Graphics Reference
In-Depth Information
are allowed, the more difficult it is to correctly resolve the state, especially in the
presence of nonuniform-reflectance objects.
Caspi et al. [
83
] studied theproblemof colored stripes inmoredetail. They carefully
modeled the relationship between the projected color, the surface reflectance, and
the camera's color response for each scene point, resulting in a set of color patterns
adapted to the environment to be scanned. The model can be written as
C
cam
=
ADP
(
C
proj
)
+
C
0
(8.5)
where
C
cam
is the observed RGB color at a camera pixel,
C
proj
is the color instruction
given to the projector, and
C
0
is the observed color with no projector illumination.
The constant 3
3 matrix
A
defines the coupling, or cross-talk, between the color
channels of the projector and the camera, and the pixel-dependent diagonal matrix
D
is related to the corresponding scene point's reflectance. The projection operator
P
accounts for the difference between the instruction given to the projector and the
actual projected color. All of the parameters of the model can be estimated prior to
scanning using a simple colorimetric calibration process. Given this model, the goal
is to choose scene-adapted color patterns that can bemaximally discriminated by the
camera. The result is a generalized Gray code that uses a different number of levels
for each color channel and was shown to improve on binary Gray codes. In the next
section, we discuss color-stripe methods in more detail.
×
8.2.3
Color-Stripe Coding Methods
Clearly, to get a high-quality (many-stripe) scan of an object using the methods in
the previous section, we need to project quite a few patterns onto it. This is fine for
stationary objects like movie props, but it presents a problem for moving objects.
For example, even if an actor is asked to stay very still, their subtle head move-
ments may lead to substantial variations over the course of ten or more projected
patterns, resulting in unusable 3D data. There is thus much research interest in
one-
shot
methods that effectively acquire many stripes simultaneously using a single
pattern. These methods typically use a static projected image of colored vertical
bars, designed so that no local neighborhood of bar-to-bar transitions is repeated
across the width of the image. Therefore, instead of using a time-multiplexed pattern
of illumination to uniquely identify the stripes as in the previous section, here we
exploit the knowledge that the spatial neighborhood of a given stripe is unique by
construction.
The key concept underlying many modern one-shot techniques is a special type
of numerical pattern called a
de Bruijn sequence
. A de Bruijn sequence of order
k
using an alphabet of
N
symbols is a cyclic sequence of length
N
k
of symbols from
the alphabet that contains each possible length-
k
subsequence exactly once. For
example, the sequence
0001002003011012013021022023031032033111211312212313213322232333
is a de Bruijn sequence of order 3 over an alphabet of four symbols. We can verify that
every possible length-3 subsequence occurs exactly once.
