Aerospace and Electronic Systems Magazine June 2017 - 26

Elimination of Resampling Errors in Wide Area Motion Imagery

Figure 4.

USAF 1951 Resolution Test Target by LaserSoft Imaging [11].

between pairs of gray and white bars. Any measurement error
caused by bleeding between pairs of gray and white bars will be
common to both ends of the measurement, and cancel. The pairs of
measurement are then averaged.
Assuming that the bars are consistent with the United States
Air Force (USAF) 1951 resolution test target in Figure 4, the dimensions match the formula:

Figure 3.

Resolution target at WPAFB from Google Earth, showing index values
from 0 to -8, and measurements for index -7.

Measurement Unit (IMU) boresight. The angular alignment of the
camera with respect to the IMU is in roll, pitch, and yaw in degrees.
The pose data and the camera models may be used to project
the images as described in [8]. The projection of the raw images
can be compared to the NITF images supplied in the data set to
analyze resolution.

IMAGE RESOLUTION
The resolution target at the WPAFB is shown in Figure 3. This image is from Google Earth (GE) [10]. The resolution target is visible
in every frame of the 20091021 data set. This target is used to measure the resolution of the raw and projected images. The resolution
target is a series of horizontal and vertical bars. For each set, there
are three white bars on a field of gray. The spacing between bars is
measured in line pairs per unit distance, in this case, meters. The
bars are arranged in order of progressively smaller line spacing. The
sets of bars are assigned an index number as shown in Figure 3. For
convenience, we will assign names of horizontal and vertical as follows: Assume that the observer is standing at lower right corner of
the figure looking northwest, from this view point the bars are horizontal and vertical as indicated in Figure 3. The index is from 0 to -8,
a larger number is a higher resolution in units of line pairs per meter.
The dimension of the bars is not publicly available, but can
be estimated by measurements made in GE. For each index, two
measurements denoted as L1, and L2 are made, see Figure 3. This
is illustrated for index -7. The measurements are made on the transition from gray to white, spanning a line pair (lp). An lp is two
bars, one white and one black as shown. Measurements from gray
to white spanning five bars will have errors caused by bleeding in
the images. This measurement error is eliminated by measuring
26

(1)

Ri = R0 2i / 6

Where: Ri = the resolution of the line pairs at index i in line pairs
per meter
i = is the index
R0 = the computed value of the resolution at index 0 in line pairs
per meter
The value of R0 is computed using Ordinary Least Squares
(OLS) to minimize the error between Equation 1 and the measured
values from GE. The value of R0 is:
R0 = 1.69 ± 0.02

(2)

Table 1.

Resolution Target Line Spacing Based on Google Earth
Measurement
Index

lp/m

m/lp

1.71

0.58

-1

1.53

0.65

-2

1.36

0.73

-3

1.21

0.82

-4

1.08

0.93

-5

0.96

1.04

-6

0.86

1.17

-7

0.76

1.31

-8

0.68

1.47

IEEE A&E SYSTEMS MAGAZINE

JUNE 2017

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine June 2017