Understanding Image Formation and Light Reflection: A Comprehensive Guide - Prof. Cornelia, Study notes of Computer Science

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A point at distance z is imaged at point^ z^ ' from the lens

z z f

and so

' ' z z

z f

f

z f

f

z z

z z

z

d

b

Points a t distance z are brought into focus at distance z '

Thus points at distance z will give rise to a blur circle of diameter

with d the diameter of the lens

z’ -z

z’ -z

P

P’

Q Q’ b d

• 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

• 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

(^222) cos 3 ( /cos ) 4

cos 4 Z

D Z

d D

Power emitted from patch DA

4

2

cos 4 f

D E L

The total power leaving a point on a surface per unit area on the surface

B ( P ) L ( P , , )cos d

If radiance independent of angle -> ingegrate over hemisphere

2

0

2

0

B ( P ) L ( P ) cos sin d d L ( P )

L d

L i i i i

e e e ( ) cos

( ) ,

,

( )

( ) ( ) ,

, , , , i i

i i e e e e E

BRDF f L unit: (^) sr^1

Scene

(Oren and Nayar)

Lambertian sphere as the light moves. (Steve Seitz)

• 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/Graphi csNotes/Shading/Shading.html)

• 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 (^) cos n

(Forsyth & Ponce)

( ) ( , )cos ( )

( , ) ( ) ( , )cos

,

, ,

s s s n s o

o o d i i i

P L P

L P P L P d

(http://graphics.cs.ucdavis.edu/GraphicsNotes/Shading/Shading.html)

http://www.cas.vanderbilt.edu/bsci111b/eye/human-eye.jpg

• 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