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Formation et Analyse d’Images Session 3. Daniela Hall 3 October 2005. Course Overview. Session 1 (19/09/05) Overview Human vision Homogenous coordinates Camera models Session 2 (26/09/05) Tensor notation Image transformations Homography computation Session 3 (3/10/05) - PowerPoint PPT Presentation
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1
Formation et Analyse d’ImagesSession 3
Daniela Hall
3 October 2005
2
Course Overview
• Session 1 (19/09/05)– Overview– Human vision – Homogenous coordinates– Camera models
• Session 2 (26/09/05)– Tensor notation– Image transformations– Homography computation
• Session 3 (3/10/05)– Camera calibration– Reflection models– Color spaces
• Session 4 (10/10/05)– Pixel based image analysis
• 17/10/05 course is replaced by Modelisation surfacique
3
Course overview
• Session 5 + 6 (24/10/05) 9:45 – 12:45– Kalman filter– Tracking of regions, pixels, and lines
• Session 7 (7/11/05)– Gaussian filter operators
• Session 8 (14/11/05)– Scale Space
• Session 9 (21/11/05)– Contrast description– Hough transform
• Session 10 (5/12/05)– Stereo vision
• Session 11 (12/12/05)– Epipolar geometry
• Session 12 (16/01/06): exercises and questions
4
Session Overview
1. Camera calibration
2. Light
3. Reflection models
4. Human color perception
5. Color spaces
5
Bi-linear interpolationPs0 Ps1
Ps3Ps2
Ps
)()()()()(
,)1(
),1(),1)(1(
3210
0
0
sssss
yssy
xssx
PDIPCPBPAIPI
dxdyDdydxC
dydxBdydxA
PPdy
PPdx
The bilinear approach computes the weighted average of the four neighboring pixels. The pixels are weighted according tothe area.
AB
CD
6
Camera calibration
• Assuming that the camera performs a exact perspective projection, the image formation process can be expressed as a projective mapping from R3 to R2.
• PI=MIS PS
• Camera calibration: process of estimating MIS
from a set of point correspondences RS PI . • Advantage: intrinsic and extrinsic camera
parameters don't need to be known. They are estimated automatically.
Ref: CVonline, LOCAL_COPIES/MOHR_TRIGGS/node16.html
7
Calibration
1. Construct a calibration object whose 3D position is known.
2. Measure image coordinates
3. Determine correspondences between 3D point RS
k and image point PIk.
4. We have 11 DoF. We need at least 5 ½ correspondences.
8
Calibration
• For each correspondence scene point RSk and image
point PIk
• which gives following equations for k=1, ..., 6
• from wich MIS can be computed
Sk
IS
Sk
IS
k
kkk RM
RM
w
iwi
3
1
)(
)(
Sk
IS
Sk
IS
k
kkk RM
RM
w
jwj
3
2
)(
)(
0))(())((
0))(())((32
31
Sk
ISk
Sk
IS
Sk
ISk
Sk
IS
RMjRM
RMiRM
9
Calibration using many points
• For k=5 ½ M has one solution.– Solution depends on precise measurements of
3D and 2D points. – If you use another 5 ½ points you will get a
different solution.
• A more stable solution is found by using large number of points and do optimisation.
10
Calibration using many points
• For each point correspondence we know (i,j) and R=(x,y,z,1)T.
• We want to know MIS.
Solve equation with your favorite algorithm (least squares, levenberg-marquart, svd,...)
0))(())((
0))(())((32
31
Sk
ISk
Sk
IS
Sk
ISk
Sk
IS
RMjRM
RMiRM
0
34
33
32
31
24
23
22
21
14
13
12
11
10000
00001
0000000000
0000000000
m
m
m
m
m
m
m
m
m
m
m
m
jzjyjxjzyx
iziyixizyx
11
Estimation of MIS
1. When intrinsic (Ci, Cj, Di, Dj, F) and extrinsic camera (3d camera position and orientation) parameters are known, compute MI
S directly:
2. If one parameter is not precisely known or you wish a stable estimation of MI
S, do calibration with a large number of points.
SIS
SCS
RC
IR
I PMPTMCP
12
Session Overview
1. Camera calibration
2. Light
3. Reflection models
4. Human color perception
5. Color spaces
13
Light
• N: surface normal• i angle between incoming light and normal• e angle between normal and camera• g angle between light and camera
camera
light
N
egi
14
Spectrum
• Light source is characterised by its spectrum. • The spectrum consists of a particular quantity of photons
per frequency. • The frequency is described by its wavelength• The visible spectrum is 380nm to 720nm• Cameras can see a larger spectrum depending on their
CCD chip
f1
15
• Albedo is the fraction of light that is reflected by a body or surface.
