Systems, Man & Cybernetics - April 2016 - 39

Ok-GMM using these HLF vectors.
For each of the N planar patches, the LLF matrix is analyzed to
The training process determined
Overall, the method
detect the HLFs, and the correthe Ok-GMM's configuration (M and
improves the pose
sponding feature vector is assigned
m) . The smallest probability densik
to the patch for each detected HLF.
ty p min
of the trained Ok-GMM for
estimation results
The assigned HLF vectors are then
the training data is recorded as the
in feature-rich
sent to the GMM plane classifier
threshold for plane classification
(GMM-PC; Figure 5) for plane clasin a later stage.
environments.
sification. The HLF vector assignAfter the training, each GMM
ment process also generates six
of GMM-PC is able to classify a
matrices, Q 1, f, Q 6, each of which
patch into one of the eight plane
types using the patch's HLF vector. To be specific, a
records the N planar patches' IPRs for HLF-1, f , HLF-6,
planar patch's HLF (or BF if an HLF is unavailable) is
respectively.
presented to the relevant GMM. The GMM's output,
k
p k ^ X m h for k = 1, f, 8, is compared with p min
GMM Plane Classifier
. If
k
^
h
The GMM-PC consists of eight GMMs, each of which has
p k X m 2 p min, the planar patch is classified as an Okbeen trained using data captured from a particular type of
plane. In case that a patch is classified as both an eleobjects and is thus able to identify a plane related to that
mentary plane and a complex plane, the complex plane
type of object when the relevant HLF vector is present. For
cla s si f icat ion over r ides t he element a r y one. A l l
simplicity, we call a GMM for detecting object type Ok for
extracted HLF vectors are presented to the GMM-PC,
and the corresponding planar patches are classified
f
,
k = 1, f, 8, an Ok-GMM. Here, O1, O2,
O8 represent doorinto the eight types of planes. The GMM-PC results in
way, hallway, stairway, parallelepiped, monitor, table, ground,
eight arrays, G k for k = 1, f, 8, each of which stores
and wall, respectively. We call a plane belonging to object Ok
an Ok-plane and a scene with object Ok an Ok-scene. In the
the indexes of the planar patches that have been classified as Ok-planes.
GMM-PC, the Oi-GMM receives all HLF-i vectors and determine if each vector's associated patch is an Oi-plane (here,
i = 1, f, 6) . The ground GMM and the wall GMM receive the
Recursive Plane Clustering
remaining BFs and classify each of the associated planar
In this stage, the classified planes, O k -planes for
patches into a ground plane or a wall plane.
k = 1, f, 4, are recursively clustered into a number of
A GMM is a probability density function represented as a
objects, Ok for k = 1, f, 4. This means that the doorway/
weighted sum of M Gaussian component densities given by
hallway/stairway/parallelepiped planes are grouped into
doorway(s)/hallway(s)/stairway(s)/parallelepiped(s) by a
M
|
^
h
recursive plane clustering (RPC) process. A monitor/
p x m = i = 1 ~ i g ^ x n i, R i h,
(3)
table/ground/wall plane is treated as a standalone object
and thus no further process is needed. Four recursive
=
3, 4, or 5)
where x is a D-dimensional (in our case, D
procedures, RPC-1, f , and RPC-4, process G1, f , G4,
vector with continuous values; ~ i, i = 1, f, M, are the
mixture weights; and g ^ x n i, R i h, i = 1, f, M, are the
respectively, and cluster the neighboring object planes
into the four types of objects by analyzing Q1, f , Q4.
component Gaussian densities with mean vector n i and
covariance matrix R i . The mixture weights satisfy
| iM= 1 ~ i = 1. The complete GMM is parameterized by n i, Experimental Results
R i and ~ i for i = 1, f, M. We denote these parameters
We collected data from various scenes inside a number of
collectively by m from now on for conciseness. In this
buildings on campus to train and/or test the methods. Five
students who are not the developers of the methods particarticle, the configuration (M and m) of an Ok-GMM is estiipated in data collection.
mated by training the GMM using a set of HLF vectors
obtained from a number of Ok-scenes. The maximum likelihood estimate of m is iteratively obtained by the expectaPose Estimation
tion maximization method. The value of M is determined
We carried out nine experiments (Group I) in featureby repeating the training process with an increasing i and
rich environments and five (Group II) in feature-sparse
observing the trained GMM's output p ^ x m h . If the mean
environments. In each experiment, the CRC user walked
with the cane in a looped trajectory (path length: 20-
of the output difference between an I-component GMM
40 m). The CRC's final position error (FPE; in percentage
and an (I + 1)-component GMM is below a threshold, we let
of path length) is used as the overall accuracy of pose
M = I because more Gaussian component densities will
estimation. The PGO method's FPE is compared with
not change the GMM's probability density.
that of the baseline (dead reckoning) method and the
We acquired 500 data sets from different Ok-scenes. After
percentage error reduction indicates the performance of
plane segmentation and feature extraction, we obtained a
PGO. The results are tabulated in Table 1. The PGO
set of HLF vectors from each dataset. We then trained the
Ap ri l 2016

