1. Computer and Robot Vision II
Chapter 12 Illumination
Presented by: 傅楸善 & 顏慕帆
指導教授: 傅楸善 博士

2. 12.1 Introduction
two key questions in understanding 3D image formation
What determines where some point on object will
appear on image?
Answer: geometric perspective projection model
What determines how bright the image of some
surface on object will be?
Answer: radiometry, general illumination models, diffuse and specular
Answer 動畫 radiometry: 輻射能測量
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4. Refraction: 折射
refraction of light bouncing off a surface patch: basic reflection phenomenon

5. 12.1 Introduction image intensity : proportional to scene radiance
scene radiance depends on
the amount of light that falls on a surface
the fraction of the incident light that is reflected
the geometry of light reflection,
i.e. viewing direction and illumination directions
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6. 12.1 Introduction image intensity : incident radiance
: bidirectional reflectance function
: lens collection
: sensor responsivity
: sensor gain
: sensor offset
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7. DC & CV Lab.
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8. Joke
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9. 12.2 Radiometry
is the measurement of the flow and transfer of radiant energy in terms of both the power emitted from or incident upon an area and the power radiated within a small solid angle about a given direction.
is the measurement of optical radiation.
輻射計量學. (Radiometry).
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10. 12.2 Radiometry irradiance: radiance: radiant intensity:
the amount of light falling on a surface
power per unit area of radiant energy falling on a surface
measured in units of watts per square meter.
radiance:
the amount of light emitted from a surface
power per unit foreshortened area emitted into a unit solid angle
measured in units of watts per square meter per steradian
radiant intensity:
of a point illumination source power per steradian
measured in units of watts per steradian
may be a function of polar and azimuth angles
Irradiance: 照光
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12. 12.2 Radiometry z-axis: along the normal to the surface element at 0
polar angle: measured from the z-axis
(pointing north)
azimuth angle: measured from x-axis
(pointing east)
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13. 12.2 Radiometry
The solid angle subtended by a surface patch is defined by the cone whose vertex is at the point of radiation and whose axis is the line segment going from the point of radiation to the center of the surface patch.
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14. 12.2 Radiometry
size of solid angle: area intercepted by the cone on a unit radius sphere centered at the point of radiation
solid angle: measured in steradians
total solid angle about a point in space:
steradians
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15. DC & CV Lab.
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16. 12.2 Radiometry : surface area
: distance from surface area to point of radiation
: angle the surface normal makes w.r.t. the cone
axis
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17. 12.2 Radiometry surface irradiance : : area of surface patch
: constant radiant intensity of point
illumination source
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18. law of inverse squares:
irradiance varies inversely as square of
distance from the illuminated surface to source

19. infinitesimal slice on annulus on sphere of
radius r , polar angle , azimuth angle
slice subtends solid angle ,
since

