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

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, surfaces ,and shadows

Reflections

Refractions

Interreflections

Scattering

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

Radiometry Radiance ( 𝑀 ): Energy carried by a ray 𝑜 𝑒𝜕 • Power per unit area perpendicular 𝜄 to direction of travel , per unit solid 𝑒𝐵 angle 𝑒𝐵cos𝜄 • Units: Watts per square meter per steradian ( 𝑋𝑛 −2 𝑡𝑠 −1 )

Radiometry Irradiance ( 𝐹 ): Energy arriving at a surface 𝑜 𝑒𝜕 • Incident power in a given direction, per unit area 𝜄 • Units: 𝑋𝑛 −2 𝑒𝐵 𝑒𝐵cos𝜄

Foreshortening: A simple observation “Perpendicular light” “Foreshortened light”

Radiometry Irradiance ( 𝐹 ): Energy arriving at a surface 𝑜 𝑒𝜕 • Incident power in a given direction, per unit area 𝜄 • Units: 𝑋𝑛 −2 𝑒𝐵 𝑒𝐵cos𝜄 For a surface receiving radiance 𝑀(𝜄, 𝜒) coming in from 𝑒𝜕 the corresponding irradiance is 𝐹 𝜄, 𝜒 = 𝑀 𝜄, 𝜒 cos𝜄 𝑒𝜕

BRDF: Bidirectional Reflectance Distribution Function source sensor Z viewing 𝜄 incident direction normal direction 𝜄 𝑠 , 𝜒 𝑠 𝜄 𝑗 𝜄 𝑠 𝜄 𝑗 , 𝜒 𝑗 Y X surface 𝜒 element Irradiance : Light per unit area incident on a surface Radiance : Light from the surface reflected in a given direction, within a given solid angle

BRDF: Bidirectional Reflectance Distribution Function source sensor Z viewing 𝜄 incident direction normal direction 𝜄 𝑠 , 𝜒 𝑠 𝜄 𝑗 𝜄 𝑠 𝜄 𝑗 , 𝜒 𝑗 Y X surface 𝜒 element 𝐹 𝑡𝑣𝑠𝑔𝑏𝑑𝑓 (𝜄 𝑗 , 𝜒 𝑗 : Irradiance at surface from direction 𝜄 𝑗 , 𝜒 𝑗 𝑀 𝑡𝑣𝑠𝑔𝑏𝑑𝑓 (𝜄 𝑠 , 𝜒 𝑠 : Radiance from surface in direction 𝜄 𝑠 , 𝜒 𝑠

BRDF: Bidirectional Reflectance Distribution Function source sensor Z viewing 𝜄 incident direction normal direction 𝜄 𝑠 , 𝜒 𝑠 𝜄 𝑗 𝜄 𝑠 𝜄 𝑗 , 𝜒 𝑗 Y X surface 𝜒 element 𝐹 𝑡𝑣𝑠𝑔𝑏𝑑𝑓 (𝜄 𝑗 , 𝜒 𝑗 : Irradiance at surface from direction 𝜄 𝑗 , 𝜒 𝑗 𝑀 𝑡𝑣𝑠𝑔𝑏𝑑𝑓 (𝜄 𝑠 , 𝜒 𝑠 : Radiance from surface in direction 𝜄 𝑠 , 𝜒 𝑠 𝑀 𝑡𝑣𝑠𝑔𝑏𝑑𝑓 (𝜄 𝑠 ,𝜒 𝑠 BRDF: 𝑔(𝜄 𝑗 , 𝜒 𝑗 ; 𝜄 𝑠 , 𝜒 𝑠 ) = 𝐹 𝑡𝑣𝑠𝑔𝑏𝑑𝑓 (𝜄 𝑗 ,𝜒 𝑗

Important properties of BRDFs source sensor Z viewing 𝜄 incident direction normal direction 𝜄 𝑠 , 𝜒 𝑠 𝜄 𝑗 𝜄 𝑠 𝜄 𝑗 , 𝜒 𝑗 Y X surface 𝜒 element Helmholtz Reciprocity: 𝑔 𝜄 𝑗 , 𝜒 𝑗 ; 𝜄 𝑠 , 𝜒 𝑠 = 𝑔 𝜄 𝑠 , 𝜒 𝑠 ; 𝜄 𝑗 , 𝜒 𝑗

Important properties of BRDFs source sensor Z viewing 𝜄 incident direction normal direction 𝜄 𝑠 , 𝜒 𝑠 𝜄 𝑗 𝜄 𝑠 𝜄 𝑗 , 𝜒 𝑗 Y X surface 𝜒 element Rotational Symmetry (Isotropy): 𝑔 𝜄 𝑗 , 𝜒 𝑗 ; 𝜄 𝑠 , 𝜒 𝑠 = 𝑔 𝜄 𝑗 , 𝜄 𝑠 , 𝜒 𝑗 − 𝜒 𝑠

BRDF’s can be incredibly complicated…

Reflection Models source incident Body (diffuse) Reflection: direction body • Diffuse Reflection reflection • Matte Appearance surface • Non-Homogeneous medium • Clay, paper, etc.

Reflection Models Body (diffuse) Reflection: • Diffuse Reflection • Matte Appearance • Non-Homogeneous medium • Clay, paper, etc.

