CPSC 441 Computer Graphics: Photon Mapping

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CPSC 441 Computer Graphics Photon Mapping

• Jinxiang Chai

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Review Ray Tracing

• Start with a camera, light(s), and geometry in
  scene
• Send rays from camera into scene
• Through pixels on image plane
• When intersection occurs
• Solve for Phong reflection model at p
• Shadow Rays
• Transmission Rays
• Reflection Rays
• Recurse

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Review Recursive Ray Tracing
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L1
L2
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2
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Review Ray Tracing

• Start with a camera, light(s), and geometry in
  scene
• Send rays from camera into scene
• Through pixels on image plane
• When intersection occurs
• Solve for Phong reflection model at p
• Shadow Rays
• Transmission Rays
• Reflection Rays
• Recurse

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Review Recursive Ray Tracing
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L1
L2
4
1
2
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Review Ray Tracing

• Start with a camera, light(s), and geometry in
  scene
• Send rays from camera into scene
• Through pixels on image plane
• When intersection occurs
• Solve for Phong reflection model at p
• Shadow Rays
• Transmission Rays
• Reflection Rays
• Recurse

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Review Recursive Ray Tracing
3
L1
L2
4
1
2
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Review Recursive Ray Tracing
3
L1
L2
4
1
2
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Review Recursive Ray Tracing
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L1
L2
4
1
2
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Review Recursive Ray Tracing
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L1
L2
4
1
2
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Review Recursive Ray Tracing
3
L1
L2
4
1
2
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Review Ray Tracing

• Start with a camera, light(s), and geometry in
  scene
• Send rays from camera into scene
• Through pixels on image plane
• When intersection occurs
• Solve for Phong reflection model at p
• Shadow Rays
• Transmission Rays
• Reflection Rays
• Recurse

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Review Recursive Ray Tracing
3
L1
L2
4
1
2
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Review Recursive Ray Tracing
3
L1
L2
4
1
2
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Review Ray Tracing

• A Ray Tree describes the increase in the number
  of rays sent each recursion
• When do you stop?
• When a ray hits nothing
• Return background color
• When a ray hits a non-transmitting and
  non-reflecting object
• At some maximum depth
• Return background color

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Outline

• Rendering equation
• Photon map

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Ray tracing and photon mapping
What are differences between two rendered
pictures?
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Ray tracing and photon mapping
caustics
Color bleeding
What are differences between two rendered
pictures?
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The Rendering Equation
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The Rendering Equation
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Global Illumination

• Various Rendering techniques solve some portion
  of the rendering equation
• If a technique approximates the integral, it is
  part of the family of Global Illumination

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Global Illumination

• Ray Tracing
• Radiosity
• Photon Mapping

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Radiosity

• Solves geometry term in form factor
• Approximates integral completely for
  diffuse-diffuse
• No reflection or transmission

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Ray Tracing

• Works well for reflection and refraction
• solves geometry eq. through ray intersection
  tests
• solves emission properly
• only solves integral for reflection and
  refraction to maxDepth
• Diffuse reflectance ignored

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Photon mapping
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Photon mapping
Two difficulties - Q how to compute the
incoming radiance Li? - Q how to
efficiently evaluate the integral?
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Photon mapping
Two difficulties - Q how to compute the
incoming radiance Li? A Compute Li based
on precomputed photon map - Q how to
efficiently evaluate the integral? A
Compute the integral based on monte carlo ray
tracing
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Photon mapping

• Is often used to simulate the interaction of
  light with a variety transparent substances
  (caustics)
• - glass
• - water
• - Diffuse inter-reflections between
  illuminated objects
• - Effects of particulate matter, e.g.
  smoke

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Photon mapping

• Phase I shoot and store photons
• - photons are shot from the light into the
  scene
• - photons are allowed to interact with
  objects in the environment
• - where photons fall are stored in special
  data structure called a photon map
• - 10000s of photons not billions (Statistical
  approximation based on density)

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Photon mapping

• Phase I shoot and store photons
• - photons are shot from the light into the
  scene
• - photons are allowed to interact with
  objects in the environment
• - where photons fall are stored in special
  data structure called a photon map
• - 10000s of photons not billions (Statistical
  approximation based on density)

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Shooting photons
Point light source
directional light
square light
general light
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Shooting photons
Point light source
directional light
square light
general light
The power of light
The number of photons
The power of an emitted photon
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Pseudocode for Emission of Photons from Point
Light Source
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Pseudocode for Emission of Photons from Point
Light Source

• Basic idea
• Radiant intensity as a probability function.
• Generate photons by sampling the probability
  function.

