Gesture-Based Interaction with Time-of-Flight Cameras

CHAPTER 2. TIME-OF-FLIGHT CAMERAS
camera.
There exists, however, a simple approach to increase the non-ambiguity range.
If two images are taken of the same scene with different modulation frequencies,
one can reconstruct the distance unambiguously up to a range that corresponds to
the least common multiple of the two corresponding non-ambiguity ranges. This
procedure is limited to cases, where the objects undergo no or only limited motion
in front of the camera. Otherwise, wrong distances will be estimated for pixels that
move across object borders from one frame to the other and thus depict different
objects at different distances in the two images.
2.7.2 Systematic Errors
As already mentioned in Section 2.6, TOF cameras can produce systematic errors, i.e.
range measurement errors that are induced by deviations from an ideal sinusoidal
signal e(t) of the illumination unit. Theoretically, these errors can be compensated
by using a higher number of samples Ak to estimate the phase shift φ (Lange, 2000;
Rapp, 2007). On the contrary, this is impractical as it would introduce higher com-
putational cost and abet motion artefacts (Kolb et al., 2009).
An alternative is to correct systematic errors in a post-processing step. This can,
for example, be done using look-up tables (Kahlmann et al., 2007) or correction func-
tions such as b-splines (Lindner and Kolb, 2006).
2.7.3 Multiple Reflections
The working principle of TOF cameras is based on the assumption that the modu-
lated light that reaches a pixel is reflected from a single object at a well defined dis-
tance and that the light travels directly back into the camera. In this case, the camera
receives a single signal s(t) that has a phase shift φ with respect to the emitted signal
e(t) that corresponds to the distance of the object. This assumption may be violated
due to multiple reflections that can occur both in the scene and inside the camera.
Multiple reflections in the scene refer to the situation when light of the active
illumination travels not solely between the camera and the imaged object, but when
it is reflected at additional objects in the scene along its path from the camera to the
object and back to the sensor. In such a case, the distance travelled by the light is
longer, which results in an increased time of flight and, thus, a false range estimate
(Gudmundsson et al., 2007b).
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Multiple reflections inside the camera have the effect that stray light from other