• Reflectance function:
Albedo
light received
light emitted
Irradiance
Radiance),,( geiR
camera
light
N
egi
16
Reflectance functions
• Specular reflection– example mirror
• Lambertian reflection– diffuse reflection, example paper, snow
17
Specular reflection
else 0,
gei and ei if ,1),,( geiR
camera
lightN
egi
18
Lambertian reflection
)cos(),,( igeiR
19
Di-chromatic reflectance model
• the reflected light R is the sum of the light reflected at the surface Rs and the light reflected from the material body RL
• Rs has the same spectrum as the light source• The spectrum of Rl is « filtered » by the material (photons are
absorbed, this changes the emitted light)• Luminance depends on surface orientation• Spectrum of chrominance is composed of light source
spectrum and absorption of surface material.
),,(),,(),,( geiRgeiRgeiR LLSs
20
Session Overview
1. Camera calibration
2. Light
3. Reflection models
4. Human color perception
5. Color spaces
21
Color perception
• The retina is composed of rods and cones.• Rods - provide "scotopic" or low intensity vision.
– Provide our night vision ability for very low illumination, – Are a thousand times more sensitive to light than cones, – Are much slower to respond to light than cones, – Are distributed primarily in the periphery of the visual field.
22
Color perception
• Cones - provide "photopic" or high acuity vision. – Provide our day vision, – Produce high resolution images, – Determine overall brightness or darkness of images, – Provide our color vision, by means of three types of cones:
• "L" or red, long wavelength sensitive, • "M" or green, medium wavelength sensitive, • "S" or blue, short wavelength sensitive.
• Cones enable our day vision and color vision. Rods take over in low illumination. However, rods cannot detect color which is why at night we see in shades of gray.
• source: http://www.hf.faa.gov/Webtraining/VisualDisplays/
23
Color perception
• Rod Sensitivity- Peak at 498 nm.• Cone Sensitivity- Red or "L" cones peak at 564 nm. - Green or "M"
cones peak at 533 nm. - Blue or "S" cones peak at 437 nm.
• This diagram shows the wavelength sensitivities of the different cones and the rods. Note the overlap in sensitivity between the green and red cones.
24
Camera sensitivity
• observed light intensity depends on:– source spectrum: S(λ)– reflectance of the observed point (i,j): P(i,j,λ)– receptive spectrum of the camera: c(λ)– p0 is the gain
400 600 800 1000 nm
S(λ)
λ
vidicon
CCD
0
0 )()(),,(),( cSjiPpjip
25
Classical RGB camera
• The filters follow a convention of the International Illumination Commission.
• They are functions of λ: r(λ), g(λ), b(λ)• They are close to the sensitivity of the human
color vision system.
26
Color pixels
0
0
0
)()(),,(0),(
)()(),,(0),(
)()(),,(0),(
),(
),(
),(
),(
dbSjiPbjiB
dgSjiPgjiG
drSjiPrjiR
jiB
jiG
jiR
jiP
27
Color bands (channels)
• It is not possible to perceive the spectrum directly.• Color is a projection of the spectrum to the
spectrum of the sensors. • Humans (and cameras) probe the spectrum at 3
positions.
0
0
0
0
0
0
)()(
)()(
)()(
dbSbB
dgSgG
drSrR
28
Session Overview
1. Camera calibration
2. Light
3. Reflection models
4. Human color perception
5. Color spaces
29
Color spaces
• RGB color space
• CMY color space
• YIQ color space
• HLS color space
30
RGB color space
• A CCD camera provides RGB images
• The luminance axis is r=g=b (diagonal)
• Each axis has 256 (8 bit) different values
• RGB colors: 2563=16777216
31
Hering color space
• Opponent color space
• Is obtained from RGB space by transformation.
• Luminance, C1 (red-green), C2 (red+green-blue)
B
G
R
gg
gg
gg
gg
ggggg
C
C
Y
gr
gb
gr
rb
rg
bgr
1
02
3
2
3
2
1
2222
B
G
R
C
C
Y
12/12/1
02
1
2
13/13/13/1
2
1
32
CMY color space
• Cyan, magenta, yellow
• CMYK: CMY + black color channel
B
G
R
B
G
R
Y
M
C
max
max
max
33
YIQ color space
• This is an approximation of– Y: luminance, – I: red – cyan, – Q: magenta - green
• Used US TVs (NTSC coding). Black and white TVs display only Y channel.
B
G
R
Q
I
Y
31.052.021.0
32.028.06.0
11.059.03.0
34
HLS space
• Hue, luminance, saturation space.
• L=R+G+B
• S=1-3*min(R,G,B)/L
elsex
gbxT
BGBRGR
BRGRx
,2
if ,
)))(()(
))()((5.0(cos
2
1
L
S T
35
Influence of color spaces for image analysis
• According to dichromatic reflectange model:– Luminance depends on surface orientation– Spectrum of chrominance is composed of light source
spectrum and absorption of surface material.• In HLS space, luminance is separated from
chrominance. For object recognition robust to changes in light source direction, use only chrominance plane for identification.
• In RGB space, changes in luminance influence all 3 channels. The above technique can not be used directly (do transformation to Hering space first).