IEEE SyStEmS, man, & CybErnEtICS magazInE

39



Table of Contents for the Digital Edition of Systems, Man & Cybernetics - April 2016

Systems, Man & Cybernetics - April 2016 - Cover1
Systems, Man & Cybernetics - April 2016 - Cover2
Systems, Man & Cybernetics - April 2016 - 1
Systems, Man & Cybernetics - April 2016 - 2
Systems, Man & Cybernetics - April 2016 - 3
Systems, Man & Cybernetics - April 2016 - 4
Systems, Man & Cybernetics - April 2016 - 5
Systems, Man & Cybernetics - April 2016 - 6
Systems, Man & Cybernetics - April 2016 - 7
Systems, Man & Cybernetics - April 2016 - 8
Systems, Man & Cybernetics - April 2016 - 9
Systems, Man & Cybernetics - April 2016 - 10
Systems, Man & Cybernetics - April 2016 - 11
Systems, Man & Cybernetics - April 2016 - 12
Systems, Man & Cybernetics - April 2016 - 13
Systems, Man & Cybernetics - April 2016 - 14
Systems, Man & Cybernetics - April 2016 - 15
Systems, Man & Cybernetics - April 2016 - 16
Systems, Man & Cybernetics - April 2016 - 17
Systems, Man & Cybernetics - April 2016 - 18
Systems, Man & Cybernetics - April 2016 - 19
Systems, Man & Cybernetics - April 2016 - 20
Systems, Man & Cybernetics - April 2016 - 21
Systems, Man & Cybernetics - April 2016 - 22
Systems, Man & Cybernetics - April 2016 - 23
Systems, Man & Cybernetics - April 2016 - 24
Systems, Man & Cybernetics - April 2016 - 25
Systems, Man & Cybernetics - April 2016 - 26
Systems, Man & Cybernetics - April 2016 - 27
Systems, Man & Cybernetics - April 2016 - 28
Systems, Man & Cybernetics - April 2016 - 29
Systems, Man & Cybernetics - April 2016 - 30
Systems, Man & Cybernetics - April 2016 - 31
Systems, Man & Cybernetics - April 2016 - 32
Systems, Man & Cybernetics - April 2016 - 33
Systems, Man & Cybernetics - April 2016 - 34
Systems, Man & Cybernetics - April 2016 - 35
Systems, Man & Cybernetics - April 2016 - 36
Systems, Man & Cybernetics - April 2016 - 37
Systems, Man & Cybernetics - April 2016 - 38
Systems, Man & Cybernetics - April 2016 - 39
Systems, Man & Cybernetics - April 2016 - 40
Systems, Man & Cybernetics - April 2016 - 41
Systems, Man & Cybernetics - April 2016 - 42
Systems, Man & Cybernetics - April 2016 - 43
Systems, Man & Cybernetics - April 2016 - 44
Systems, Man & Cybernetics - April 2016 - 45
Systems, Man & Cybernetics - April 2016 - 46
Systems, Man & Cybernetics - April 2016 - 47
Systems, Man & Cybernetics - April 2016 - 48
Systems, Man & Cybernetics - April 2016 - 49
Systems, Man & Cybernetics - April 2016 - 50
Systems, Man & Cybernetics - April 2016 - 51
Systems, Man & Cybernetics - April 2016 - 52
Systems, Man & Cybernetics - April 2016 - 53
Systems, Man & Cybernetics - April 2016 - 54
Systems, Man & Cybernetics - April 2016 - 55
Systems, Man & Cybernetics - April 2016 - 56
Systems, Man & Cybernetics - April 2016 - Cover3
Systems, Man & Cybernetics - April 2016 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/smc_202110
https://www.nxtbook.com/nxtbooks/ieee/smc_202107
https://www.nxtbook.com/nxtbooks/ieee/smc_202104
https://www.nxtbook.com/nxtbooks/ieee/smc_202101
https://www.nxtbook.com/nxtbooks/ieee/smc_202010
https://www.nxtbook.com/nxtbooks/ieee/smc_202007
https://www.nxtbook.com/nxtbooks/ieee/smc_202004
https://www.nxtbook.com/nxtbooks/ieee/smc_202001
https://www.nxtbook.com/nxtbooks/ieee/smc_201910
https://www.nxtbook.com/nxtbooks/ieee/smc_201907
https://www.nxtbook.com/nxtbooks/ieee/smc_201904
https://www.nxtbook.com/nxtbooks/ieee/smc_201901
https://www.nxtbook.com/nxtbooks/ieee/smc_201810
https://www.nxtbook.com/nxtbooks/ieee/smc_201807
https://www.nxtbook.com/nxtbooks/ieee/smc_201804
https://www.nxtbook.com/nxtbooks/ieee/smc_201801
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1017
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0717
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0417
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0117
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1016
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0716
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0416
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0116
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1015
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0715
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0415
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0115
https://www.nxtbookmedia.com