CS4495/6495 Introduction to Computer Vision 5A-L1 Photometry Slides - - PowerPoint PPT Presentation

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CS4495/6495 Introduction to Computer Vision 5A-L1 Photometry Slides - - PowerPoint PPT Presentation

Jun 21, 2023 469 likes β€’869 views

CS4495/6495 Introduction to Computer Vision 5A-L1 Photometry Slides by Yin Li Thanks to Srinivasa Narasimhan, Shree Nayar, David Kreigman, Marc Pollefeys Photometry: Measuring light Lighting Camera Physical Models Computer Scene Lights,

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SLIDE 1

5A-L1 Photometry

CS4495/6495 Introduction to Computer Vision

Slides by Yin Li Thanks to Srinivasa Narasimhan, Shree Nayar, David Kreigman, Marc Pollefeys

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SLIDE 2

Photometry: Measuring light

Camera Computer Lighting Scene Physical Models

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SLIDE 3

Lights, surfaces ,and shadows

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SLIDE 4

Reflections

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SLIDE 5

Refractions

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Interreflections

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Scattering

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SLIDE 8
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SLIDE 9

Surface appearance

  • Image intensity = 𝑔(normal, surface reflectance, illumination)
  • Surface reflection depends on both the viewing and

illumination directions

source sensor surface element normal

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SLIDE 10

Radiometry

Radiance (𝑀): Energy carried by a ray

  • Power per unit area perpendicular

to direction of travel, per unit solid angle

  • Units: Watts per square meter per

steradian (π‘‹π‘›βˆ’2π‘‘π‘ βˆ’1)

𝑒𝐡 π‘œ πœ„ π‘’πœ• 𝑒𝐡cosπœ„

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SLIDE 11

Radiometry

Irradiance (𝐹): Energy arriving at a surface

  • Incident power in a given direction,

per unit area

  • Units: π‘‹π‘›βˆ’2

𝑒𝐡 π‘œ πœ„ π‘’πœ• 𝑒𝐡cosπœ„

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SLIDE 12

Foreshortening: A simple observation

β€œPerpendicular light” β€œForeshortened light”

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𝑒𝐡

Radiometry

Irradiance (𝐹): Energy arriving at a surface

  • Incident power in a given direction,

per unit area

  • Units: π‘‹π‘›βˆ’2

For a surface receiving radiance 𝑀(πœ„, πœ’) coming in from π‘’πœ• the corresponding irradiance is 𝐹 πœ„, πœ’ = 𝑀 πœ„, πœ’ cosπœ„ π‘’πœ•

π‘œ πœ„ π‘’πœ• 𝑒𝐡cosπœ„

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SLIDE 14

BRDF: Bidirectional Reflectance Distribution Function

Irradiance: Light per unit area incident on a surface Radiance: Light from the surface reflected in a given direction, within a given solid angle X Y Z πœ„ πœ’ source sensor surface element normal incident direction πœ„π‘—, πœ’π‘— viewing direction πœ„π‘ , πœ’π‘  πœ„π‘— πœ„π‘ 

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𝐹𝑑𝑣𝑠𝑔𝑏𝑑𝑓(πœ„π‘—, πœ’π‘— : Irradiance at surface from direction πœ„π‘—, πœ’π‘— 𝑀𝑑𝑣𝑠𝑔𝑏𝑑𝑓(πœ„π‘ , πœ’π‘  : Radiance from surface in direction πœ„π‘ , πœ’π‘ 

BRDF: Bidirectional Reflectance Distribution Function

source sensor surface element normal incident direction πœ„π‘—, πœ’π‘— viewing direction πœ„π‘ , πœ’π‘  X Y Z πœ„ πœ’ πœ„π‘— πœ„π‘ 

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BRDF: 𝑔(πœ„π‘—, πœ’π‘—; πœ„π‘ , πœ’π‘ ) =

𝑀𝑑𝑣𝑠𝑔𝑏𝑑𝑓(πœ„π‘ ,πœ’π‘  𝐹𝑑𝑣𝑠𝑔𝑏𝑑𝑓(πœ„π‘—,πœ’π‘—

BRDF: Bidirectional Reflectance Distribution Function

source sensor surface element normal incident direction πœ„π‘—, πœ’π‘— viewing direction πœ„π‘ , πœ’π‘  X Y Z πœ„ πœ’ 𝐹𝑑𝑣𝑠𝑔𝑏𝑑𝑓(πœ„π‘—, πœ’π‘— : Irradiance at surface from direction πœ„π‘—, πœ’π‘— 𝑀𝑑𝑣𝑠𝑔𝑏𝑑𝑓(πœ„π‘ , πœ’π‘  : Radiance from surface in direction πœ„π‘ , πœ’π‘  πœ„π‘— πœ„π‘ 

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Important properties of BRDFs

Helmholtz Reciprocity: 𝑔 πœ„π‘—, πœ’π‘—; πœ„π‘ , πœ’π‘  = 𝑔 πœ„π‘ , πœ’π‘ ; πœ„π‘—, πœ’π‘—

source sensor surface element normal incident direction πœ„π‘—, πœ’π‘— viewing direction πœ„π‘ , πœ’π‘  X Y Z πœ„ πœ’ πœ„π‘— πœ„π‘ 

