Oct 10, 2005 1 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 F
60
Embed
Oct 10, 20051 Image Formation: Light Sources + Reflectance + Sensors Light is produced in different amounts at different wavelengths by each light source.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
• 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
Oct 10, 2005 2
Image Formation
Light Sources
Object
Transmittance
Absorption
Reflectance
Observer
Ambient
Point Uniform
Oct 10, 2005 3
The multiplicative model E()() holds for many types of surfaces (not all, e.g. feathers). Interpretation: wavelengths do not interfere
Image Formation
Oct 10, 2005 4
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}
Illumination Reflectance Observer
Oct 10, 2005 5
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
Oct 10, 2005 6
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
)=cb()mb()+cI()mI(),
where cb()mb(is the body reflectance and cI()mI() 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.
Oct 10, 2005 7
Dichromatic Reflection Model
Reflected Light
Body Reflection
Interface (Surface) Reflection
Shafer S.A. 1985
)()()()()( ,,, yxyxyx IIBB CmCmC
Type INeutral Interface Reflection,Objects with high oil, water content
Type II”Full” Dichromatic Reflection ModelObjects as silk, wool, coloured
paper
Type IIISpecial Version of the Dichromatic Reflection ModelAdaptable for Metals
Tominaga, 1994
•Interface reflection is mirror-like, mI() is close to a delta function. The commonly used Phong model assumes mI() =cosk(), 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 $mb() = cos(), where iis the incident angle, i.e. the angle between the surface normal and the light source direction.
Oct 10, 2005 8
Dichromatic Reflection Model
)()()()()( ,,, yxyxyx SSBB CmCmC
Oct 10, 2005 9
R
G
B
Illuminant color
Diffuse component
T
S
Skewed-T in Histogram
A Physical Approach to colour Image Understanding – Klinker, Shafer, and Kanade. IJCV 1990
Figure courtesy ofD. Forsyth
Oct 10, 2005 10R
G
B
R
G
B
Diffuseregion
Boundary ofspecularity
Figure courtesy ofD. Forsyth
Skewed-T in Histogram
Oct 10, 2005 11
Dichromatic Reflection Model in Chromaticity Representation
Chromaticity = Colour modulo intensity
BGRR
R
BGR
GG
BGRB
B
1 BGR
Oct 10, 2005 12
Gamma Correction
• The dichromatic model is only valid for linear cameras!
• The phosphor dots are not a linear system (voltage vs. intensity)
Oct 10, 2005 13
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
Oct 10, 2005 14
No gamma correction
Oct 10, 2005 15
Gamma corrected to 1.7
Oct 10, 2005 16
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?
Oct 10, 2005 17
Illumination 1.
If Spectra of Light Source Changes
Spectra of Reflected Light Changes
Oct 10, 2005 18
Illumination 2.
Daylight
Tungsten
Fluorescence
Oct 10, 2005 19
Modelling Source of Light: Most Common Lights are Close to Black Body Radiators.
Judd et al., 1964CIE standard
“Typical Daylight” 5700KRange 4000 – 25000K
Black Body
T, Kelvin
Oct 10, 2005 20
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
Oct 10, 2005 21
The black-body locus (the colours of heated black-bodies).
Oct 10, 2005 22
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
Oct 10, 2005 23
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
Oct 10, 2005 24
Oct 10, 2005 25
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:
Oct 10, 2005 26
Lighting and Illuminants(3)
Oct 10, 2005 27
Lighting and Illuminants(5)
Oct 10, 2005 28
reflectance spectrophotometer to acquire spectral reflectance data
Oct 10, 2005 29
Spectral Albedo
Oct 10, 2005 30
Spectral Albedo
Oct 10, 2005 31
Additive colour Mixing
Oct 10, 2005 32
Subtractive colour Mixing
Oct 10, 2005 33
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).
Oct 10, 2005 34
colour Matching Process
Basis for industrial colour standards
Oct 10, 2005 35
colour Matching Experiment 1
Image courtesy Bill Freeman
Oct 10, 2005 36
colour Matching Experiment 1
Image courtesy Bill Freeman
Oct 10, 2005 37
colour Matching Experiment 1
Image courtesy Bill Freeman
Oct 10, 2005 38
colour Matching Experiment 2
Image courtesy Bill Freeman
Oct 10, 2005 39
colour Matching Experiment 2
Image courtesy Bill Freeman
Oct 10, 2005 40
colour Matching Experiment 2
Image courtesy Bill Freeman
Oct 10, 2005 41
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.
Oct 10, 2005 42
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
Oct 10, 2005 43
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.
Oct 10, 2005 44
Human Photoreceptors
Fovea Periphery
Oct 10, 2005 45
Human Cone Sensitivities
• Spectral sensitivity of L, M, S cones in human eye
Oct 10, 2005 46
Grassman’s Laws
Oct 10, 2005 47
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.
Oct 10, 2005 48
• monochromatic• 645.2, 526.3, 444.4 nm.• negative parts -> some colours can be matched only subtractively.
RBG colour Matching
Figure courtesy ofD. Forsyth
Oct 10, 2005 49
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 ofD. Forsyth
Oct 10, 2005 50
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!
Oct 10, 2005 51
RGB colour Space
The colours that can be displayed on a typical computer monitor (phosphor limitations keep the space quite small)
Oct 10, 2005 52
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
008856.0 if , 116
16787.7
008856.0 if , )( where
)()(200
)()(500
008856.0 if , )(3.903
008856.0 if , 16)(116
3
1
*
*
3
1
*
tt
tttf
Z
Zf
Y
Yfb
Y
Yf
X
Xfa
Y
Y
Y
YY
Y
Y
Y
L
nn
nn
nn
nn
Oct 10, 2005 53
Figures courtesy ofD. Forsyth
McAdam ellipses
10 times actual size Actual size
Oct 10, 2005 54
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)
Oct 10, 2005 55
Land’s Mondrian Experiments
• Squares of colour with the same colour radiance yield very different colour perceptions
Integration to recover surface lightness (unknown constant)
Figure courtesy ofD. Forsyth
Oct 10, 2005 59
colour Retinex
Images courtesy John McCann
Oct 10, 2005 60
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