Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a...
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Transcript of Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a...
![Page 1: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/1.jpg)
Image formation 2
![Page 2: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/2.jpg)
Blur circle
A point at distance z is imaged at point 'z from the lens
fzz
11
'
1
and so
)()()(
'' zzfz
f
fz
fzz
|''|'
zzz
db
Points a t distance are brought into focus at distance z 'z
Thus points at distance will give rise to a blur circle of diameterz
with d the diameter of the lens
-zz’
-zz’
P
P’
Q
Q’db
![Page 3: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/3.jpg)
Irradiance, E
• Light power per unit area (watts per square meter) incident on a surface.
• If surface tilts away from light, same amount of light strikes bigger surface (less irradiance)(no foreshortening)
• E times pixel area times exposure time -> pixel intensity
light
surface
![Page 4: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/4.jpg)
Radiance, L
• Amount of light radiated from a surface into a given solid angle per unit area (watts per square meter per steradian).
• Note: the area is the foreshortened area, as seen from the direction that the light is being emitted.
• Brightness corresponds roughly to radiance
light
surface
![Page 5: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/5.jpg)
Solid angle
• The solid angle subtended by a cone of rays is the area of a unit sphere (centered at the cone origin) intersected by the cone
• A hemisphere cover 2 sterradians
![Page 6: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/6.jpg)
![Page 7: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/7.jpg)
3
2
2
2
cos4)cos/(
cos
4
Z
D
Z
Dd
Power emitted from patch DA
![Page 8: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/8.jpg)
Relationship :Image Irradiance and Scene Radiance
4
2
cos4
f
DLE
![Page 9: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/9.jpg)
![Page 10: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/10.jpg)
Radiosity
The total power leaving a point on a surface per unit area on the surface
dPLPB cos),,()(
If radiance independent of angle -> ingegrate over hemisphere
2
0
2
0
)(sincos)()(
PLddPLPB
![Page 11: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/11.jpg)
BRDF
dL
L
iiii
eee
cos)(
)(
,
,
)(
)()(
,
,,,,
ii
eeeeii
E
LfBRDF
unit: 1sr
![Page 12: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/12.jpg)
Special Cases: Lambertian
1
),,,( eeiif
• Albedo is fraction of light reflected.
•Diffuse objects (cloth, matte paint).
• Brightness doesn’t depend on viewpoint.
• Does depend on angle between light and surface.
Surface normal
Light )cos(),( eeL
Note: reflected light is with strength proportional to cos of angle with surface normal, but the area is foreshortened
![Page 13: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/13.jpg)
Lambertian Examples
Scene
(Oren and Nayar)
Lambertian sphere as the light moves.
(Steve Seitz)
![Page 14: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/14.jpg)
Specular surfaces
• Another important class of surfaces is specular, or mirror-like.– radiation arriving along
a direction leaves along the specular direction
– reflect about normal– some fraction is
absorbed, some reflected
– on real surfaces, energy usually goes into a lobe of directions
(http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html)
![Page 15: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/15.jpg)
Specular surfaces
(http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html)
•Brightness depends on viewing direction.
![Page 16: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/16.jpg)
Phong’s model• Vision algorithms rarely depend
on the exact shape of the specular lobe.
• Typically:– very, very small --- mirror– small -- blurry mirror– bigger -- see only light
sources as “specularities”– very big -- faint specularities
• Phong’s model– reflected energy falls off with
cosn
(Forsyth & Ponce)
![Page 17: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/17.jpg)
Lambertian + Specular Model
)(cos),()(
cos),()(),(
,
,,
osn
sss
iiidoo
PLP
dPLPPL
![Page 18: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/18.jpg)
Lambertian + specular
• Two parameters: how shiny, what kind of shiny.• Advantages
– easy to manipulate– very often quite close true
• Disadvantages– some surfaces are not
• e.g. underside of CD’s, feathers of many birds, blue spots on many marine crustaceans and fish, most rough surfaces, oil films (skin!), wet surfaces
– Generally, very little advantage in modelling behaviour of light at a surface in more detail -- it is quite difficult to understand behaviour of L+S surfaces (but in graphics???)
![Page 19: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/19.jpg)
Lambertian+Specular+Ambient
(http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html)
![Page 20: Image formation 2. Blur circle A point at distance is imaged at point from the lens and so Points a t distance are brought into focus at distance Thus.](https://reader030.fdocuments.us/reader030/viewer/2022032704/56649d605503460f94a40c65/html5/thumbnails/20.jpg)
http://www.cas.vanderbilt.edu/bsci111b/eye/human-eye.jpg
Human Eye• pupil: 1-8mm• Refracting power
(1/f) 60-68 diopters (1 diopter = 1m-1)
• Macula lutea: region at center of retina
• Blind spot: where ganglion cell axons exit retina from the optiv nerve