1. 3-D Computer Vision CSc83029 / Ioannis Stamos 3-D Computer Vision CSc 83029 Radiometry and Reflectance

2. 3-D Computer Vision CSc83029 / Ioannis Stamos From 2D to 3D  DEPTH from TWO or MORE IMAGES  Stereo  Optical Flow -> Factorization Method.  SHAPE from SINGLE IMAGE CUES  SHAPE from SHADING  SHAPE from TEXTURE  …

3. 3-D Computer Vision CSc83029 / Ioannis Stamos Shading Encodes Shape

4. 3-D Computer Vision CSc83029 / Ioannis Stamos Radiometry and Reflectance n I Image Intensity I = f ( orientation n, surface reflectance, illumination, imaging system ) L Surface Element Note: Image Intensity Understanding is an under-constrained problem!

5. 3-D Computer Vision CSc83029 / Ioannis Stamos Solid Angle δω=(δA cosθ)/R (steradian) δ δω 2

6. Solid Angle δω=(δA cosθ)/R (steradian) δ δω 2 Foreshortened Area δA’ δω= δA’/R (steradian) 2

7. Solid Angle δω=(δA cosθ)/R (steradian) δ δω 2 Foreshortened Area Unit Sphere δA’ δω= δA’/R (steradian) 2 Solid Angle Sustained by a hemisphere = 2π

8. n Source Flux Radiant Intensity of Source: Light flux (power) emitted per unit solid angle: J=dΦ/dω (watts/steradian) dω dA Surface Irradiance: Flux incident per unit surface area: E=dΦ/dA (watts/m ) Does not depend on where the light is coming from! 2

9. Flux=dΦ Surface Radiance(Brightness): Flux emitted per unit foreshortened area, per unit solid angle: L= d Φ/(dA cosθ r )dω (watts/m. steradian) Note: L depends on direction θr Surface can radiate into whole hemisphere L is proportional to irradiance E Depends on reflectance properties of surface dω dA 2 2 θrθr 2

10. 3-D Computer Vision CSc83029 / Ioannis Stamos Surface Radiance & Image Irradiance E=δP/δI:Irradiance at point p (Watts/m ) δP= (δO * cosθ)* L * ΔΩ, L scene radiance at P. 2 L (Watts/m * steradian) 2 Trucco & Verri

11. 3-D Computer Vision CSc83029 / Ioannis Stamos F=f/d: F-number: How much light is captured by the camera Trucco & Verri

12. 3-D Computer Vision CSc83029 / Ioannis Stamos Radiometry and Reflectance n I Image Intensity I = f ( orientation n, surface reflectance, illumination, imaging system ) Scene radiance L Image irradiance 1 / F-number of lens E Optics Brightness falloff Assume Image irradiance is proportional to scene radiance

13. 3-D Computer Vision CSc83029 / Ioannis Stamos Bi-Directional Reflectance Distribution Function (BRDF) n y x z φ θ

14. 3-D Computer Vision CSc83029 / Ioannis Stamos Bi-Directional Reflectance Distribution Function (BRDF) n y x z φ θ : Irradiance due to source in direction : Radiance of surface in direction BRDF:

15. 3-D Computer Vision CSc83029 / Ioannis Stamos Bi-Directional Reflectance Distribution Function (BRDF) n y x z φ θ : Irradiance due to source in direction : Radiance of surface in direction BRDF: For Rotationally Symmetric Reflectance Properties: BDRF:ISOTROPIC SURFACES *Bird Feathers are often Non-Isotropic.

16. 3-D Computer Vision CSc83029 / Ioannis Stamos Reflectance Models *Reflection: An Electromagnetic Phenomenon λ τ σh Two Approaches to deriving Reflectance Models: Physical Optics (Wave Optics) Geometrical Optics (Ray Optics) Geometrical Models are approximation to Physical Models. But easier to use.

17. 3-D Computer Vision CSc83029 / Ioannis Stamos Surface Reflection Body Reflection Internal scattering Body Reflection: *Diffuse Reflection *Matte Appearance *Non-Homogeneous Medium Surface Reflection: *Specular Reflection *Glossy Appearance *Highlights. *Dominant for Metals Image Intensity: Diffuse Comp + Specular Comp

18. Lambertian Reflectance Model Albedo: intrinsic brightness or color of surface n Theta is the angle between source direction and surface normal s A Lambertian (diffuse) surface scatters light equally in all directions

19. 3-D Computer Vision CSc83029 / Ioannis Stamos Lambertian Reflectance Model Surface appears equally bright from all viewing directions A Lambertian (diffuse) surface scatters light equally in all directions Albedo: intrinsic brightness or color of surface Illumination strength n s

20. 3-D Computer Vision CSc83029 / Ioannis Stamos Lambertian Reflectance Model A Lambertian sphere n s Surface normal n Direction of illumination s Commonly used in Computer Vision and Graphics Effective albedo

21. 3-D Computer Vision CSc83029 / Ioannis Stamos What Information Does Shading Encode In regions of constant albedo, changes of intensity correspond to changes in the surface normal of the scene

22. 3-D Computer Vision CSc83029 / Ioannis Stamos Ideal Specular Model (Mirrors) n Perfect reflector sr *Very SMOOTH surface *All incident energy reflected in a single direction v Viewer received light only when v=r

23. 3-D Computer Vision CSc83029 / Ioannis Stamos Phong Reflectance Model b=0.3, c=0.7, n=2 b=0.7, c=0.3, n=0.5 diffuse specular v: viewing direction α θi n s r

24. 3-D Computer Vision CSc83029 / Ioannis Stamos Torrance-Sparrow Model Specular Reflection from Rough Surfaces. Surface Micro-Structure Model Facet orientation Mean orientation α Micro-facet Orientation Model: (example) (Gaussian Model) Isotropic σ: roughness parameter

25. 3-D Computer Vision CSc83029 / Ioannis Stamos Torrance-Sparrow Model Masking and Shadowing Effects shadow Masked Light n s r v Specular Direction Radiance Geometric Factor G (Masking-Shadowing) n’ β

26. 3-D Computer Vision CSc83029 / Ioannis Stamos Gradient Space (p,q) Surface normal can be represented by the intersection of the normal with a plane. p q x y Source z 1.0