**Skin Rendering**

**Wanho Choi **

**(wanochoi.com)**

**Skin**

### •

### Very

**complicated structure**

https://wtamu.edu/~cbaird/sq/2015/11/23/how-does-the-outer-layer-of-skin-cells-on-my-finger-detect-when-i-am-touching-an-object/ http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.226.4533&rep=rep1&type=pdf

**Most Materials**

### •

### They have

**two main components.**

### •

### Reflection =

**specular reflection + diﬀuse reflection**

https://blog.selfshadow.com/publications/s2015-shading-course/hoffman/s2015_pbs_physics_math_slides.pdf

**view dependent**

**Subsurface Scattering (SSS)**

### •

### Light goes beneath the skin surface,

**scatters and gets partially absorbed, and then exits somewhere else.**

### •

### Beneath the skin surface, the incoming light quickly becomes

**diﬀuse as it scatters.**

https://blog.selfshadow.com/publications/s2013-shading-course/hoffman/s2013_pbs_physics_math_notes.pdf

**incident light**

**surface reflection **

**(specular)**

**subsurface scattering **

**(=diﬀuse)**

**General Diﬀuse vis-a-vis SSS**

https://eo-college.org/courses/echoes-in-space/lessons/geometry/topic/the-scattering-mechanisms/

**BRDF**

### •

**Bidirectional Reflectance Distribution Function**

http://www.codinglabs.net/article_physically_based_rendering_cook_torrance.aspx

**BSSRDF**

### •

**Bidirectional Surface Scattering Reflectance Distribution Function**

### •

### BRDF is a

**special case of BSSRDF**

### (BRDF assumes light enters and exits at the

**same point.)**

**Subsurface Scattering (SSS)**

**Comparison**

https://slideplayer.com/slide/4491049/

**Single vs Multiple Scattering**

### •

**Single-layer scattering: dipole model (milk, marble, or ketchup, etc.)**

### •

**Multi-layer scattering: multipole model (skin)**

**Multi-layer Skin Model**

**Skin Surface Reflectance**

### •

**Direct reflection: about 6%**

### •

**Fresnel reflection with the topmost oily layer**

### •

### Reflects directly without being colored (

**white specular color)**

### •

### Not a perfect mirror-like reflection duet to the fine-scale roughness (

**BRDF)**

### •

**Kelemen/Szirmay-Kalos model > Blinn-Phong model**

**Kelemen/Szirmay-Katos Model**

### •

**Specular surface reflectance model**

### •

**Analytic BRDF**

### •

**Approximation of Torrance/Sparrow model**

### •

### The

**Phong model fails to capture increased specularity at grazing angles.**

**Varying Specular Parameters**

### •

### Diﬀerence is subtle but apparent

### •

**Two-channel map that specifies and .**

*m*

*ρ*

_{s}

_{s}

**Skin Subsurface Reflectance**

### •

### The input light

**exits the surface in a 3D neighborhood surrounding the point of entry.**

### •

**Scattering: partially absorbed & acquiring color**

### •

### Two or

**three-layer model is enough**

### •

### The

**narrow scattering of the epidermis on top of the broad scattering dermis**

### •

### Sometimes light travels completely through

**thin regions such as ears.**

**SSS as Diﬀusion**

### •

### For highly scattering media, the distribution of light loses tends to

**isotropy. **

### •

### It means that the entered light is randomly likely to end up coming out in

**any direction.**

### •

### This eﬀectively makes the scattering sort of a "

**blurring" function.**

### •

### Therefore, the

**subsurface scattering can be approximated as a diﬀusion phenomenon.**

**Simple Laser Pointer Experiment**

### •

### Consider a flat and very thin surface in a dark room with a white

**laser beam illuminating it.**

### •

### We will see a glow

**around the center point where the laser beam is striking the surface.**

### •

### Light

**disappears smoothly in proportion to the distance from the laser center.**

### •

### It is same in all directions, so it can be described as

**1D diﬀusion profile curve.**

### •

### The profile is

**color dependent: red light scatters much farther than green and blue.**

** Expansion to Skin**

### •

### A very narrow patch of incoming light creates a larger, colored patch of outgoing light.

### •

### Every region on the surface needs to do this and all the overlapping,

### colored patches sum to give a

**translucent appearance.**

https://tryingtobeananimator.wordpress.com/2017/03/20/subsurface-scattering/

## =

**BSSRDF Approximation**

*L(x*

_{o}

_{o}

*, ω*

_{o}

_{o}

_{) = ∫}

### Ω

*S(x*

*i*

*, ω*

*i*

*; x*

*o*

*, ω*

*o*

*) L(x*

*i*

*, ω*

*i*

*) (n*

*i*

*⋅ ω*

*i*

*) dω*

*i*

*L(x*

_{o}

_{o}

*, ω*

_{o}

_{o}

_{) = ∫}

### Ω

*R(∥x*

_{diﬀusion profile}

_{diﬀusion profile}

*i*

*, − x*

*o*

*∥) L(x*

*i*

*, ω*

*i*

*) (n*

*i*

*⋅ ω*

*i*

*) dω*

*i*

**BRDF**

**How to Use Diﬀusion Profile**

### •

**Collect all incoming light for each location.**

### -

**Sum all incident lights ignoring the directions,**

### except for an N・L term for each light and Fresnel transmittance terms.)

### - Only the

**total amount of incoming light is important**

### •

**Spread it around into neighboring locations based on the profile.**

### : equally in all directions

**Analytic Formula for Diﬀusion Profile**

### •

**Dipole model [Jensen et al. 2001]**

### •

**Multipole model [Donner and Jensen 2005]**

**Analytic Formula for Diﬀusion Profile**

### •

**Dipole model [Jensen et al. 2001]**

### •

**Multipole model [Donner and Jensen 2005]**

http://graphics.snu.ac.kr/class/graphics2011/materials/paper02_fast_skin.pdf

**layer 1**

**layer 2**

**to satisfy the boundary condition, **

**we have to mirror that dipole!**

**Sum-of-Gaussians**

### •

### Skin’s

**diﬀusion profile as a sum of several Gaussians.**

*R(r) ≈ =*

_{∑}

*k*

*i=1*

*w*

_{i}

_{i}

### 1

*2πv*

*e*

*−r*

### 2

_{/(2v)}

https://developer.nvidia.com/gpugems/gpugems3/part-iii-rendering/chapter-14-advanced-techniques-realistic-real-time-skin
_{/(2v)}