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Photon mapping

• Phase I shoot and store photons
• - photons are shot from the light into the
  scene
• - photons are allowed to interact with
  objects in the environment
• - where photons fall are stored in special
  data structure called a photon map
• - 10000s of photons not billions (Statistical
  approximation based on density)

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Photon tracing

• Photons are only stored when it hits diffuse
  surface
• Specular surface does not store any photons.

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Photon map
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Photon map
What information does each photon store?
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Photon map

• The photon

Placed in K-D tree for efficient access
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Three photon maps

• Caustic photon map
• - interact with at least one specular surface
• Global photon map
• - interact with diffuse surfaces only
• Volume photon map
• - indirect illumination of participating
  medium

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Global photon map

• Basic idea
• - Launch photons from the light sources in all
  directions
• - Store a photon (position, power and
  direction) in each intersection of the photon
  with the scene.
• - Compute the kind of interaction with the
  surface by using the Russian roulette.

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Global photon map

• The types of interactions are
• - Diffusion the photon is reflected in a
  random direction (projected hemisphere) or taking
  into account a BRDF.
• - Reflection Perfect reflection of the
  photon.
• - Refraction The photon is refracted using
  Snell's law.
• - Absorption We don't launch that photon
  again.

The Russian roulette method decides which
interaction to consider in function of the
material.
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Caustics photon map

• The global photon map has very weak caustics
  effects. We need to construct an additional map
  only for caustics.
• - Launch the rays only over the objects that
  can generate caustics.
• - Store the photons when they hit a diffuse
  surface only if previously it hit a reflective or
  refractive surface.

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Caustics and global photon map
The global photon map
The caustics photon map
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Photon Mapping

• Pass 2 Gather illumination
• - use ray tracing
• - direct illumination determined by ray
  tracing
• - indirect illumination determined by
  stochastically sampling photon map (gather photon
  within volume in the required direction)

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Rendering using photon map
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Rendering using photon map
Two main issues - How to compute incoming
radiance Li? - How to evaluate the integral
efficiently?
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Basic idea radiance estimate
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Basic idea radiance estimate
How to evaluate reflected radiance based on the
photon map?
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Basic idea radiance estimate
Evaluate the radiance based on nearby photons
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Basic idea radiance estimate
Evaluate the radiance based on nearby
photons Find N photons with the shortest
distance to the intersection point
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Radiance estimate using photon map
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Radiance estimate using photon map
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Radiance estimate using photon map
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Radiance estimate using photon map
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Radiance estimate using photon map
locally flat surface
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Radiance estimate using photon map
locally flat surface
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Radiance estimated using photon map
200000 photons
100 photons
500 photons
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Photon mapping rendering
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Photon mapping rendering
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Photon mapping rendering
Li,l direct illumination by light from the light
sources Li,c causticsindirect illumination from
the light sources via specular surface Li,d
indirect illumination from the light sources
(diffuse inter-reflection)
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Light sources
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Light sources
Li,l
Li,c
Li,d
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Photon mapping rendering
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Photon mapping rendering
Diffuse surfaces
Specular surfaces
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Photon mapping the
rendering equation
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Photon mapping the
rendering equation
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Accurate evaluation of the direct illumination
Similar to the evaluation of shadow rays in ray
tracing
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Photon mapping the
rendering equation
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Evaluation of the Specular and Glossy term
Similar to the evaluation of reflection rays in
ray tracing
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Photon mapping the
rendering equation
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Evaluation of the caustics
Evaluate this term using the caustics photon map
directly
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Photon mapping the
rendering equation
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Evaluation of the indirect diffuse illumination
Accurate evaluation of the integral using monte
carlo ray tracing method
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Results

• global photon map
• 200000 photons
• 100 photons for estimate

Ray tracing
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Cornell box with water