Aerospace and Electronic Systems Magazine October 2017 - 52
Student Research Highlight:
DOI. No. 10.1109/MAES.2017.160223
Gyro-Aided Visual Tracking Using Iterative Earth
Mover's Distance
Gang Yao, Ashwin Dani, University of Connecticut, Storrs, CT, USA
INTRODUCTION
Visual tracking is an important problem in the field of robotics,
especially for the cameras mounted on agile flying robots. The information generated from these images by the tracking algorithm
can be used by autonomous vehicle navigation [1], or human-robot
interaction [2], [3]. Image-based tracking algorithms are categorized as point tracking, kernel tracking, or silhouette tracking [4].
First, distinguishing features, such as color, shape, and region are
selected to identify objects for visual tracking. Then, the tracked
object is modeled, on the basis of the selected features. The correspondence or similarity measurement between the target and the
candidate across frames is constructed, such as the sum of squared
differences of the pixel intensity values [5], the mutual information
(MI) [6], [7], the normalized cross correlation, and the Bhattacharyya coefficient [8]. Supervised or unsupervised online learning
algorithms are also used for visual tracking.
In real-world tracking applications, variations in appearance
are a common phenomenon caused by illumination changes,
moderate pose changes, or partial occlusions. The Earth mover's
distance (EMD) as a similarity measure, also known as 1-Wasserstein distance [9], [10], is robust in these situations [11]. However,
the major problem with the EMD is its computational complexity. Several algorithms for the efficient computation of the EMD
are proposed [12], [13]. In the context of visual tracking, although
the EMD has the merit of being robust to moderate appearance
variations, the efficiency is still a problem. Because solving the
EMD is a transportation problem-a linear programming problem
[11], the direct differential method cannot be used. There are some
efforts to employ the EMD for object tracking. The differential
EMD (DEMD) algorithm [14] is first proposed for visual tracking,
which adopts the sensitivity analysis to approximate the derivative
of the EMD. However, the selection of the basic variables and the
process of identifying and deleting the redundant constraints still
affect the efficiency of the algorithm [14]. The DEMD algorithm
combined with the Gaussian mixture model, which has fewer paAuthors' current address: G. Yao, A. Dani, University of Connecticut, Electrical and Computer Engineering, 347 Fairfield
Way, Storrs, CT 06269, USA, E-mail: (gang.yao@uconn.edu,
ashwin.dani@uconn.edu).
Manuscript received October 16, 2016, revised March 29, 2017,
and ready for publication May 7, 2017.
Review handled by W. Dou.
0885/8985/17/$26.00 © 2017 IEEE
52
rameters for EMD optimization, is proposed in [15]. The EMD as
the similarity measure combined with the particle filter for visual
tracking is proposed in [16].
The success of a tracking algorithm depends on the assumption
that the object motion is smooth and contains only small displacements. However, in practice, this assumption is always violated
due to the abrupt rotation and shaking movement of the camera
mounted on a robot, such as a flying quadcopter. Efforts have been
made to combine the gyroscope data with tracking algorithms,
such as the Kanade-Lucas-Tomasi tracker [17] or the MI tracker
[7].
In this article, a new visual tracking algorithm called iterative
EMD (iEMD), on the basis of the optimization of the EMD between templates, is presented. A preliminary version of this work
was recently published in [18].
PROBLEM FORMULATION
The EMD between the target model and the candidate model is
used as the similarity measure, as shown in Figure 1. Solving the
EMD is a transportation problem-a linear programming problem.
Intuitively, given the target model and the candidate model, one
is thought of as a set of factories, and the other as a set of shops.
Suppose that a given amount of goods produced by the factories
is required to be delivered to the shops, each with a given limited
capacity. The cost to ship a unit of goods from every factory to
different shops is not equivalent. Then, the EMD is considered as
the smallest overall cost of sending the goods (weights) from a set
of factories (target model) to a set of shops (candidate model). The
EMD is defined in vector-matrix notation as [11]
D = min dT f
f
s.t. Hf = w ( y ); f ≥ 0,
(1)
N N
T
where d = [d11 , d1NC , d NT 1 , d NT NC ] ∈ T C is the known
N N
T
ground distance vector, f = [ f11 , f1, NC , f NT 1, f NT NC ] ∈ T C
NT + N C
T
T T
is the flow vector, w(y) = [qˆ (y ) , pˆ ] ∈
is the weight
vector consisting of qˆ (y) ∈ NC from the normalized histogram
N
of the candidate model, and pˆ ∈ T from target model, where
NT
NC
(
N
T
u =1 pˆ u = v =1 qˆv = 1, and H ∈ + NC )× NT NC is the known matrix
consisting of 0s and 1s. In our case, the colors of the target are
chosen as features and represented by the three-dimensional CIE
L*a*b color space. The color histograms of the candidate template
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