Announcements

Project status reports on Wednesday

prepare 5 minute ppt presentation

should contain:

problem statement (1 slide)

description of approach (1 slide)

some images (1 slide)

current status + plans (1 slide)

Light

Readings

Szeliski, 2.2, 2.3.2

Properties of light

Today

What is light?

How do we measure it?

How does light propagate?

How does light interact with matter?

What is light?

Slide 6

The light field

Known as the plenoptic function

If you know R, you can predict how the scene would appear from any viewpoint. How?

Stanford light field gantry

More info on light fields

If you’re interested to read more:

The plenoptic function

Original reference: E. Adelson and J. Bergen, "The Plenoptic Function and the Elements of Early Vision," in M. Landy and J. A. Movshon, (eds) Computational Models of Visual Processing, MIT Press 1991.

L. McMillan and G. Bishop, “Plenoptic Modeling: An Image-Based Rendering System”, Proc. SIGGRAPH, 1995, pp. 39-46.

The light field

M. Levoy and P. Hanrahan, “Light Field Rendering”, Proc SIGGRAPH 96, pp. 31-42.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, "The lumigraph," in Proc. SIGGRAPH, 1996, pp. 43-54.

What is light?

The visible light spectrum

We “see” electromagnetic radiation in a range of wavelengths

Light spectrum

The appearance of light depends on its power spectrum

How much power (or energy) at each wavelength

The human visual system

Color perception

Light hits the retina, which contains photosensitive cells

Density of rods and cones

Rods and cones are non-uniformly distributed on the retina

Rods responsible for intensity, cones responsible for color

Fovea - Small region (1 or 2°) at the center of the visual field containing the highest density of cones (and no rods).

Less visual acuity in the periphery—many rods wired to the same neuron

Demonstrations of visual acuity

Brightness contrast and constancy

The apparent brightness depends on the surrounding region

brightness contrast: a constant colored region seem lighter or darker depending on the surround:

http://www.sandlotscience.com/Contrast/Checker_Board_2.htm

brightness constancy: a surface looks the same under widely varying lighting conditions.

Light response is nonlinear

Our visual system has a large dynamic range

We can resolve both light and dark things at the same time

One mechanism for achieving this is that we sense light intensity on a logarithmic scale

an exponential intensity ramp will be seen as a linear ramp

Another mechanism is adaptation

rods and cones adapt to be more sensitive in low light, less sensitive in bright light.

Visual dynamic range

After images

Tired photoreceptors

Send out negative response after a strong stimulus

Color perception

Three types of cones

Each is sensitive in a different region of the spectrum

but regions overlap

Short (S) corresponds to blue

Medium (M) corresponds to green

Long (L) corresponds to red

Different sensitivities: we are more sensitive to green than red

varies from person to person (and with age)

Colorblindness—deficiency in at least one type of cone

Color perception

Rods and cones act as filters on the spectrum

To get the output of a filter, multiply its response curve by the spectrum, integrate over all wavelengths

Each cone yields one number

Q: How can we represent an entire spectrum with 3 numbers?

Perception summary

The mapping from radiance to perceived color is quite complex!

We throw away most of the data

We apply a logarithm

Brightness affected by pupil size

Brightness contrast and constancy effects

Afterimages

The same is true for cameras

But we have tools to correct for these effects

See Rick’s lecture notes on Computational Photography and HDR

Light transport

Light sources

Basic types

point source

directional source

a point source that is infinitely far away

area source

a union of point sources

More generally

a light field can describe *any* distribution of light sources

Slide 26

Slide 27

The interaction of light and matter

What happens when a light ray hits a point on an object?

Some of the light gets absorbed

converted to other forms of energy (e.g., heat)

Some gets transmitted through the object

possibly bent, through “refraction”

Some gets reflected

as we saw before, it could be reflected in multiple directions at once

Let’s consider the case of reflection in detail

In the most general case, a single incoming ray could be reflected in all directions. How can we describe the amount of light reflected in each direction?

The BRDF

The Bidirectional Reflection Distribution Function

Given an incoming ray and outgoing ray
what proportion of the incoming light is reflected along outgoing ray?

Constraints on the BRDF

Energy conservation

Quantity of outgoing light ≤ quantity of incident light

integral of BRDF ≤ 1

Helmholtz reciprocity

reversing the path of light produces the same reflectance

Diffuse reflection

Diffuse reflection

Dull, matte surfaces like chalk or latex paint

Microfacets scatter incoming light randomly

Effect is that light is reflected equally in all directions

Diffuse reflection

Specular reflection

Phong illumination model

Phong approximation of surface reflectance

Assume reflectance is modeled by three components

Diffuse term

Specular term

Ambient term (to compensate for inter-reflected light)

BRDF models

Phenomenological

Phong [75]

Ward [92]

Lafortune et al. [97]

Ashikhmin et al. [00]

Physical

Cook-Torrance [81]

Dichromatic [Shafer 85]

He et al. [91]

Here we’re listing only some well-known examples

Measuring the BRDF

Gonioreflectometer

Device for capturing the BRDF by moving a camera + light source

Need careful control of illumination, environment

BRDF databases

MERL (Matusik et al.): 100 isotropic, 4 nonisotropic, dense

CURET (Columbia-Utrect): 60 samples, more sparsely sampled, but also bidirectional texure functions (BTF)


Project status reports on Wednesday
	prepare 5 minute ppt presentation
	should contain:
		problem statement (1 slide)
		description of approach (1 slide)
		some images (1 slide)
		current status + plans (1 slide)


	Today
		What is light?
		How do we measure it?
		How does light propagate?
		How does light interact with matter?



