1. Representations of Visual Appearance COMS 6160 [Fall 2006], Lecture 2 Ravi Ramamoorthi http://www.cs.columbia.edu/~ravir/6160

2. Outline  Basic preliminaries: Light Field, Radiance, Irradiance  Plenoptic Function and BRDF  Reflection Equation

6. Radiance  Power per unit projected area perpendicular to the ray per unit solid angle in the direction of the ray  Symbol: L(x,ω) (W/m 2 sr)  Flux given by dΦ = L(x,ω) cos θ dω dA

7. Radiance properties  Radiance is constant as it propagates along ray  Derived from conservation of flux  Fundamental in Light Transport.

10. Radiance properties  Sensor response proportional to surface radiance (constant of proportionality is throughput)  Far away surface: See more, but subtends smaller angle  Wall is equally bright across range of viewing distances Consequences  Radiance associated with rays in a ray tracer  All other radiometric quantities derived from radiance  Acquire functions of incoming and outgoing radiance

11. Irradiance, Radiosity  Irradiance E is the radiant power per unit area  Integrate incoming radiance over hemisphere  Projected solid angle (cos θ dω)  Uniform illumination: Irradiance = π [CW 24,25]  Units: W/m 2  Radiosity  Power per unit area leaving surface (like irradiance)

13. Outline  Basic preliminaries: Light Field, Radiance, Irradiance  Plenoptic Function and BRDF  Reflection Equation

14. Plenoptic Function  Radiance at each wavelength in every direction for every spatial location at every time instance  7D function (x,y,z,θ,φ,λ,t)  Measured appearance is ratio of outgoing radiance to incoming (ir)radiance. 14D function in general  This course is about subsets of this 14D function  Acquisition of appropriate slices (BRDFs one example)  Efficient Representation for rendering, editing, storage

15. BRDF  Reflected Radiance proportional to Irradiance  Constant proportionality: BRDF [CW pp 28,29]  Bidirectional Reflection Distribution Function  (4 Vars)  Reflectance Equation [CW pp 30]

17. Specular Term (Phong)

18. Specular Term (Blinn-Phong) Reflected Light (Output Image) Emission Incident Light (from light source) Sum over all light sources Blinn-Phong model (using half-angle) (s is shininess)

21. Outline  Basic preliminaries: Light Field, Radiance, Irradiance  Plenoptic Function and BRDF  Reflection Equation

22. Reflection Equation Reflected Light (Output Image) Emission Incident Light (from light source) BRDF Cosine of Incident angle

23. Reflection Equation Reflected Light (Output Image) Emission Incident Light (from light source) BRDF Cosine of Incident angle Sum over all light sources

24. Reflection Equation Reflected Light (Output Image) Emission Incident Light (from light source) BRDF Cosine of Incident angle Replace sum with integral