Reflection Models incident surface source Surface Reflection: direction reflection • Specular Reflection • Glossy Appearance surface • Highlights • Dominant for Metals

Reflection Models Surface Reflection: • Specular Reflection • Glossy Appearance • Highlights • Dominant for Metals

Reflection Models surface source incident reflection direction Image Intensity = body Body Reflection + reflection Surface Reflection surface

Diffuse Reflection and Lambertian BRDF • Only body reflection, and no specular reflection • Lamberts law – essentially a patch looks equally bright from every direction.

Diffuse Reflection and Lambertian BRDF

Diffuse Reflection and Lambertian BRDF source intensity 𝐽 sensor incident viewing normal 𝑜 direction direction 𝜄 𝑗 𝜄 𝑠 𝑡 𝑤 surface element • Surface appears equally bright from all directions! (independent of 𝑤 )

Diffuse Reflection and Lambertian BRDF source intensity 𝐽 sensor incident viewing normal 𝑜 direction direction 𝜄 𝑗 𝜄 𝑠 𝑡 𝑤 surface element • Lambertian BRDF is simply a constant – the albedo : 𝑔(𝜄 𝑗 , 𝜒 𝑗 ; 𝜄 𝑠 , 𝜒 𝑠 ) = 𝜍 𝑒

Diffuse Reflection and Lambertian BRDF source intensity 𝐽 sensor incident viewing normal 𝑜 direction direction 𝜄 𝑗 𝑡 𝑤 surface element • Surface Radiance: 𝑀 = 𝜍 𝑒 𝐽 cos 𝜄 𝑗 = 𝜍 𝑒 𝐽 ( 𝑜 ⋅ 𝑡 ) source intensity

Diffuse Reflection and Lambertian BRDF source intensity 𝐽 sensor incident viewing normal 𝑜 direction direction 𝜄 𝑗 𝑡 𝑤 surface element • Surface Radiance: 𝑀 = 𝜍 𝑒 𝐽 cos 𝜄 𝑗 = 𝜍 𝑒 𝐽 ( 𝑜 ⋅ 𝑡 ) source intensity

Specular Reflection and Mirror BRDF How about a mirror? Reflection only at mirror angle

Specular Reflection and Mirror BRDF specular/mirror source intensity 𝐽 direction 𝑛 𝜄 𝑛 , 𝜒 𝑛 incident normal 𝑜 viewing direction 𝑡 direction 𝜄 𝑗 𝜄 𝑤 sensor 𝜄 𝑗 , 𝜒 𝑗 𝑤 𝜄 𝑤 , 𝜒 𝑤 surface element • All incident light reflected in a single direction (visible when 𝑤 = 𝑛 )

Specular Reflection and Mirror BRDF specular/mirror source intensity 𝐽 direction 𝑛 𝜄 𝑛 , 𝜒 𝑛 incident normal 𝑜 viewing direction 𝑡 direction 𝜄 𝑗 𝜄 𝑤 sensor 𝜄 𝑗 , 𝜒 𝑗 𝑤 𝜄 𝑤 , 𝜒 𝑤 surface element • Mirror BRDF is simply a double-delta function: 𝑔(𝜄 𝑗 , 𝜚 𝑗 ; 𝜄 𝑤 , 𝜚 𝑤 ) = 𝜍 𝑡 𝜀(𝜄 𝑗 − 𝜄 𝑤 ) 𝜀(𝜚 𝑗 + 𝜌 − 𝜚 𝜑 )

Specular Reflection and Mirror BRDF specular/mirror source intensity 𝐽 direction 𝑛 𝜄 𝑛 , 𝜒 𝑛 incident normal 𝑜 viewing direction 𝑡 direction 𝜄 𝑗 𝜄 𝑤 sensor 𝜄 𝑗 , 𝜒 𝑗 𝑤 𝜄 𝑤 , 𝜒 𝑤 surface element • Surface Radiance: 𝑀 = 𝐽 𝜍 𝑡 𝜀 𝜄 𝑗 − 𝜄 𝑤 𝜀 𝜒 𝑗 + 𝜌 − 𝜒 𝑤

Specular Reflection and Mirror BRDF specular/mirror source intensity 𝐽 direction 𝑛 𝜄 𝑛 , 𝜒 𝑛 incident normal 𝑜 viewing direction 𝑡 direction 𝜄 𝑗 𝜄 𝑤 sensor 𝜄 𝑗 , 𝜒 𝑗 𝑤 𝜄 𝑤 , 𝜒 𝑤 surface element • Surface Radiance: 𝑀 = 𝐽𝜍 𝑡 𝜀 𝑛 − 𝑤 or 𝐽 𝜍 𝑡 𝜀 𝑜 − ℎ ( ℎ is the “half angle”)

Specular Reflection and Glossy BRDF 𝑙 𝑀 = 𝐽 𝜍 𝑡 𝑛 ⋅ 𝑤

Specular reflection Moving the light source Changing the exponent

Phong Reflection Model The BRDF of many surfaces can be approximated by: Lambertian + Specular Model source source normal Lambertian Specular Model

Diffuse + Specular Reflection diffuse specular diffuse + specular