Sensor Planning for Range Cameras via a Coverage Strength Model
Jose Luis Alarcon Herrera, Aaron Mavrinac, and Xiang Chen
Abstract—A method for sensor planning based on a pre-
viously developed coverage strength model is presented. The
approach taken is known as generate-and-test: a feasible
solution is predefined and then tested using the coverage model.
The relationship between the resolution of the imaging system
and its performance is the key component to perform sensor
planning of range cameras. Experimental results are presented;
the inverse correlation between coverage performance and
measurement error demonstrates the usefulness of the model
in the sensor planning context.
I. INTRODUCTION
Sensor planning toward optimal camera placement is an
important aspect of system integration in machine vision.
The goal of sensor planning is to improve the performance
of the vision system, the performance herein is defined as
the ability of the system to repeatedly complete a task under
controlled conditions. Several methods have been proposed
to solve this problem. Typically a set of feasible camera con-
figurations is defined as well as some metric for performance;
optimal camera placement is generally achieved by maxi-
mizing coverage. This is particulary useful for large multi-
camera configurations. However, some machine vision tasks
such as industrial inspections require monocular systems and
rely more on an approach that takes in to account the task’s
parameters in detail. As discussed in Mavrinac et al. [1] a
global view of the system where coverage is defined as a
bivalent condition of visibility is not sufficient; points in the
field of view can be fully covered, partially covered or not
covered at all, therefore, to express the vagueness of coverage
the model assigns coverage strength a value in the range
[0, 1]. Our task of three-dimensional measurement based on
laser scanners is used primarily in industrial inspections
where the parameters involved in the scene are strictly
controlled, (e.g. no external occlusion is allowed, etc.). Our
previously developed coverage model [2], [1] is well suited to
a generate-and-test approach. Our coverage metric has been
shown to closely reflect the task’s a posteriori performance
[2], [3], [1]. Currently there exists no feasible technique
for numerical optimization using this model; in this paper
we employ the generate-and-test approach to perform sensor
planning. The main purpose of the current brief is to test
the usefulness of the coverage strength model in the sensor
planning context. The experimental results are expected to
This research was supported in part by the National Council of Science
and Technology of Mexico (CONACyT) and by the Natural Sciences and
Engineering Research Council of Canada (NSERC). The authors would like
to acknowledge the support provided by Vista Solutions Inc.
J. L. Alarcon Herrera, A. Mavrinac and X. Chen are with the
Department of Electrical & Computer Engineering, University of
Windsor, 401 Sunset Ave., Windsor, Ontario, Canada, N9B 3P4.
{alarconj,mavrin1,xchen}@uwindsor.ca
provide preliminary effort toward optimal sensor placement;
this is mentioned later in Section VI.
In sensor planning and optimal camera placement, static
occlusion and dynamic occlusion present an issue for the
maximization of coverage; objects in the scene occlude
points of interest, thus preventing the cameras from imaging
the entire scene. Dynamic occlusion has been handled using
a probabilistic model by Mittal and Davis [4] and Chen and
Davis [5]. In the context of laser-based systems, the work
of Pito [6] also deals with occlusion, approaching the next-
best-view problem by focusing on minimizing occlusion.
As shown in the work of Scott et al. [7] maximizing
coverage also involves achieving certain degree of overlap
for the case of n-ocular tasks such as surface modeling and
reconstruction. In more recent work Scott [8] models the
laser scanner system in detail. Prieto et al. [9] give special
attention to the effects of the angle between the laser plane
and the optical axis of the camera. However, the authors do
not include the effects of focal length and aperture diameter
in the estimation of good camera placement.
Sensor planning requires a priori information of the system
such as camera parameters that allow the computation of
some performance metric. A performance metric is then used
to assign some meaningful value to a particular camera con-
figuration before it can be selected as a good configuration.
Ram et al. [10] developed a performance metric considering
such factors as direction of view and zoom. However, the
authors neglect distortion caused by perspective projection.
Erdem and Sclaroff [11] propose the use of a more realistic
model for coverage. The work of Gonza´lez-Banos et al.
[12] is more concerned with the accurate representation of
performance. In a laser based task, the authors parameterize
visibility using conditions such as direction of view and
range within the working distance of the camera. Other
examples are found in the work of Angella et al. [13] and
Ho¨rster et al [14].
The sensor planning literature shows different ways in
which coverage is modeled and parameterized; however,
most existing models are bivalent and do not always en-
capsulate all the parameters related to the overall description
of coverage. Some models are concerned only with direction
of view and zoom such as that of Ram et al. [10], Reed and
Allen [15] provide an excellent example, working to solve
the next-best-view problem, they consider not only visibility
but resolution and direction as well. Their work is also an
example of the generate-and-test approach.
This paper is organized as follows. in Section II, we give
an overview of the camera parameters and some concepts that
are relevant to our task. In Section III, we build the necessary
2011 IEEE/ASME International Conference on
Advanced Intelligent Mechatronics (AIM2011)
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