Tracking objects in bowl-shaped imaging systems
Technologies for determining a distance of an object from a vehicle include a computing device to identify an object captured in a fisheye image generated by a fisheye camera of the vehicle. The computing device projects a contour of the identified object on a selected virtual plane that is located outside the vehicle and selected from a predefined set of virtual planes based on a location of the identified object relative to the vehicle. The computing device identifies a bottom of the projected contour on the selected virtual plane and determines an intersection point of an imaginary line with a ground plane coincident with a plane on which the vehicle is positioned. The imaginary line passes through each of the identified bottom of the projected contour and the fisheye camera. The computing device determines a location of the identified object relative to the vehicle based on the determined intersection point and the identified bottom of the projected contour.
1. A computing device for determining a distance of an object from a vehicle, the computing device comprising:
a fisheye camera to capture a fisheye image;
an object projection module to (i) identify an object captured in the fisheye image and (ii) project a contour of the identified object on a selected virtual plane that is located outside the vehicle and selected from a predefined set of virtual planes based on a location of the identified object relative to the vehicle; and
a location determination module to (i) identify a bottom of the projected contour on the selected virtual plane, (ii) determine an intersection point of an imaginary line with a ground plane coincident with a plane on which the vehicle is positioned, wherein the imaginary line passes through each of the identified bottom of the projected contour and the fisheye camera, and (iii) determine a location of the identified object relative to the vehicle based on the determined intersection point and the identified bottom of the projected contour.
2. The computing device of claim 1 , wherein to determine the location of the identified object relative to the vehicle comprises to apply a Kalman filter based on the determined intersection point and the identified bottom of the projected contour.
3. The computing device of claim 2 , wherein to apply the Kalman filter comprises to:
determine a state vector of the Kalman filter according to {right arrow over (x)}=[x p y p z b ] T ;
determine a measurement vector of the Kalman filter according to {right arrow over (z)}=[x b y b z b ] T ;
apply the Kalman filter based on the determined state vector and the determined measurement vector, wherein:
x p , y p , and z p , are three-dimensional coordinates of the intersection point; and
x b , y b , and z b are three-dimensional coordinates of the bottom of the identified object.
4. The computing device of claim 3 , wherein to apply the Kalman filter comprises to:
determine a Jacobian according to
∂
z
∂
x
=
[
1
-
z
b
z
a
0
-
1
z
a
(
x
p
-
x
a
)
0
1
-
z
b
z
a
-
1
z
a
(
y
p
-
y
a
)
0
0
1
]
;
and
apply an extended Kalman filter based on the determined state vector, the determined measurement vector, and the determined Jacobian,
wherein x a , y a , and z a are three-dimensional coordinates of the fisheye camera.
5. The computing device of claim 1 , wherein to project the contour of the identified object comprises to select a virtual plane that is nearest the identified object and on which to project the contour of the identified object.
6. The computing device of claim 1 , wherein to project the contour of the identified object comprises to:
determine a reference line intersecting the fisheye camera and a location of the identified object; and
project the contour of the identified object to a virtual plane that the reference line intersects.
7. The computing device of claim 1 , wherein to identify the bottom of the projected contour comprises to:
determine a bounding box of the projected contour on the virtual plane; and
identify a middle point of a bottom of the bounding box.
8. The computing device of claim 7 , wherein the intersection point is an intersection point of a center of the fisheye camera with the middle point of the bottom of the bounding box.
9. The computing device of claim 7 , wherein the bounding box is a smallest rectangular box bounding the projected contour.
10. The computing device of claim 1 , wherein to determine the intersection point of the line with the ground plane comprises to determine the intersection point according to
x
p
=
-
z
b
z
a
-
z
b
x
a
+
z
a
z
a
-
z
b
x
b
,
y
p
=
-
z
b
z
a
-
z
b
y
a
+
z
a
z
a
-
z
b
y
b
,
and z p =0, wherein:
x p , y p , and z p are three-dimensional coordinates of the intersection point;
x a , y a , and z a are three-dimensional coordinates of the fisheye camera; and
x b , y b , and z b are three-dimensional coordinates of the bottom of the identified object.
11. The computing device of claim 1 , wherein the predefined set of virtual planes comprises at least twice as many virtual planes as there are fisheye cameras of the vehicle.
12. The computing device of claim 1 , wherein each virtual plane of the predefined set of virtual planes is orthogonal to the ground plane.
13. The computing device of claim 1 , wherein:
the predefined set of virtual planes consists of eight virtual planes;
a first and second virtual plane of the eight virtual planes are parallel to a side of the vehicle;
a third and fourth virtual plane of the eight virtual planes are parallel to a rear of the vehicle and orthogonal to the side of the vehicle;
a fifth and sixth virtual plane of the eight virtual planes are parallel to one another and at forty-five degree angles with respect to the first and third virtual planes;
a seventh and eighth virtual plane of the eight virtual planes are parallel to one another, orthogonal to the fifth and sixth virtual planes, and at forty-five degree angles with respect to the first and third virtual planes; and
each virtual plane of the predefined set of virtual planes is orthogonal to the ground plane.
14. The computing device of claim 1 , wherein the computing device is embodied as an in-vehicle computing system.
15. One or more non-transitory machine-readable storage media comprising a plurality of instructions stored thereon that, in response to execution by a computing device, cause the computing device to:
identify an object captured in a fisheye image generated by a fisheye camera of the vehicle;
project a contour of the identified object on a selected virtual plane that is located outside the vehicle and selected from a predefined set of virtual planes based on a location of the identified object relative to the vehicle;
identify a bottom of the projected contour on the selected virtual plane;
determine an intersection point of an imaginary line with a ground plane coincident with a plane on which the vehicle is positioned, wherein the imaginary line passes through each of the identified bottom of the projected contour and the fisheye camera; and
determine a location of the identified object relative to the vehicle based on the determined intersection point and the identified bottom of the projected contour.