20. Outline:外形;輪廓
Silhouette:輪廓

21. 12.2.1 Bidirectional Reflectance Function
The bidirectional reflectance distribution function
is the fraction of incident light emitted in one direction when the surface is illuminated from another direction.
ratio of the scene radiance to the scene irradiance
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23. 12.2.1 Bidirectional Reflectance Function
differential reflectance model:
: polar angle between surface normal and lens center
: azimuth angle of the sensor
: emitting from
: incident to
: irradiance of the incident light at the illuminated surface
: radiance of the reflected light
: ratio of the scene radiance to the scene irradiance
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24. 12.2.1 Bidirectional Reflectance Function
The differential emitted radiance in the direction due to the incident differential irradiance in the direction is equal to the incident differential irradiance times the bidirectional reflectance distribution function
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25. 12.2.1 Bidirectional Reflectance Function
For many surfaces the dependence of on the azimuth angles and is only a dependence on their difference
except surfaces with oriented microstructure
e.g. mineral called tiger’s eye, iridescent feathers of
some birds
Mineral:礦物
Iridescent: 彩虹色的
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26. 12.2.1 Bidirectional Reflectance Function
An ideal Lambertian surface is one that appears equally bright from all viewing directions and reflects all incident light absorbing none
Lambertian surface:
perfectly diffusing surface with
matte appearance
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27. 12.2.1 Bidirectional Reflectance Function
reflectivity r:
unitless fraction called reflectance factor
white writing paper: r = 0.68
white ceilings or yellow paper: r = 0.6
dark brown paper: r = 0.13
Blotting paper: 吸墨紙
Velvet: 1. 天鵝絨,絲絨
2. 天鵝絨裙衫
3. 鹿角上之絨毛狀皮
4. 天鵝絨似的東西
5. 【舊】【俚】意外之財
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28. white blotting paper: r = 0.8
dark velvet: r = 0.004
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29. 12.2.1 Bidirectional Reflectance Function
bidirectional reflectance distribution function for Lambertian surface
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30. : irradiance, : radiance
: polar angel, : azimuth angle, : reflectivity
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34. DC & CV Lab.
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37. 12.2.1 Bidirectional Reflectance Function
differential relationship for emitted radiance for Lambertian surface
Lambertian surface: consistent brightness no matter what viewing direction
power radiated into a fixed solid angle: same in any direction
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38. Example 12.1
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39. Joke
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40. 12.2 Photometry
photometry: study of radiant light energy resulting in physical sensation
brightness: attribute of sensation by which observer aware of differences of observed radiant energy
radiometry radiant energy
photometry luminous energy
radiometry power( radiant flux )
photometry luminous flux
Luminous: a.
1. 發光的;夜光的;光輝的
2. 照亮了的
3. 清楚的,明白易懂的
4. 有見識的
Flux n.
1. 流出
2. 漲潮
3. 變遷
4. 【物】通量
5. 【化】助熔劑
vt.
1. 使成流體;使熔化
2. 使出血
vi.
1. 變成流體;熔化
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41. On Internet
Photometry: is the science of measuring visible light in units that are weighted according to the sensitivity of the human eye.
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42. 12.2 Photometry lumen: unit of luminous flux
luminous intensity: ( w.r.t. radiance intensity )
luminous flux leaving point source per unit solid angle
has units of lumens per steradian
candela: one lumen per steradian
illuminance: ( w.r.t. irradiance )
luminous flux per unit area incident upon a surface
in units of lumens per square meter
one lux: one lumen per square meter
foot-candle: one lumen per square foot
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43. 12.2 Photometry one foot =0.3048 meter
1 lux = foot - candles = foot - candles
luminance: ( w.r.t. radiance )
luminous flux per unit solid angle per unit of projected area
in units of lumens per square meter per steradian
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44. 12.2.3 Torrance-Sparrow Model
: diffuse reflection from Lambertian surface facets :
specular reflection from mirrorlike surface facets
dependent on the view point whereas is not
: reflected light from roughened surface
consider surfaces:
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45. Torrance-Sparrow model:
: proportion of specular reflection depending on surface
: wavelength of light
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47. : unit positional vector of the light source
: unit surface normal
: unit positional vector of the light source
: unit positional vector of the sensor
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48. Lens Collection
lens collection: portion of reflected light coming through lens to film
: distance between the image plane and the lens
: distance between the object and the lens
: distance between the lens and the image of the
object
: diameter of the lens
: angle between the ray from the object patch to
the lens center
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50. Lens Collection
irradiance incident on differential area coming from differential area , having radiance ,
and passing through a lens having
aperture area
: foreshortened area of aperture stop
seen by
: distance from to the aperture
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51. Lens Collection
solid angle subtended by aperture stop as seen from :
differential radiant power passing through aperture due to
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52. 12.2.4 Lens Collection radiant power passing through aperture from
irradiance incident to :
(radiant power reaching is )
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53. 12.2.4 Lens Collection assume , then , thus lens magnification is
hence , therefore
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54. 12.2.4 Lens Collection since then the lens collection C is given by
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55. Image Intensity
The image intensity gray level I associated with some small area of the image plane can then be represented as the integral of all light collected at the given pixel position coming from the observed surface patch, modified by sensor gain g and bias b
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56. 12.2.5 Image Intensity : light wavelength
: sensor responsivity to light at wavelength
: radiance of observed surface patch
: solid angle subtended by the viewing cone of camera for the pixel
: distance to the observed patch
: power received for the pixel position
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57. 12.3 Photometric Stereo
In photometric stereo there is one camera but K light sources having known intensities and incident vectors to a given surface patch.
In photometric stereo the camera sees the surface patch K times, one time when each light source is activated and the remaining ones are deactivated.
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58. 12.3 Photometric Stereo
: observed gray levels produced by the model of Lambertian reflectance
