3-D Computer Vision CSc 83029

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

2. 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-D Computer Vision CSc83029 / Ioannis Stamos

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

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

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

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

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

8. Source Flux dω n dA Radiant Intensity of Source: Light flux (power) emitted per unit solid angle: J=dΦ/dω (watts/steradian) 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. 2 Flux=dΦ θr dω dA Surface Radiance(Brightness): Flux emitted per unit foreshortened area, per unit solid angle: L= d Φ/(dA cosθr)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 2 2

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

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

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

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

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

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

16. Reflectance Models *Reflection: An Electromagnetic Phenomenon λ σh τ 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. 3-D Computer Vision CSc83029 / Ioannis Stamos

17. 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 3-D Computer Vision CSc83029 / Ioannis Stamos

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

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

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

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

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

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

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

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

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