Reflectance & Lighting

Transcription

1 Reflectance & Lighting Computer Vision I CSE5A Lecture 6

2 Last lecture in a nutshell Need for lenses (blur from pinhole) Thin lens equation Distortion and aberrations Vignetting CS5A, Winter 007 Computer Vision I

3 Radiometry Read Chapter 4 of Ponce & Forsyth Homework 1 Assigned Outline Solid Angle Irradiance Radiance BRDF Lambertian/Phong BRDF

4 Solid Angle By analogy with angle (in radians), the solid angle subtended by a region at a point is the area projected on a unit sphere centered at that point The solid angle subtended by a patch area da is given by dω = dacosθ r

5 Radiance Power is energy per unit time (watts) Radiance: Power traveling at some point in a specified direction, per unit area perpendicular to the direction of travel, per unit solid angle (θ, φ) dω x da Symbol: L(x,θ,φ) Units: watts per square meter per steradian : w/(m sr 1 )

6 Radiance Power is energy per unit time θ (θ, φ) dω Radiance: Power traveling at some point in a specified direction, per unit area perpendicular to the direction of travel, per unit solid angle x da Symbol: L(x,θ,φ) Units: watts per square meter per steradian : w/(m sr 1 ) L = P ( dacosθ ) dω Power emitted from patch, but radiance in direction different from surface normal

7 Radiance properties In free space, radiance is constant as it propagates along a ray Derived from conservation of flux Fundamental in Light Transport. dφ = Ldω da = L dω da = dφ dω = da r dω = da r 1 1 da da dω da = = dω da r L = L 1

8 Radiance transfer What is the power received by a small area da at distance r from a small area da 1 emitting radiance L? From definition of radiance P L = ( dacosθ ) dω From definition of solid angle P = LdA1 cosθ1dω1 > = L r da da 1 cosθ cosθ 1 dω = dacosθ r

9 Irradiance How much light is arriving at a surface? Units of irradiance: Watts/m This is a function of incoming angle. A surface experiencing radiance L(x,θ,φ) coming in from solid angle dω experiences irradiance: de( x) = L ( x, θ, φ) cosθdω Crucial property: Total Irradiance arriving at the surface is given by adding irradiance over all incoming angles Total irradiance is E( x) = = ππ / 0 0 L hemisphere L ( x, θ, φ) ( x, θ, φ) cosθdω cosθ sinθdθ dφ L(x,θ,φ) φ θ N x x

10 Intermezzo: Camera s s sensor Measured pixel intensity is a function of irradiance integrated over pixel s area over a range of wavelengths For some time I = E( x, y, λ, t) s( x, y) q( λ) dydxdλ dt t λ x y Ideally, it s a linear function of the radiance, but the camera response C(.) may not be linear I C = t λ x y E( x, y, λ, t) s( x, y) q( λ) dydxdλ dt

11 Image sensor Two types : 1. CCD. CMOS

12 CCD separate photo sensor at regular positions no scanning charge-coupled devices (CCDs) : interline transfer and frame transfer photosensitive storage

13 CMOS Each photo sensor has its own amplifier More noise (reduced by subtracting black image) Lower sensitivity (lower fill rate) Uses standard CMOS technology Allows to put other components on chip Smart pixels

14 CCD vs. CMOS Mature technology Specific technology High production cost High power consumption Higher fill rate Blooming Sequential readout Recent technology Standard IC technology Cheap Low power Less sensitive Per pixel amplification Random pixel access Smart pixels On chip integration with other components

15 Color Cameras We consider 3 concepts: 1. Prism (with 3 sensors). Filter mosaic 3. Filter wheel and X3

16 Prism color camera Separate light in 3 beams using dichroic prism Requires 3 sensors & precise alignment Good color separation

17 Filter mosaic Coat filter directly on sensor Demosaicing (obtain full colour & full resolution image)

18 Filter wheel Rotate multiple filters in front of lens Allows more than 3 colour bands Only suitable for static scenes

19 Prism vs. mosaic vs. wheel approach Prism Mosaic Wheel # sensors Separation High Average Good Cost High Low Average Framerate High High Low Artefacts Low Aliasing Motion Bands or more High-end cameras Low-end cameras Scientific applications

20 newer color CMOS sensor Foveon s X3 better image quality smarter pixels

21 Radiometry of thin lenses What is image irradiance E for a radiance L emitted from a point P?

22 Radiometry of thin lenses δa δa Let δω be the solid angle subtended by δa (or δa ) from the center of the lens δω = δa'cosα = δacos β ( z' / cosα ) ( z / cosα ) δa δa' = cosα cos β z z'

23 Radiometry of thin lenses δa δa δω = δa'cosα = δacos β ( z' / cosα ) ( z / cosα ) δa δa' = cosα cos β z z' Let Ω be the solid angle subtended by the lens from P. π Ω = 4 d cosα ( z / cosα ) π = 4 d z 3 cosα

24 Radiometry of thin lenses δa δa δω = π Ω = 4 δp δa'cosα ( z' / cosα ) ( z / cosα ) d cosα = δacos β π = 4 d z π d 4 z 3 cosα δa δa' LδAcos 3 cosα z = cos β z' ( z / cosα ) The power δp emitted from the patch δa with radiance L and falling on the lens is: = LΩδAcos β = α cos β

25 Radiometry of thin lenses δa δa δω = π Ω = 4 δa'cosα ( z' / cosα ) ( z / cosα ) d cosα ( z / cosα ) = δacos β π d = 4 z δa δa' cosα = cos β π d 3 δp = LΩδAcos β = LδAcos α cos β 4 z δp π d δa 3 E = = L cos α cos β CSE 5A, δa' Winter z δa' 3 cosα z z' d E = π cos 4 α L 4 z E: Image irradiance L: emitted radiance d : Lens diameter Z: depth Image Irradiance α: Angle of patch from optical axis