Analysis of Subsurface Scattering under Generic Illumination Y. Mukaigawa K. Suzuki Y. Yagi Osaka University, Japan ICPR2008

Subsurface Scattering Light scattering in translucent media OpaqueTranslucent Light Camera Peers et al. SIGGRAPH2006 BRDF: Light Camera Subsurface scattering BSSRDF: Bidirectional Reflectance Distribution Function Bidirectional Scattering Surface Reflectance Distribution Function

Translucent objects Typical translucent object  marble, milk, and skin Actually, many objects in our living environment are also translucent. fruit vegetable milk marble soap candleskin plastic cloth paper egg One of the reasons that many photometric analyzing methods do not work well in our living environment is they cannot treat the subsurface scattering.

Related work BSSRDF measurement using special lighting devices Projector [Tariq et al. VMV2006] Fiber optic spectrometer [Weirich et al. SIGGRAPH2006 ] Laser beam [Goesele et al. SIGGRAPH2004] Projector [Peers et al. SIGGRAPH2006] Measurement under strictly controlled illumination

Our goal Analysis of subsurface scattering under generic illumination Inputs: single image, 3-D shape, illumination Outputs: reflectance properties Inverse rendering of translucent object 3-D shape illumination reflectance properties image rendering inverse rendering KnownUnknown

Dipole Model for BSSRDF Decomposition of the BSSRDF into  Fresnel functions: F t ( ,  )  Diffuse subsurface reflectance: R(d) R(d) is the function of the distance d between x i and x o.  Including two inherent parameters of the material scattering coefficient:  s absorption coefficient:  a d xixi xoxo (Jensen et al. SIGGRAPH2001) Example of R(d) Skin （ σ s =0.74,σ a =0.032 ） Apple （ σ s =2.29,σ a =0.003 ） d [mm] R(d)R(d)

Inputs: 1. Estimating R(d) for several distances d. 2. Fitting of the dipole model. Outputs: two parameters  scattering coefficient  s.  absorption coefficient  a. Flow of the proposed method Single image 3-D shapeIlluminationCamera parameters + R(d)R(d) d estimated R(d) dipole model fitting Additional information

Formulation and solution Divide object surfaces into m small patches P 1,P 2,..., P m. Radiance l j of the patch P j is formulated by Quantization of the distances d jk. by n discrete distances d' 1, d' 2,..., d' n.  Calculate only R' 1, R' 2,..., R' n.  Linear solution, if n < m. R(d)R(d) d d' 1 d' 2 d' 3 d' 4 d' 5 irradiance radiance PkPk PjPj R(d jk ) ckck ljlj d jk unknownknown Ill-posed problem m 2 unknowns > m constraints

Model fitting Dipole model fitting to the estimated R' i Estimation of  scattering coefficient  s  absorption coefficient  a Discrete estimation  R' 1,..., R' n for the quantized distances d' 1,..., d' n Continuous estimation  R(d) for every distance d R(d)R(d) d d' 1 d' 2 d' 3 d' 4 d' 5 R' i R(d)R(d)

Simulated scene Evaluate how the quantization of the distance affects the accuracy of the estimated parameters. Parameter estimation  finding the best parameter set that minimizes the error Illumination  s =2.19  a =0.002  =1.3 Rendered image parameters ss aa  d (mm) Min Max Step Range and step of the parameters.

Results of parameter estimation sampling Quantization (mm) ss aa PSNR (dB) Ground truth Estimated parameters and the PSNRs large small inaccurate unstable quantization (mm) PSNR(dB) best

Dipole model fitting The parametric model of R(d) input image regenerated image （ PSNR 47.9dB ） Estimated R(d) d （ mm ） R(d)R(d) Ground truth Estimated model  s =2.19  a =0.002  s =2.34  a =0.009

Real scene Evaluate the stability 3 materials:  Polypropylene (PP)  Polyethylene (PE)  Polyoxymethylene (POM) 2 shapes:  Cube  Pyramid (with base) 2 illuminations:  Left and right directions. In total, 12 images (3x2x2) Environment for image capture Camera Light source Target object Target objects PPPEPOM

Input images (3 materials x 2 shapes x 2 illuminations) LeftRightLeftRight CubePyramid PP PE POM

Estimated parameters aa ss PP PE POM PPPOMPE Parameters for each material  Similar parameters for each material except for some outliers.   s of the cube under right illumination is always outlier. Averaged parameters  R(d) for each material Rendered images using estimated parameters d [mm] R(d) PP POM PE R(d)R(d)

The first step of the inverse rendering for translucent objects. Conclusion A new method to analyze subsurface scattering from a single image taken under generic illumination  Linear solution by quantizing the distance between patches.  Parameter estimation by fitting dipole model. Future works  improvement of stability and accuracy