Aerospace and Electronic Systems Magazine October 2017 - 53
and target template are generated. The weight w(y) of the histogram of templates is generated by convolving the color histogram
with the Epanechnikov kernel [8]. The L2 distance of every two
centroid colors is calculated as the ground distance.
STUDENT CONTRIBUTIONS
The optimization problem in (1) is solved using the iEMD algorithm. The key components of the algorithm are a) representing the
EMD as a function of the weights of the histogram of the candidate
model, and b) applying the gradient method to the EMD. To relate
the EMD with the weight vector, the primal problem in (1) is restated in its dual form as follows [19]
D = max w T (y )π
π
s.t.
HT π ≤ d
(2)
where π ∈ NT + NC is a vector of variables to be optimized in the dual
problem. By solving this dual problem in (2), the optimal solution
D* is calculated and directly represented as the linear equation of
weights. However, considering the computational efficiency, the
optimal solution (EMD) is first calculated from the primal problem
in (1) using the transportation simplex method. The transportation
simplex method is a streamlined simplex algorithm, which is built
on the special structure of the transportation problem. To reduce
the number of iterations of the transportation simplex method, the
Russell's method is used to compute the initial basic feasible solution [11].
Then, on the basis of the properties of the transportation problem and the relationship between the primal problem and its dual
problem, the EMD is represented as the function of the weights by
the matrix transformation. The computation of the EMD is a transportation problem, which has exactly NT + NC - 1 basic variables fB
∈ NT + NC −1, and each constraint is a linear combination of the other
Figure 1.
The EMD comparison of the two templates, which are the image patches inside the red rectangle boxes; pˆ and qˆ (y) are the histograms of the target
template image and the candidate template image, NT and NC are the bin numbers of the histograms, and y is the two-dimensional displacement of the
centroid of candidate template image related to the centroid of target template image. The displacement y, corresponding to the smallest EMD, is the
location of the centroid of the target image in the new frame.
OCTOBER 2017
IEEE A&E SYSTEMS MAGAZINE
53
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