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SLIDE 18

Important properties of BRDFs

Rotational Symmetry (Isotropy): 𝑔 πœ„π‘—, πœ’π‘—; πœ„π‘ , πœ’π‘  = 𝑔 πœ„π‘—, πœ„π‘ , πœ’π‘— βˆ’ πœ’π‘ 

source sensor surface element normal incident direction πœ„π‘—, πœ’π‘— viewing direction πœ„π‘ , πœ’π‘  X Y Z πœ„ πœ’ πœ„π‘— πœ„π‘ 

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SLIDE 19

BRDF’s can be incredibly complicated…

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Reflection Models

Body (diffuse) Reflection:

  • Diffuse Reflection
  • Matte Appearance
  • Non-Homogeneous

medium

  • Clay, paper, etc.

source surface incident direction body reflection

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SLIDE 21

Reflection Models

Body (diffuse) Reflection:

  • Diffuse Reflection
  • Matte Appearance
  • Non-Homogeneous

medium

  • Clay, paper, etc.
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SLIDE 22

Reflection Models

source surface reflection surface incident direction

Surface Reflection:

  • Specular Reflection
  • Glossy Appearance
  • Highlights
  • Dominant for Metals
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SLIDE 23

Reflection Models

Surface Reflection:

  • Specular Reflection
  • Glossy Appearance
  • Highlights
  • Dominant for Metals
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SLIDE 24

Reflection Models

source surface incident direction body reflection surface reflection

Image Intensity = Body Reflection + Surface Reflection

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Diffuse Reflection and Lambertian BRDF

  • Only body reflection, and no specular reflection
  • Lamberts law – essentially a patch looks

equally bright from every direction.

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Diffuse Reflection and Lambertian BRDF

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SLIDE 27

Diffuse Reflection and Lambertian BRDF

  • Surface appears equally bright from all directions!

(independent of 𝑀 )

source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 viewing direction 𝑀 πœ„π‘— πœ„π‘ 

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Diffuse Reflection and Lambertian BRDF

  • Lambertian BRDF is simply a constant – the albedo:

𝑔(πœ„π‘—, πœ’π‘—; πœ„π‘ , πœ’π‘ ) = πœπ‘’

source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 viewing direction 𝑀 πœ„π‘— πœ„π‘ 

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Diffuse Reflection and Lambertian BRDF

  • Surface Radiance: 𝑀 = πœπ‘’ 𝐽 cos πœ„π‘— = πœπ‘’ 𝐽 ( π‘œ β‹… 𝑑

)

source intensity source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 viewing direction 𝑀 πœ„π‘—

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Diffuse Reflection and Lambertian BRDF

  • Surface Radiance: 𝑀 = πœπ‘’ 𝐽 cos πœ„π‘— = πœπ‘’ 𝐽 ( π‘œ β‹… 𝑑

)

source intensity source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 viewing direction 𝑀 πœ„π‘—

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SLIDE 31

Specular Reflection and Mirror BRDF

How about a mirror? Reflection only at mirror angle

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SLIDE 32

Specular Reflection and Mirror BRDF

  • All incident light reflected in a single direction (visible

when 𝑀 = 𝑛)

source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 πœ„π‘—, πœ’π‘— viewing direction 𝑀 πœ„π‘€, πœ’π‘€ πœ„π‘— πœ„π‘€ specular/mirror direction 𝑛 πœ„π‘›, πœ’π‘›

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Specular Reflection and Mirror BRDF

  • Mirror BRDF is simply a double-delta function:

𝑔(πœ„π‘—, πœšπ‘—; πœ„π‘€, πœšπ‘€) = πœπ‘‘πœ€(πœ„π‘— βˆ’ πœ„π‘€) πœ€(πœšπ‘— + 𝜌 βˆ’ πœšπœ‘)

source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 πœ„π‘—, πœ’π‘— viewing direction 𝑀 πœ„π‘€, πœ’π‘€ πœ„π‘— πœ„π‘€ specular/mirror direction 𝑛 πœ„π‘›, πœ’π‘›

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Specular Reflection and Mirror BRDF

  • Surface Radiance:

𝑀 = 𝐽 πœπ‘‘ πœ€ πœ„π‘— βˆ’ πœ„π‘€ πœ€ πœ’π‘— + 𝜌 βˆ’ πœ’π‘€

source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 πœ„π‘—, πœ’π‘— viewing direction 𝑀 πœ„π‘€, πœ’π‘€ πœ„π‘— specular/mirror direction 𝑛 πœ„π‘›, πœ’π‘› πœ„π‘€

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Specular Reflection and Mirror BRDF

  • Surface Radiance:

𝑀 = π½πœπ‘‘πœ€ 𝑛 βˆ’ 𝑀

  • r 𝐽 πœπ‘‘ πœ€ π‘œ βˆ’ β„Ž

(β„Ž is the β€œhalf angle”)

source intensity 𝐽 sensor surface element normal π‘œ incident direction 𝑑 πœ„π‘—, πœ’π‘— viewing direction 𝑀 πœ„π‘€, πœ’π‘€ πœ„π‘— specular/mirror direction 𝑛 πœ„π‘›, πœ’π‘› πœ„π‘€

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Specular Reflection and Glossy BRDF

𝑀 = 𝐽 πœπ‘‘ 𝑛 β‹… 𝑀 𝑙

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Specular reflection

Moving the light source Changing the exponent

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Phong Reflection Model

The BRDF of many surfaces can be approximated by: Lambertian + Specular Model

source

Lambertian

source

Specular Model

normal

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Diffuse + Specular Reflection

diffuse specular diffuse + specular