		Known as the plenoptic function
		If you know R, you can predict how the scene would appear from any viewpoint. How?


	If you’re interested to read more:

	The plenoptic function
		Original reference: E. Adelson and J. Bergen, "The Plenoptic Function and the Elements of Early Vision," in M. Landy and J. A. Movshon, (eds) Computational Models of Visual Processing, MIT Press 1991.
		L. McMillan and G. Bishop, “Plenoptic Modeling: An Image-Based Rendering System”, Proc. SIGGRAPH, 1995, pp. 39-46.

	The light field
		M. Levoy and P. Hanrahan, “Light Field Rendering”, Proc SIGGRAPH 96, pp. 31-42.
		S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, "The lumigraph," in Proc. SIGGRAPH, 1996, pp. 43-54.


	We “see” electromagnetic radiation in a range of wavelengths


	The appearance of light depends on its power spectrum
		How much power (or energy) at each wavelength


	Color perception
		Light hits the retina, which contains photosensitive cells


	Rods and cones are non-uniformly distributed on the retina
		Rods responsible for intensity, cones responsible for color
		Fovea - Small region (1 or 2°) at the center of the visual field containing the highest density of cones (and no rods).
		Less visual acuity in the periphery—many rods wired to the same neuron


The apparent brightness depends on the surrounding region
	brightness contrast: a constant colored region seem lighter or darker depending on the surround:






		http://www.sandlotscience.com/Contrast/Checker_Board_2.htm

	brightness constancy: a surface looks the same under widely varying lighting conditions.


Our visual system has a large dynamic range
	We can resolve both light and dark things at the same time
	One mechanism for achieving this is that we sense light intensity on a logarithmic scale
		an exponential intensity ramp will be seen as a linear ramp
	Another mechanism is adaptation
		rods and cones adapt to be more sensitive in low light, less sensitive in bright light.


	Tired photoreceptors
		Send out negative response after a strong stimulus


Three types of cones
	Each is sensitive in a different region of the spectrum
		but regions overlap
		Short (S) corresponds to blue
		Medium (M) corresponds to green
		Long (L) corresponds to red
	Different sensitivities: we are more sensitive to green than red
		varies from person to person (and with age)
	Colorblindness—deficiency in at least one type of cone


Rods and cones act as filters on the spectrum
	To get the output of a filter, multiply its response curve by the spectrum, integrate over all wavelengths
		Each cone yields one number
	Q: How can we represent an entire spectrum with 3 numbers?


The mapping from radiance to perceived color is quite complex!
	We throw away most of the data
	We apply a logarithm
	Brightness affected by pupil size
	Brightness contrast and constancy effects
	Afterimages

The same is true for cameras
	But we have tools to correct for these effects
		See Rick’s lecture notes on Computational Photography and HDR


Basic types
	point source
	directional source
		a point source that is infinitely far away
	area source
		a union of point sources

More generally
	a light field can describe any distribution of light sources


What happens when a light ray hits a point on an object?
	Some of the light gets absorbed
		converted to other forms of energy (e.g., heat)
	Some gets transmitted through the object
		possibly bent, through “refraction”
	Some gets reflected
		as we saw before, it could be reflected in multiple directions at once

Let’s consider the case of reflection in detail
	In the most general case, a single incoming ray could be reflected in all directions. How can we describe the amount of light reflected in each direction?


	The Bidirectional Reflection Distribution Function
		Given an incoming ray and outgoing ray what proportion of the incoming light is reflected along outgoing ray?


Energy conservation
	Quantity of outgoing light ≤ quantity of incident light
		integral of BRDF ≤ 1

Helmholtz reciprocity
	reversing the path of light produces the same reflectance


	Diffuse reflection
		Dull, matte surfaces like chalk or latex paint
		Microfacets scatter incoming light randomly
		Effect is that light is reflected equally in all directions


Phong approximation of surface reflectance
	Assume reflectance is modeled by three components
		Diffuse term
		Specular term
		Ambient term (to compensate for inter-reflected light)


	Phenomenological
		Phong [75]
		Ward [92]
		Lafortune et al. [97]
		Ashikhmin et al. [00]
	Physical
		Cook-Torrance [81]
		Dichromatic [Shafer 85]
		He et al. [91]

	Here we’re listing only some well-known examples


	Gonioreflectometer
		Device for capturing the BRDF by moving a camera + light source
		Need careful control of illumination, environment


	MERL (Matusik et al.): 100 isotropic, 4 nonisotropic, dense











	CURET (Columbia-Utrect): 60 samples, more sparsely sampled, but also bidirectional texure functions (BTF)