Analysis and Synthesis of Facial Expressions - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 248

the scene are represented by 3-D shape models and their motion and deformation
are tracked over time using a model-based estimation method. Given the normal
information, the current lighting is estimated with a linear algorithm of low
computational complexity using an orthogonal set of light maps.

Light Maps

Instead of explicitly modeling light sources and surface reflection properties in
the computer graphics scene and calculating shading effects during the rendering
process as it is done in by some researchers (Bozdagi et al., 1994; Stauder, 1995;
and Eisert et al., 1998b), the shading and shadowing effects are here described
by a linear superposition of several light maps which are attached to the object
surface. Light maps are, similar to texture maps, two-dimensional images that
are wrapped around the object containing shading, instead of color information.
During rendering, the unshaded texture map

()

I

C
tex

{ }

repre-
senting the three color components and the light map L( u ) are multiplied
according to

u

with C ∈ R , G , B

() () ()

C C

tex

I u = I u ⋅ L u (3)

()

C I . The two-dimensional coordinate
u specifies the position in both texture map and light map that are assumed to
have the same mapping to the surface. For a static scene and viewpoint-
independent surface reflections, the light map can be computed off-line which
allows the use of more sophisticated shading methods as, e.g., radiosity algo-
rithms (Goral et al., 1984), without slowing down the final rendering. This
approach, however, can only be used if both object and light sources do not move.
To overcome this limitation, we use a linear combination of scaled light maps
instead of a single one

in order to obtain a shaded texture map u

N − 1

() () ()

∑

C C

tex

C
i

I u = I u ⋅ α L u

. (4)

i

i = 0

α and thus blending between different light
maps L i , different lighting scenarios can be created. Moreover, the light map
approach can also model wrinkles and creases which are difficult to describe by

C
i

By varying the scaling parameter