  Use of low-cost depth sensors, such as a stereo camera setup with
illuminators, is of particular interest for numerous applications ranging from
robotics and transportation to mixed and augmented reality. The ability to
quantify noise is crucial for these applications, e.g., when the sensor is used
for map generation or to develop a sensor scheduling policy in a multi-sensor
setup. Range error models provide uncertainty estimates and help weigh the data
correctly in instances where range measurements are taken from different
vantage points or with different sensors. The weighing is important to fuse
range data into a map in a meaningful way, i.e., the high confidence data is
relied on most heavily. Such a model is derived in this work. We show that the
range error for stereo systems with integrated illuminators is cubic and
validate the proposed model experimentally with an off-the-shelf structured
light stereo system. The experiments confirm the validity of the model and
simplify the application of this type of sensor in robotics. The proposed error
model is relevant to any stereo system with low ambient light where the main
light source is located at the camera system. Among others, this is the case
for structured light stereo systems and night stereo systems with headlights.
In this work, we propose that the range error is cubic in range for stereo
systems with integrated illuminators. Experimental validation with an
off-the-shelf structured light stereo system shows that the exponent is between
2.4 and 2.6. The deviation is attributed to our model considering only shot
noise.
