1. eight
light and image

2. Light as a ray Light is most frequently thought of as a set of rays
Traveling from a light source
To a viewer
By way of some surface(s) that reflect it

3. Light as a ray Light is most frequently thought of as a set of rays
Traveling from a light source
To a viewer
By way of some surface(s) that reflect it
Often, it’s many surfaces

4. Pinhole camera object Placing Produces object
a very small hole
in very a dark box
Produces
a faint image
on the opposite side of the box
Technically, the image is upside-down
image plane
light ray
hole
object

5. Pinhole camera The hole constrains where the rays can project
Farther objects must project closer to the center
Nearer objects, toward the sides

6. Pinhole camera The hole constrains where the rays can project
Farther objects produce smaller images
Nearer objects, larger images

7. Perspective projection
object
Image plane
A camera projects a 3D world down to a 2D world
The particular type of projection is called perspective projection
We can describe perspective projection in terms of coordinates
light ray Y f y Z
Y = height of object Z = depth y = “height” of projection (note image is really upside down) f = focal length
y/f = Y/Z y = fY/Z

8. Perspective projection
(X, Y, Z)
Image plane
A camera projects a 3D world down to a 2D world
The particular type of projection is called perspective projection
We can describe perspective projection in terms of coordinates
light ray Y f
(x,y) Z
x = fX/Z
y = fY/Z
(x,y) = (fX/Z, fY/Z)

9. Perspective projection
(X, Y, Z)
Image plane
Decreasing the focal length makes the image smaller
But also increases your field of view
Lenses with short focal lengths are therefore called wide-angle lenses
light ray Y f
(x,y) Z
x = fX/Z
y = fY/Z
(x,y) = (fX/Z, fY/Z)

10. Perspective projection
(X, Y, Z)
Image plane
Increasing the focal length makes the image bigger
But decreases your field of view
Lenses with large focal lengths are called telephoto lenses
light ray Y f Z
(x,y)
x = fX/Z
y = fY/Z
(x,y) = (fX/Z, fY/Z)

11. Light as a ray Light is most frequently thought of as a set of rays
Traveling from a light source
To a viewer
By way of some surface(s) that reflect it

12. Lambertian reflection
Surface reflection
Surface reflectance is very complicated
There are two main models of reflectance
Specular (glossy) surfaces bounce it directly off
Lambertian (matte) bounce it evenly in all directions
incident ray
reflected rays
specular reflection
(highlights)
incident ray
reflected rays
Lambertian reflection
(matte/diffuse)

13. Specular reflection Mirror-like reflection
Mirrors are near-perfect specular reflectors
Incident and reflected rays have at (almost) the same angle
In practice, there’s some scattering
All wavelengths are (usually) reflected equally
So reflection has the color of the light
incident ray
reflected rays

14. Lambertian reflection
Lambertian/diffuse/matte reflection
Perfect non-glossy paint
Light reflected equally in all directions
Brightness depends on illumination angle
When light hits and an angle, it’s spread out over a wider area (1/sin θ times wider)
So the intensity of the light coming out is dimmed by sin θ
Not all wavelengths are reflected equally
The reflection has the color of the surface (at least if the light is white) θ d θ
d/sin θ
beam spreads out by 1/sin θ

15. Surface normals θ (For reasons that will be clearer later)
We usually measure the angle a little differently
We use the angle between the light and
A line sticking straight out from the surface
This is called the surface’s normal
This means the dimming factor is cos θ
Because we measured θ differently
surface normal θ d θ
d/cos θ
beam spreads out by 1/cos θ

16. Specular and diffuse reflection

17. Shape from shading
Perceptual system computes surface curvature from intensity gradients
Bias to assume light source is above the head

18. Modeling Pictorial techniques to bring out object shape
Chiaroscuro very important
Point-lights generate
strong shadows
Highlights
Carvaggio, Incredulity of St. Thomas

19. Modeling

20. Modeling with lighting
Key light
Offset from camera
Mood, modeling
Fill light
Fills in rest of scene
Keeps shadows under control
Others
Back light, rim light, …

