Recovering dual-level rough surface parameters from simple lighting. Graphics Seminar, Fall 2010

Transcription

1 Recovering dual-level rough surface parameters from simple lighting Chun-Po Wang Noah Snavely Steve Marschner Graphics Seminar, Fall 2010

2 Motivation and Goal Many surfaces are rough

3 Motivation and Goal Many surfaces are rough

4 Motivation and Goal Goal: build a model for rough surface Perfect mirror Micro-level roughness Meso-level roughness Non-visible roughness Visible roughness

5 The Inverse Problem iphone screen Goal: fit a low-dimensional model Use only one or a few photos Use simple, inaccurate lighting and camera position Use simple techniques E.g., statistical analysis Reflection Metal cabinet (rough surface)

6 The Inverse Problem iphone What is the roughness in the micro- and meso-level? Reflection What is the size of these bumps? Metal cabinet

7 Related works [Torrance et al., 1967] Micro-facet model The surface consists of small, randomly disposed, mirror-like facets [Cook et al., 1981] Two or more scales of roughness

8 Related works [Ramamoorthi et al., 2001] Spherical Harmonics A signal processing framework for inverse rendering under general illumination conditions [Han et al., 2007] Spherical Harmonics This paper shows how meso-level structure is mixed into micro-level structure by altering the underlying BRDF

9 Outline Surface model Problem formulation Recovering roughness Model Micro-level, Meso-level Factoring mixed roughness

10 Surface model

11 Surface model Micro-level Meso-level

12 Surface model at Micro-level Cook-Torrance model Vectors L: direction of the light V: direction of the viewer N: (global) surface normal H: half vector of L and V Terms D: facet slope distribution function F: Fresnel term G: geometrical attenuation factor

13 Facet slope distribution function Describe how rough a surface is E.g., Gaussian model D Small m Large m α

14 Surface model at Meso-level Microfacets at the visible level Facet slope distribution function is not enough: no width information Simulated by bump mapping 1. Height displacement 2. Width of the bumps Model bump maps as stationary random process How to describe this random process? How many parameters are needed? We want to use only 2

15 Height displacement Modeled by the scale of the bump map Small scale Large scale

16 Width of the bumps image 2D autocorrelation Autocorrelation: the spatial (or time-domain) similarity of a signal to itself τ y τ x X τ Idea: model as a normalized 2D Gaussian function One parameter: the variance of the Gaussian function

17 Bump map generation We can also generate bump map from a single parameter By using Fourier transform and random phasing For synthesizing images

18 Bump map generation Generate bump maps from one parameter Wiener-Khinchin Theorem The power spectral density of a stationary random process is the Fourier transform of the corresponding autocorrelation function

19 Bump map generation (cont.) The procedure: 1. Generate 2D Gaussian function as the autocorrelation function 2. Compute its Fourier transform, and take square root. This is the magnitude of the Fourier transform of the signal we want. 3. Randomly permute the phase of the Fourier transform 4. Do inverse Fourier transform to get the noise signal

20 Parameters of our model Micro-level Root mean square slope of facets Meso-level Width of the bumps Height displacement (scale)

21 Demo Images are rendered by PBRT Light Camera Rough surface

22 Micro-level roughness = 0.001

23 Micro-level roughness = 0.003

24 Micro-level roughness = 0.01

25 Micro-level roughness = 0.03

26 Micro-level roughness = 0.1

27 Meso-level roughness (scale) = 0

28 Meso-level roughness (scale) = 0.025

29 Meso-level roughness (scale) = 0.05

30 Meso-level roughness (scale) = 0.075

31 Meso-level roughness (scale) = 0.1

32 1

33 The Inverse Problem

34 Problem formulation Goal: recover low dimensional parameters in micro- and meso-level Can be used to generate renderings which look similar to the real surface at different distances Assumptions The surface can be modeled by random facets at two very different scales The pattern in the meso-level is stationary

35 What we want are Output At Micro-level Root mean square slope of facets in microlevel At Meso-level Width of the bumps Height displacement Possible solutions?

36 Problem formulation Perfect mirror Reflection as transform function C = g(f(a)) = (g f)(a) Micro-level + Meso-level A Parameters C B = f(a) C = g(b) B Micro-level

37 Transform in Micro-level In [Ramamoorthi et al., 2001] Reflected light field as a convolution of the lighting and BRDF Sharp env. map + rough surface = Blurred env. map + perfect mirror The transform function is a convolution of the env. map and the BRDF Sphere Harmonics Powerful tool, but may be overkill f()

38 Transform in Meso-level Tranform function: a look-up function The environment map is scrambled g()

39 Recover mixed-roughness The transform function (g f) f: A convolution function (micro-level) g: A look-up function (meso-level) What is the property of this transform function? (g f)()? Width of the bumps Height displacement R.M.S. slope Meso-level Micro-level

40 Method for width of the bumps Autocorrelation? Rectified and normalized

41 Recover the width of the bumps Directly applying autocorrelation to the reflected image does not work Autocorrelation of the surface patch Our autocorrelation model

42 Recover the width of the bumps (cont.) Negative 2nd partial derivative Bump map derivative Bump map derivative autocorrelation autocorrelation Bump map Autocorrelation negative 2nd derivative Bump map derivative Autocorrelation

43 Recover the width of the bumps (cont.) Proof idea: Assume the surface is diffuse The brightness of a point on the surface is related to the slope of the facet there The brightness is related to the derivative of the bump map The autocorrelation of the derivative of the bump map is the negative second derivative of the autocorrelation of the bump map itself Bump map derivative Bump map derivative autocorrelation autocorrelation Bump map Autocorrelation negative 2nd derivative Bump map derivative Autocorrelation

44 Recover the width of the bumps (cont.) Therefore, we can fit negative 2nd derivative of our autocorrelation model to the patch Autocorrelation of the surface patch Negative 2nd derivative of our autocorrelation model

45 The direction of derivatives? Direction = light direction When the surface is diffuse The lighting is directional How about in general case? Seems to hold for environment lighting Not true when the surface is not diffuse

46 Diffuse surface Directional light

47 Diffuse surface Environment lighting

48 Microfacet surface Directional light

49 Autocorrelation of real surfaces White, painted wall in an apartment Lit by daylight

50 Autocorrelation of real surfaces (cont.) White, painted wall in Upson Hall 4F Lit by daylight

51 Recover mixed-roughness The 2-level of roughness can be mixed by Looking at the surface at distance, or Panning the camera or the surface, then averaging all images A surface lit by B/W environment light Randomly move the surface and average the result images

52 Recover mixed-roughness (cont.) Applying techniques in single-level problem to recover parameter of mixed roughness How to factor this into 2 levels of parameters?

53 Summary A dual-level model for rough surface Micro-level: microfacet model Meso-level: visible bumps modeled by bump maps with certain autocorrelation Possible methods to recover parameters Width of the bumps Fitting autocorrelation with negative 2nd derivative of Gaussian function Height displacement Root mean square slope of facets

54 On-going works How to: Recover micro-level roughness by simpler method, given our model for the surface? Apply autocorrelation to non-diffuse surface and general lighting condition? Factor mixed roughness?

55 Thank you for your attention!