n: surface normal vector of the surface patch having
Lambertian reflectance
r: reflectivity of the Lambertian surface reflectance
g: sensor gain
b: sensor offset
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59. 12.3 Photometric Stereo
if camera has been photometrically calibrated, g, b known
let and
in matrix form
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60. 12.3 Photometric Stereo
if surface normal n known then least-squares solution for reflectivity r:
if K = 3 a solution for unit surface normal n:
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61. 12.3 Photometric Stereo if K > 3, a least-squares solution:
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62. 12.3 Photometric Stereo
if g, b unknown camera must be calibrated as follows:
geometric setup with known incident angle of light source to surface normal surfaces of known reflectivities illuminated by known intensity light source
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63. 12.3 Photometric Stereo
: known intensity of light source for kth trial
: known incident direction of light source for kth trial
: known unit length surface normal vector
: known reflectivity of surface illuminated for kth trial
: observed value from the camera
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64. 12.3 Photometric Stereo let then unknown gain g and offset b satisfy
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65. 12.3 Photometric Stereo this leads to the least-squares solution for
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66. Joke
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67. 12.4 Shape from Shading
nonplanar Lambertian surfaces of constant reflectance factor: appear shaded
this shading: secondary clue to shape of the observed surface
shape from shading: recovers shape of Lambertian surface from image shading
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68. 12.4 Shape from Shading
: unit vector of distant point light source direction
assume surface viewed by distant camera so perspective projection approximated by orthographic projection
surface point position : projected to image position
: surface expression
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69. 12.4 Shape from Shading unit vector normal to the surface at :
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70. 12.4 Shape from Shading gray level at , within multiplicative constant
Where and
Reflectance:反射比 反射係數
如果是 planar 代表 p,q=constant
: reflectance map
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71. 12.4 Shape from Shading : penalty constant
relaxation method: minimizing original error and a smoothness term criterion function to be minimized by choice of p, q
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72. Horn Robot Vision Fig
two orthographic shaded view of the same surface caption
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73. Horn Robot Vision Fig
a block diagram of Dent de Morcles region in southwestern Switzerland
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75. 12.4 Shape from Shading uniform brightness if planar surfaces since ,
constant surfaces with curvature: surfaces with
, provide information about surface height
first-order Taylor expression for g:
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76. 12.4 Shape from Shading
with boundary conditions on , we can solve unknown surface height and partial derivatives ,
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77. Shape from Focus
possible to recover shape from the shading profile of object edges
basic idea: cameras do not have infinite depth of field
The degree to which edges may be defocused is related to how far the 3D edge is away from the depths at which the edges are sharply in focus.
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78. Joke
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79. 12.5 Polarization illumination source characterized by four factors
directionality: relative to surface normal in bidirectional reflectance
intensity: energy coming out from source
spectral distribution: function of wavelength
polarization: time-varying vibration of light energy in certain direction
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80. Examples
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81. 12.5 Polarization
polarization: time-varying vibration of the light energy in certain direction
linearly polarized: changes direction by every period
circularly polarized: phase angle difference of ,thus
elliptically polarized phase angle difference of and different amplitude
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82. Mathematical Meaning of Polarization
polarization of light mathematically described by using wave theory
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83. linearly polarized
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84. circularly polarized
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85. Usefulness of Polarization in Machine Vision
At Brewster’s angle, the parallel polarized light is totally transmitted and the perpendicularly polarized light is partially transmitted and partially reflected.
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86. Usefulness of Polarization in Machine Vision
This effect can be used to remove the specular reflections from the window or metal surfaces by looking through them at Brewster’s angle.
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87. DC & CV Lab.
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88.
No Filter With Polarizer With Warm Polarizer
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89. 12.5.1 Representation of Light Using the Coherency Matrix
natural light: completely unpolarized
Coherency Matrix: Representation method of polarization
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90. 12.5.2 Representation of Light Intensity
The intensity of any light can be represented as a sum of two intensities of two orthogonal polarization components.
S-pol: component polarized perpendicularly to the incidence plane
P-pol: component polarized parallel to the incidence plane
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91. 12.6 Fresnel Equation
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92. 12.7 Reflection of Polarized Light
ergodic light: time average of the light equivalent to its ensemble average
Ensemble
n.【法】[C]
1. 整體;總效果
2. 整套服裝
3. 【音】合奏,合唱
4. 小型合奏(或合唱)團;劇團[G
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93. 12.8 A New Bidirectional Reflectance Function
用 s-pol and p-pol重新定義 BRDF
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94. 12.9 Image Intensity image intensity can be written in terms of
illumination parameters
sensor parameters
bidirectional reflectance function
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95. 12.10 Related Work
reflectance models: have been used in computer graphics and image analysis
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96. Joke
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97. Project due Mar. 15 use correlation to do image matching
find to minimize
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98. DC & CV Lab.
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99. DC & CV Lab.
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100. DC & CV Lab.
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101. P.S. 1
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102. P.S. 2
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