21. Rim lighting key fill rim
John Lasseter, Toy Story (USA, 1995)
key
fill
rim
Used to emphasize outline of an object in shadow
Key light leaves left edge of character in shadow
Can’t make out object boundaries
Spooky (Tom Hanks isn’t supposed to be spooky)
Weak rim light brings up contrast at object boundary
Tom Hanks safely de-spooked

22. The Boris Karloff effect

23. The Locket (USA, 1947)

24. Cohen bros., Blood Simple (USA, 1984)

25. The French Connection (1971)

26. Dark City (1998)

27. Dark city

28. Dark City

29. Dark City

30. Dark City

31. Subsurface scattering
Translucent materials don’t reflect light directly
It bounces around inside the material for a while and comes out in a different location
This is important for modeling skin and wax

32. Components of reflection and transmission
                     
specular
diffuse
SSS
combined

33. Problems with pinhole cameras
object
Because the aperture (hole) is so small, pinhole cameras let very little light in
This means you need to use very bright lights or very long exposures to capture images on film
image plane
light ray
small aperture
object

34. Problems with pinhole cameras
object
We can make the aperture larger
But then it doesn’t constraint where the rays go
We lose focus
Light from objects spreads out
Images of objects overlap
image plane
light rays
big aperture
object

35. Thin lens projection
A lens allows many rays to focus to the same point
Brighter image
But only focuses a single depth plane
Image plane
lens
light rays
aperture

36. Depth of field

37. Thin lens projection
That’s partly why cameras with lenses still have an aperture
By shrinking the aperture
We get closer to a pinhole camera
And we get wider depth of field
Image plane
lens
light rays
aperture

38. Aperture and depth of field

39. Deep focus

40. Citizen Kane (Welles, 1941)

41. Citizen Kane

42. Shallow focus
Rules of the Game, (Renoir, 1939)

43. magnetic field
electric field
time
Light as a wave
Light is an oscillation between electric and magnetic fields
Frequency/wavelength determines apparent color
But color is perceptual property, not a physical one
Amplitude determines apparent brightness
High frequency
Short wavelength
Low frequency
Long wavelength

44. Oscillation stretch time speed
Occurs when two forces are in opposition
Causes energy to alternate between two forms
Guitar string
Motion stretches the string
Which slows the motion
And eventually reverses it
But then the stretch reverses
And so on …
Commonly takes the form of a sine wave
speed(t) = cos ωt
stretch(t) = sin ωt
ω is the frequency of the oscillation (how often it repeats)

45. Waves Waves are oscillations that move through space
Frequency Rate of cycling
Period (how far between cycles)
Amplitude (intensity): Size of the oscillation
w(x) = A sin(ωx)

46. Chromatic aberration
A lens actually focuses different wavelengths (colors) at slightly different depths
In extreme cases, this leads to a colored blur around bright lights
blue/violet artifacts

47. The human eye Lens and iris Photoreceptors Retinal processing
Rods (b/w)
Cones (color)
Fovea
Small (size of thumbnail at 3’)
High resolution
Color vision
Macula, and periphery Low resolution, wide FOV
Retinal processing
Gain control
Edge enhancement?
Simple motion detection
lens/iris
rods
cones
retinal
ganglion

48. Chromatic aberration in the eye
blue is
poorly
focused on
the
retina
green is
well
focused on
the
retina
The blue photoreceptors of the eye evolved first
So the have lower resolution
And nature didn’t try to fix the chromatic aberration of the eye
So blue light is significantly out of focus on the retina
Blue backgrounds in PowerPoint are evil

49. Photoreceptors Rods Cones Colors seem to fade in low light
Found mostly in the macula and periphery
Very sensitive to light
But don’t detect color
Cones
Found in the fovea
Less sensitive
Color sensitive
Colors seem to fade in low light

50. Trichromacy
Having different cones for every possible wavelength would be bad
We just have three kinds of cones
“Blue” cones: short wavelengths
“Green” cones: intermediate wavelengths
“Red” cones: long wavelengths
However, their responses overlap
The eye reduces all the wavelengths at a given pixel to just the total “amount” of “red”, “green”, and “blue”

51. Components of a color image