16. The one or more non-transitory machine-readable storage media of claim 15 , wherein to determine the location of the identified object relative to the vehicle comprises to:
determine a state vector of a Kalman filter according to {right arrow over (x)}=[x p y p z b ] T ;
determine a measurement vector of the Kalman filter according to {right arrow over (z)}=[x b y b z b ] T ; and
apply the Kalman filter based on the determined state vector and the determined measurement vector,
wherein x p , y p , and z p are three-dimensional coordinates of the determined intersection point and x b , y b , and z b are three-dimensional coordinates of the identified bottom of the projected contour.
17. The one or more non-transitory machine-readable storage media of claim 16 , wherein to apply the Kalman filter further comprises to:
determine a Jacobian according to
∂
z
∂
x
=
[
1
-
z
b
z
a
0
-
1
z
a
(
x
p
-
x
a
)
0
1
-
z
b
z
a
-
1
z
a
(
y
p
-
y
a
)
0
0
1
]
;
and
apply an extended Kalman filter based on the determined state vector, the determined measurement vector, and the determined Jacobian,
wherein x a , y a , and z a are three-dimensional coordinates of the fisheye camera.
18. The one or more non-transitory machine-readable storage media of claim 15 , wherein to project the contour of the identified object comprises to select a virtual plane that is nearest the identified object and on which to project the contour of the identified object.
19. The one or more non-transitory machine-readable storage media of claim 15 , wherein to identify the bottom of the projected contour comprises to (i) determine a bounding box of the projected contour on the virtual plane and (ii) identify a middle point of a bottom of the bounding box; and
wherein to determine the intersection point of the line with the ground plane comprises to determine an intersection point of a center of the fisheye camera with the middle point of the bottom of the bounding box.
20. The one or more non-transitory machine-readable storage media of claim 15 , wherein to determine the intersection point of the line with the plane ground comprises to determine the intersection point according to
x
p
=
-
z
b
z
a
-
z
b
x
a
+
z
a
z
a
-
z
b
x
b
,
y
p
=
-
z
b
z
a
-
z
b
y
a
+
z
a
z
a
-
z
b
y
b
,
and z p =0 wherein:
x p , y p , and z p are three-dimensional coordinates of the intersection point;
x a , y a , and z a are three-dimensional coordinates of the fisheye camera; and
x b , y b , and z b are three-dimensional coordinates of the bottom of the identified object.
21. A method for determining a distance of an object from a vehicle by a computing device of the vehicle, the method comprising:
identifying, by the computing device, an object captured in a fisheye image generated by a fisheye camera of the vehicle;
projecting, by the computing device, a contour of the identified object on a selected virtual plane that is located outside the vehicle and selected from a predefined set of virtual planes based on a location of the identified object relative to the vehicle;
identifying, by the computing device, a bottom of the projected contour on the selected virtual plane;
determining, by the computing device, an intersection point of an imaginary line with a ground plane coincident with a plane on which the vehicle is positioned, wherein the imaginary line passes through each of the identified bottom of the projected contour and the fisheye camera; and
determining, by the computing device, a location of the identified object relative to the vehicle based on the determined intersection point and the identified bottom of the projected contour.
22. The method of claim 21 , wherein determining the location of the identified object relative to the vehicle comprises applying a Kalman filter based on the determined intersection point and the identified bottom of the projected contour by:
determining a state vector of the Kalman filter according to {right arrow over (x)}=[x p y p z b ] T ;
determining a measurement vector of the Kalman filter according to {right arrow over (z)}=[x b y b z b ] T ;
applying the Kalman filter based on the determined state vector and the determined measurement vector, wherein:
x p , y p , and z p are three-dimensional coordinates of the intersection point; and
x b , y b and z b are three-dimensional coordinates of the bottom of the identified object.
23. The method of claim 22 , wherein applying the Kalman filter further comprises:
determining a Jacobian according to
∂
z
∂
x
=
[
1
-
z
b
z
a
0
-
1
z
a
(
x
p
-
x
a
)
0
1
-
z
b
z
a
-
1
z
a
(
y
p
-
y
a
)
0
0
1
]
;
and
applying an extended Kalman filter based on the determined state vector, the determined measurement vector, and the determined Jacobian,
wherein x a , y a , and z a are three-dimensional coordinates of the fisheye camera.
24. The method of claim 21 , wherein identifying the bottom of the projected contour comprises (i) determining a bounding box of the projected contour on the virtual plane and (ii) identifying a middle point of a bottom of the bounding box; and
wherein determining the intersection point of the line with the ground plane comprises determining an intersection point of a center of the fisheye camera with the middle point of the bottom of the bounding box.
25. The method of claim 21 , wherein determining the intersection point of the line with the ground plane comprises determining the intersection point according to
x
p
=
-
z
b
z
a
-
z
b
x
a
+
z
a
z
a
-
z
b
x
b
,
y
p
=
-
z
b
z
a
-
z
b
y
a
+
z
a
z
a
-
z
b
y
b
,
and z p =0 , wherein:
x p , y p , and z p are three-dimensional coordinates of the intersection point;
x a , y a , and z a are three-dimensional coordinates of the fisheye camera; and
x b , y b , and z b are three-dimensional coordinates of the bottom of the identified object.