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# Global Illumination for Image Synthesis

Global Illumination for Image Synthesis. 사실적 영상합성을 위한 전역조명 모델. transparency, caustics, etc. area light source. color bleeding. glossy reflection. non-polygonal geometry. soft shadow. 사실적 영상합성을 위한 전역조명 모델. Photo-realistic Rendering Framework. 사실적 영상합성을 위한 전역조명 모델.

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## Global Illumination for Image Synthesis

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1. Global Illumination for Image Synthesis

2. 사실적 영상합성을 위한 전역조명 모델 • transparency, caustics, etc. area light source color bleeding glossy reflection non-polygonal geometry soft shadow

3. 사실적 영상합성을 위한 전역조명 모델 • Photo-realistic Rendering Framework

4. 사실적 영상합성을 위한 전역조명 모델 • radiometry: measurement of light energy • irradiance(W/m2): the incident radiant power on a surface, per unit surface area (cf. radiosity) • radiance(W/srm2): the power per unit projected surface area, per unit solid angle Pixel values in image are proportional to radiance received from that direction.

5. 사실적 영상합성을 위한 전역조명 모델 • Materials- three forms

6. Bidirectional Reflectance Distribution Function • reciprocity

7. Rendering Equation • Input: • Light sources • Geometry of surfaces • Reflectance characteristics of surfaces • Output: value of radiance at all surface points and in all directions

8. Rendering Equation

9. Monte Carlo Integration • application of Monte Carlo integration to the RE • Generate N random samples xi. (uniformly over the entire integration domain) • Estimator: • Expected value of estimator: • Standard deviation:

10. Monte Carlo Integration • the average value of f with p: the expected value • a pdf p: S (space)→R, and x, a random variable x ~ p, - μ: a measure on the space the random variables occupy - S: dμ=dA=dxdy (area), dμ=dω=sinθdθdφ(direction) • Given a function f : S→R, and a random variable x ~ p, we can approximate the expected value of f(x) by a sum:

11. Monte Carlo Integration • an integral of a single function g rather than fp • p must be positive where g is nonzero. • For g/p with low variance (a similar shape) → choosing p intelligently: importance sampling • stratified sampling: to partition S, the domain of the integral, into several smaller domains Si, and evaluate the integral • example: the expected error → 0, if p = g/I

12. Monte Carlo Integration • generate samples according to density function p(x) • non-uniform • integration over hemisphere:

13. Monte Carlo Integration • hemisphere integration example • Irradiance due to light source:

14. image plane A B C D E Ray Tracing • Forward vs. Backward ray tracing • : What photons contribute to the image?

15. Direct Illumination: the reflected radiance coming directly from the light sources • integrate the incoming radiance over the hemisphere, multiply by the BRDF and cosine factors : the majority of samples is unconnected to the light source → wasted!!

16. Direct Illumination

17. Direct Illumination • Using Monte Carlo integration, the following parameters can be chosen: • Total number of shadow rays : How many paths will be generated for each radiance • Shadow rays per light source : How many of these paths will be sent to each light source → more paths to bright light sources, closer lights • Distribution of shadow rays within a light source : How to distribute the paths within each light source

18. Direct Illumination • single light source illumination • uniform sampling of light source area : p(y) = 1/Asource • uniform sampling of solid angle subtended by light source

19. light source sampling hemisphere sampling surface sampling Direct Illumination • multiple light source illumination • Separate computation for each of the light sources, & sum up the total contributions • all combined light sources → a single integration domain a. select a light source ki b. PDFp(y|ki) → a surface point yi on the light k c. the combined PDF for a sampled point yi on the combined are of all light sources: pL(k)p(y|k)

20. Indirect Illumination • paths of length > 1 • Many different path generators possible → The entire hemisphere needs to be considered • importance sampling • the cosine factor cos(Ψi, Nx) • BRDF fr(x, Θ↔ Ψi) • the incident radiance field Lr(r(x, Ψi)) • a combination of any of the above

21. Indirect Illumination surface sampling source shooting receiver shooting - 2 visibility terms - 1 visibility term - 1 visibility term & can be 0 & 1 ray intersection & 1 ray intersection

22. Radiosity • diffuse illumination, B(x) = πL(x)

23. Photon Mapping • 2 passes: • Shoot light-rays (“photons”) and store = “photons” are traced from the light sources into the scene → photon map : a caustic + a global photon map • Shoot viewing rays, interpolate = direct illumination + specular reflections, transmission, caustics + indirect illumination

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