Hello everyone, and welcome to the final blog
post of my advanced ray tracing course journey! In this project, I worked on
implementing the subsurface scattering (SSS) algorithm described in Jensen’s 2001
paper titled “A Practical Model for Subsurface Light Transport.” [1] I must say
that this has been one of the most challenging papers I have encountered so
far, as it contains extensive mathematical theories on how to render
translucent materials.
 |
| Dragon Scene rendered with Subsurface Scattering (SSS) |
Introduction
Jensen's paper introduces a
method for approximating subsurface scattering using a bidirectional surface
scattering distribution function (BSSRDF). [1] Subsurface scattering is essential
for rendering translucent materials realistically because many materials, like
skin, are somewhat translucent in real life. Without this effect, objects may
appear completely opaque and unnatural. Subsurface scattering models how light
enters a surface, scatters inside the material (often multiple times), and
exits at a different point, resulting in a softer and more realistic
appearance.
The BSSRDF is an advanced
version of the bidirectional reflectance distribution function (BRDF). While
the BRDF assumes that light enters and exits the material at the same
point, which working well for opaque surfaces, it produces a rigid and unrealistic
appearance for translucent materials. In contrast, the BSSRDF models light
entering at one point and exiting at another, making it suitable for simulating
materials like marble, skin, and milk. By adjusting specific coefficients, we
can replicate the unique visual characteristics of various materials.
Jensen's approximation breaks
down subsurface scattering into two components:
- Single Scattering:
Light enters the surface, scatters once, and then exits.
- Multiple Scattering:
Light enters, scatters multiple times within the material, and exits at a
different point.
Both components are necessary
because relying solely on multiple scattering cannot adequately capture the
effects of single scattering. Together, they create a realistic representation
of how light interacts with translucent surfaces.
Below image is an example of the difference between the use of BRDF and BSSRDF.
 |
| (a) BRDF (b)BSSRDF (in 5 minutes) (c) BSSRDF a full Monte Carlo simulation (in 1250 minutes) |
Theory
In this section, I will
explain the mathematics behind the different terms and how they are applied in
practice.
The realistic appearance of translucent
materials, such as skin, marble, depends on two essential properties:
- Reduced Scattering Coefficient (σs′): This
coefficient describes how light scatters within the material, taking into
account that scattering is not always perfectly random.
- Absorption Coefficient (σa): This measures
the amount of light that is absorbed by the material as it travels through it.
These properties are crucial for accurately
simulating subsurface scattering. Different materials, for example, milk and
marble, have unique values for σs′ and σa, which define how light interacts with
them. You can see coefficient table below.
 |
| Coefficient table for different materials |
From these two coefficients, we can calculate
the extinction coefficient (σt), which represents the total light attenuation,
or how quickly light loses energy, within the material: σt=σs′+σa
The extinction coefficient is a crucial parameter in rendering translucent objects, as it determines how far light can
travel before being scattered or absorbed. By using these values, we can
recreate the subtle, glowing effects that make translucent materials appear
lifelike.
Single Scattering
Single scattering occurs when light enters the material, scatters once, and exits the surface. This is modeled using Monte Carlo integration:
 |
| Single scattering |
- When a ray intersects a translucent object, compute the entry point.
- Trace the refracted ray into the medium and randomly sample scattering distances using an exponential distribution: t=−log(ξ)/σt(x) where ξ is a random number between 0 and 1.
- Compute the attenuation and contribution of light exiting at the sampled point using the scattering equation.
Multiple Scattering
Multiple scattering involves light scattering many times inside the surface before exiting. The dipole approximation simplifies this by:
 |
| Multiple scattering |
- Randomly sampling exit points on the object’s surface.
Calculating the distance from the entry point to the real source and virtual source for each exit point: where dr and dv are distances to the real and virtual sources, respectively.
- Accumulating contributions from multiple exit points to approximate the final scattered light.
Results
 |
David Scene with SSS 10000 single scattering samples,
and 100 multiple scattering samples, rendered in 5min 14sec |
 |
Stanford Bunny Scene with SSS 2000 single scattering samples,
and 5000 multiple scattering samples, rendered in 3min 29 sec |
|
 |
Dragon Scene with SSS 100 single scattering samples,
and 100 multiple scattering samples, rendered in 74 sec |
|
Comparsion BRDF with BSSRDF
 |
| Dragon Scene with BRDF |
 |
| Standford Bunny Scene with BRDF |
|
| Stanford Bunny Scene with BSSRDF |
|
|
| David Scene with BSSRDF |
Final Notes
Working on subsurface scattering using Jensen’s BSSRDF model
has been both challenging and rewarding journey. The paper itself is complex,
and implementing its concepts proved to be just as demanding. By using marble
coefficients in my scenes, I have achieved some promising results, although
they do not yet fully match the quality demonstrated in the paper.
The scattering calculations have been particularly tricky,
and I suspect there may be issues with division or weighting in my
implementation that have caused noise in the output images. I plan to carefully
review these calculations to ensure there are no errors, such as division by
zero or incorrect weighting factors.
Despite these challenges, this project has significantly
advanced my understanding of subsurface scattering. The results so far are
encouraging, and I am excited to continue refining the implementation to
capture the realistic translucency materials like skin or milk.
References
[1] Henrik Wann Jensen, Stephen R. Marschner, Marc Levoy, and Pat Hanrahan, 'A Practical Model for Subsurface Light Transport', 2001
Comments
Post a Comment