IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV - 5

Saavedra-Ruiz et al.
frame (template) to the corresponding points in the
other image frame (scene). To compute the homography,
at least four matches are needed. Then, knowing
the homography between two images and the dimensions
of the template T ¼½wT;hTT, it is possible to
apply a perspective transform that maps the template
position from the template image to the scene image
using the following equation:
Figure 2.
Feature matching between the features of the template FT and the
features of the scene image FS.
the pose of the landing platform, even when no detection
has been obtained.
FEATURE-BASED OBJECT DETECTION
Object detection is a crucial task in robotic perception.
Feature-based detectors and descriptors are widely used,
due to their speed in computing the salient features of
images. For increased robustness in object detection, these
features should be invariant to rotation, scale and affine
transformations over several frames [29]. To find correspondences
between two images, we consider a set of features
in the template image FT 2 Rn and the current
frame FS 2 Rm, where n;m 2 Z represent the number of
features in each image. Each feature in the template and
scene frames is associated with a descriptor DT 2
Rnk;DSD 2 Rmk, where k is the dimension of the
descriptor for each feature.
With a set of descriptors, it is possible to compute
matches between image pairs by performing distance
calculations, such as the Euclidean distance between
the descriptors of the template and the scene, as shown
in (1). Two features are matched when the closest
descriptors between two images in the descriptor space
have been found. As a result, similar features in the
template image ðxi;yiÞ are matched with the similar
pair ðxi;0 y0
iÞ in the current image frame, as illustrated
in Figure 2
di ¼ min
Xn
i¼1
Xm
j¼1
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðDT
ði;kÞÞ2ðDS
ðj;kÞÞ2
:
(1)
2
4
x
y
1
3
5 ¼ H
2
4
x
y
1
3
5 ¼
2
4
h11 h12 h13
h21 h22 h23
h31 h32 h33
3
5
2
4
x
y
1
3
5:
(2)
In (2), ½x; y; 1T are the coordinates of points (e.g., corners)
in the template image and ½x;0 y;0 1T are the same
points mapped in the scene image, where H : R3 ! R3.
Object detection with feature-based methods and homography
calculations tends to speed up the process and can
provide a reliable estimation of the location of the object
of interest in the current image frame.
SYSTEM OBSERVATIONS
Using the homography matrix, the corners and centroid of
the template detected in the current image frame can be
computed. Pc t 2 R52 is defined as a vector of coordinates,
where each row corresponds to a x; y point at time
index t.
These points are used to determine the observations
that will be fed into the Kalman filter. The vector of observations
at time t is defined as Zt ¼½Pc
where Pc
ði¼5Þ
t
are the x; y centroid coordinates of the landing
pad; Ow;Oh are the width and height of the template,
respectively; and u represents the angle of the template
with respect to the x axis of the image, as shown in
Figure 3.
ði¼5Þ
t ;Ow;Oh; u,
HOMOGRAPHYMATRIX
Finding correspondences between image pairs allows
us to compute the homography matrix H 2 R33.This
matrix is a transform that maps points from one image
MAY 2022
Figure 3.
System's observations and coordinate system. The vector Zt is
created at each time-step based on the width and height (Ow;Oh),
the orientation u and the position of the centroid (x; y) of the template
in the current image frame.
IEEE A&E SYSTEMS MAGAZINE
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IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV

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