Illumination The Why the What and the How Sameer Agarwal Computer Vision Laboratory UCSD Illumination The Why the What and the How p 1 49 Why is it hard 1 Each Scene is a dynamical system 2 Objects interact with their environments 3 The presence of a new object changes the energy balance in the scene 4 The problem is under constrained Illumination The Why the What and the How p 2 49 Direct Illumination Illumination The Why the What and the How p 3 49 Global Illumination Illumination The Why the What and the How p 4 49 The Solution The Distant Scene The Local Scene The Synthetic Objects Illumination The Why the What and the How p 5 49 Distant Scene A Model of incoming light Contributes direct illumination only The reflections in the scene do not affect the distant illumination Modelled using a envionment map Illumination The Why the What and the How p 6 49 Local Scene A model of the local geometry of the scene A model of the local reflectance in the scene estimated from the scene or prior knowledge Contributes direct as well as indirect illumination to the synthetic objects Illumination The Why the What and the How p 7 49 Synthetic Objects A model of the geometry of the objects A model of the reflectance of the object Illumination The Why the What and the How p 8 49 The Method Capture the distant illumination in the scene Measure the local BRDF Model the synthetic objects and the local geometry Render the objects and the local scene using full global illuminations Composit into the original scene using differential rendering Illumination The Why the What and the How p 9 49 Anatomy of a light source What is a light source What is the space of all light sources How can we move about in this space Illumination The Why the What and the How p 10 49 Definitions Radiance Radiance is the amount of energy per unit time per unit solid angle per unit area in the direction of travel or The number of photons striking a point from a particular direction per second Radiance remains constant along a line in free space Illumination The Why the What and the How p 11 49 Definitions Free Space F A bounded open connected subset of 3d eucledian space F is the boundary of F Set of rays M F The set of all closed directed lines x1 x2 s t 1 x1 6 x2 2 x1 x2 F 3 The line joining x1 and x2 is contained entirely in F Illumination The Why the What and the How p 12 49 Ray Manifold Given a z0 let r be a ray which passes through x0 x0 y0 z0 in the direction p0 q0 1 then we make the association r x0 y0 p0 q0 Ray Manifold Given a free space F the set of rays M F is a 4 D manifold Illumination The Why the What and the How p 13 49 Ray Manifold R M F 0 R is the radiance along a ray r Radiance remains constant along in a line in free space Rz0 x0 y0 p0 q0 Rz1 x z1 z0 p0 y0 z1 z0 q0 p0 q0 Illumination The Why the What and the How p 14 49 The Lightsource Hypercube Given a plane Pz0 consider the set of rays hx hx M x y p q x 2 2 hy hy y 2 2 hp hp p 2 2 hq hq q 2 2 each having uniform radiance R hx hy hp hq Illumination The Why the What and the How p 15 49 Lightsource Hypercube Some integration shows that the radiant flux from this set of rays is Z hp 2 Z hq 2 dpdq hx hy R hx hy hp hq 2 2 2 hp 2 hq 2 1 p q set 1 R hx hy hp hq hx hy Z hp 2 Z hp 2 hq 2 dpdq 2 2 2 hq 2 1 p q 1 so that 1 Illumination The Why the What and the How p 16 49 Lightsource Hypercube Let I denote the indicator function on the interval 1 2 1 2 A uniform cubic source of unit flux centered at position 0 0 z0 is a source with the radiance function Rz0 x y p q R hx hy hp hq I y p q x I I I hx hy hp hq The set of all light sources can now be obtained by restricting the coordinates in various manners Illumination The Why the What and the How p 17 49 Light Sources Real Source Ideal model Overcast Sky Uniform Source Laser Single Ray Flourescent Tube Linear Source Sunlight Directed Point Source h x hy hp hq 0 0 0 0 0 0 0 Illumination The Why the What and the How p 18 49 Light Sources Real Source Ideal model hx hy hp hq Louveres Fan of rays 0 0 Small Panel Light Point Source 0 0 Light through crack Parallel Rays 0 0 0 Rotating spotlight Fan of rays 0 0 0 Illumination The Why the What and the How p 19 49 Source Rays That minimal subset Msrc M F s t if they are removed the radiance on the manifold M F would be identically zero Illumination The Why the What and the How p 20 49 Radiance Map St Peter s Basilica An omni directional high dynamic range image that records the incident illumination conditions at a particular point in space Illumination The Why the What and the How p 21 49 Real Pixels are floats 2 d I L cos4 t 4 h LP e 1 2 L Scene Radiance d2 e 4 t exposure There is no bound on the magnitude of I Illumination The Why the What and the How p 22 49 The radiometric response function M I M f I M is the observed image brightness M is bounded with finite dynamic range Estimating I requires estimating g f 1 Illumination The Why the What and the How p 23 49 Estimating g Use multiple exposures to estimate g Non Parametric Regression Debevec Malik Parametric Regression Mitsunaga Nayar Illumination The Why the What and the How p 24 49 Debevec Malik The range of f is discrete and finite f is monotonic and smooth Mi j g Mi j g Mi j log g Mi j f Ii j Ii j L i Pi e j log Li log Pi log ej 3 4 5 6 Illumination The Why the What and the How p 25 49 Non Parametric Regression O XX i j 2 g Mi j log Li Pi log ej X g 00 z 2 z g 00 z g z 1 2g z g z 1 Illumination The Why the What and the How p 26 49 Mitsunaga Nayar Assume a flexible polynomial model Perform regression to estimate the parameters of the mode Ii j g Mi j N X n cn Mi j n 0 Illumination The Why the What and the How …
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