IEEE Robotics & Automation Magazine - June 2011 - 27
In our approach, we detect the objects by simultaneously
collecting the information provided by all the parts in
the scene.
Our object recognition process is composed of three
main steps: 1) a set of hypotheses is generated, which indicate possible locations for objects in the point cloud, 2)
a selection of the best hypotheses is done following a set of
criteria, and 3) model fitting and verification is applied.
Hypotheses Generation
Given an initial partition P ¼ fS1 , . . . , SM g of a 3-D point
cloud representing an indoor environment, we first obtain
the corresponding feature vector fi for each part Si . Each
feature vector is then matched to a subset of words A & C
from the learned vocabulary (activation), which constitute
possible interpretations of the part S . Each element of an
activated word casts a vote for a possible object location.
This scheme is known as probabilistic Hough voting [16],
and an example is shown in Figure 4. In this case, a part in
the scene activates a word representing backs of chairs.
Each element in A casts a vote for the center of the chair
inside the point cloud.
Formally and following [16], given a feature vector f
representing a part S located at position l in a 3-D point
cloud, the probability of finding an object of class o at position x is
X
p(o, xjAi , f , l)p(Ai j f , l):
(2)
p(o, xj f , l) ¼
i
The term p(o, xjAi , f , l) represents the probability of finding the object o at the location x , given that feature f at
position l activated the word Ai . The term p(Ai j f , l) indicates the probability that the feature vector f matches the
word Ai .
On the basis of [16], we make two further assumptions.
First, the probability of finding an object given an activated
word Ai is independent of the feature vector f . Second, the
activation of a word Ai by feature vector f is independent
of the location of the corresponding part S. Thus,
p(o, xj f , l) ¼
X
p(o, xjAi , l)p(Ai j f ):
(3)
i
It remains to describe each term in (3). The term p(Ai jf )
represents the activation of Ai by f . Following [16], we do
not activate just one vocabulary word, but several of them.
Each activation is assigned a probability indicating how
well the feature vector f matches the code book entry Ai as
w( f , Ai )
,
p(Ai jf ) ¼ P
w( f , Aj )
Figure 4. Example word activation and corresponding 2-D
voting space.
The term p(o, xjAi , l) represents the probability of finding object o at position x, given the activated word Ai at
location l. Once a word is activated, each of its elements a
d. Here l is the posicasts a vote to the position xv ¼ l þ ~
tion of the part S found in the point cloud, and ~
d is the relation vector of the element's shape model (see the
"Hypotheses Selection" section). Finally, we define the
probability p(o, xjAi , l) as
p(o, xjAi , l) ¼
1
#(Ai , o),
0:0,
if x ¼ xv ,
otherwise,
(5)
where #(Ai , o) indicates the number of elements a in word
Ai that pertain to object o.
Hypotheses Selection
The final score V(o, x) of a hypothesis representing an
object and its position can be obtained by accumulating
evidence of all parts found in the scene
V(o, x) ¼
X
p(o, xjfk , lk )p(fk jlk ):
(6)
k
The first term in this expression is calculated as in (3), and
the second term p(fk jlk ) is assumed to be a uniform
distribution.
Following the approach in [16], the different object
hypotheses are found as local maxima in the voting space
using a search window whose size corresponds to the width
of the particular object class we are looking for. We project
the votes onto the (x,y)-plane in order to simplify this search
(see Figure 4). After obtaining the local maxima, we apply a
threshold to select the best hypotheses. Moreover the
hypotheses are checked for inconsistencies in the space. In
our case, two hypotheses for the same type of object at two
different locations xi and xj are inconsistent if the 2-D convex hulls of the objects centered at xi and xj overlap. This
condition assumes that all objects are lying on the floor.
(4)
j
where w(f , Ai ) is a distance function proportional to the
inverse of the Euclidean distance between vector f and the
mean vector of cluster Ai .
Model Fitting and Verification
Having detected positions where a certain object type is
likely to be found, we verify the detection and select the
best model for the object along with its pose. To be able to
do this, we first need to retrieve the most important parts
JUNE 2011
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IEEE ROBOTICS & AUTOMATION MAGAZINE
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27
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