Koivisto. Spectral albedo’s of common materials:

26 Oct 10, 200526 Lighting and Illuminants (3)

27 Oct 10, 200527 Lighting and Illuminants (5)

28 Oct 10, 200528 reflectance spectrophotometer to acquire spectral reflectance data

29 Oct 10, 200529 Spectral Albedo

30 Oct 10, 200530 Spectral Albedo

31 Oct 10, 200531 Additive colour Mixing

32 Oct 10, 200532 Subtractive colour Mixing

33 Oct 10, 200533 colour matching experiments - I Show a split field to subjects; one side shows the light whose colour one wants to measure, the other a weighted mixture of primaries (fixed lights).

34 Oct 10, 200534 colour Matching Process Basis for industrial colour standards

35 Oct 10, 200535 colour Matching Experiment 1 Image courtesy Bill Freeman

36 Oct 10, 200536 colour Matching Experiment 1 Image courtesy Bill Freeman

37 Oct 10, 200537 colour Matching Experiment 1 Image courtesy Bill Freeman

38 Oct 10, 200538 colour Matching Experiment 2 Image courtesy Bill Freeman

39 Oct 10, 200539 colour Matching Experiment 2 Image courtesy Bill Freeman

40 Oct 10, 200540 colour Matching Experiment 2 Image courtesy Bill Freeman

41 Oct 10, 200541 Colour matching experiments - II Many colours can be represented as a positive weighted sum of A, B, C write M=a A + b B + c C where the = sign should be read as “matches” This is additive matching. Gives a colour description system - two people who agree on A, B, C need only supply (a, b, c) to describe a colour.

42 Oct 10, 200542 Subtractive matching Some colours can’t be matched like this: instead, must write M+a A = b B+c C This is subtractive matching. Interpret this as (-a, b, c) Problem for building monitors: Choose R, G, B such that positive linear combinations match a large set of colours

43 Oct 10, 200543 The principle of trichromacy Experimental facts: –Three primaries will work for most people if we allow subtractive matching Exceptional people can match with two or only one primary. This could be caused by a variety of deficiencies. –Most people make the same matches. There are some anomalous trichromats, who use three primaries but make different combinations to match.

44 Oct 10, 200544 Human Photoreceptors FoveaPeriphery

45 Oct 10, 200545 Human Cone Sensitivities Spectral sensitivity of L, M, S cones in human eye

46 Oct 10, 200546 Grassman’s Laws

47 Oct 10, 200547 Linear colour spaces A choice of primaries yields a linear colour space --- the coordinates of a colour are given by the weights of the primaries used to match it. Choice of primaries is equivalent to choice of colour space. RGB: primaries are monochromatic energies are 645.2nm, 526.3nm, 444.4nm. CIE XYZ: Primaries are imaginary, but have other convenient properties. colour coordinates are (X,Y,Z), where X is the amount of the X primary, etc.

48 Oct 10, 200548 monochromatic 645.2, 526.3, 444.4 nm. negative parts -> some colours can be matched only subtractively. RBG colour Matching Figure courtesy of D. Forsyth

49 Oct 10, 200549 CIE XYZ: colour matching functions are positive everywhere, but primaries are imaginary. Usually draw x, y, where x=X/(X+Y+Z) y=Y/(X+Y+Z) So overall brightness is ignored. CIE XYZ colour Matching Figure courtesy of D. Forsyth

50 Oct 10, 200550 Geometry of colour (CIE) White is in the center, with saturation increasing towards the boundary Mixing two coloured lights creates colours on a straight line Mixing 3 colours creates colours within a triangle Curved edge means there are no 3 actual lights that can create all colours that humans perceive!

51 Oct 10, 200551 RGB colour Space The colours that can be displayed on a typical computer monitor (phosphor limitations keep the space quite small)

52 Oct 10, 200552 Uniform colour spaces McAdam ellipses (next slide) demonstrate that differences in x,y are a poor guide to differences in colour –Each ellipse shows colours that are perceived to be the same Construct colour spaces so that differences in coordinates are a good guide to differences in colour. Two spaces are commonly used: Lab and Luv The “uniformity” applies only to small differences in colour

53 Oct 10, 200553 Figures courtesy of D. Forsyth McAdam ellipses 10 times actual size Actual size

54 Oct 10, 200554 Human colour Constancy Colour constancy: determine hue and saturation under different colours of lighting Lightness constancy: gray-level reflectance under differing intensity of lighting Humans can perceive –colour a surface would have under white light –colour of reflected light (separate surface colour from measured colour) –colour of illuminant (limited)

55 Oct 10, 200555 Land’s Mondrian Experiments Squares of colour with the same colour radiance yield very different colour perceptions Photometer: 1.0, 0.3, 0.3 Audience: “Red”Audience: “Blue” White light Red light Blue Red Blue Red

56 Oct 10, 200556 Basic Model for Lightness Constancy Assumptions: –Planar frontal scene –Lambertian reflectance –Linear camera response Modeling assumptions for scene –Piecewise constant surface reflectance –Slowly-varying Illumination

57 Oct 10, 200557 1-D Lightness “Retinex” Threshold gradient image to find surface (patch) boundaries Figure courtesy of D. Forsyth

58 Oct 10, 200558 1-D Lightness “Retinex” Integration to recover surface lightness (unknown constant) Figure courtesy of D. Forsyth

59 Oct 10, 200559 colour Retinex Images courtesy John McCann

60 Oct 10, 200560 Colour constancy Following methods have been used: –Average reflectance across scene is known (often fails) –Brightest patch is white –Gamut (collection of all colours) falls within known range –Known reference colour (colour chart, skin colour…) –Specular reflections have the colour of the illumination This is an open problem


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