Curvature-Based Shading of Translucent Materials, such as

Human Skin

Konstantin KolchinDMP Inc.

Introduction and Previous Work

Subsurface scattering in translucent materials transfers light away from the entrance point. The result depends on local geometry.

To describe this, Nicodemus et al. 1977 introduced Bidirectional Surface Scattering Distribution Function (BSSRDF).

Introduction and Previous Work, cont.

Jensen et al. 2001. Dipole-source model for BSSRDF.

Jensen and Buhler 2002. Hierarchical rendering with the dipole-model BSSRDF.

Borshukov and Lewis 2003. Texture-space diffusion. Dachsbacher and Stamminger 2003. Translucent

shadow maps. Mertens et al. 2005. Importance sampling of

BSSRDF in screen plane.

Introduction and Previous Work, cont.

d'Eon and Luebke 2007. Texture-space diffusion extended with stretch correction.

Diffusion approximation

)(),())(,(),( iioidi)( iiitiiii

xxxx dAdRNNFLS x

The integral is four-dimensional. To render subsurface scattering in real time, one have to calculate this integral in real time.

),(1),( ootooo

NFL x

Notation

Scattering neighborhood factor

Similarly to Hao and Varshney 2004, we integrate first over surface and then over directions. The surface integral is called the scattering neighborhood factor (SNF), p, so that

dpLNFL )()()(1)( iootoo

Integration of SNF using Monge’s form

Our suggestion is to compute SNF using Monge’s form.

Any smooth surface can be locally represented in Monge’s form

or, with axes taken along the principal curvature directions,

),( 213 xxfx

222

2113 xkxkx

21, xx

Integration of SNF using Monge’s form, cont.

Expression for SNF, , becomes

where is defined by

and

)()())(()( d3222111)( it xx dARxkxkNFpS

)(S

03222111 xkxk

22

22

21

213222111i 1/)( xkxkxkxkN

),,( 21 kkp

Possible simplificationsExample 1

One of possible simplifications is to replace Ft with its average value. SNF is then expressed in terms of a simple integral that can be precalculated.

ba

dxdxRFbxabaI/

21dt1 )()(),( x

Possible simplificationsExample 1, cont.

Possible simplificationsExample 2

Another approximation is 1. to set curvature to constant 2. to neglect tangential dependenceGeometrically, this means to locally replace the

object surface with a paraboloid.

Possible simplifications Example 2, cont.

a – ‘true’ curvatures, b,c,d – constant curvature (2 times difference)

a b

c d

We suggest a new method for shading 3D objects with translucent appearance. It can be used for real-time rendering.

Summary

Future work

To generalize the method to higher-order surface derivatives.

To adapt it to low-frequency illumination (using spherical harmonics).

To solve the problem for simple shapes, such as a sphere or cylinder.

That’s all

Thank you for your attention