Geolocating an object using a single camera
A camera mounted on a seafaring vessel obtains an image showing an object. The distance to the object is computed using, in part, a normal vector of the plane containing the camera and the horizon.
1. A method, comprising:
obtaining an image showing a horizon and an object from a camera mounted on a seafaring vessel at a height h from sea level in calm water;
obtaining a roll angle θ roll and a pitch angle θ pitch of the vessel from an inertial measurement unit;
identifying a plane passing through the camera and the horizon, the plane identified as passing through the position of the camera and a line at sea level a distance D away from the camera given by D=A sin(θ roll )sin(θ pitch )h 1/2 , where h is measured in meters and A is equal to 3.6 km/m 1/2 ;
identifying a normal vector to the plane;
identifying a distance from the seafaring vessel to the object using the normal vector to the plane; and
on an augmented reality interface, displaying an augmented reality image including the object and the distance from the seafaring vessel to the object.
2. The method of claim 1 , in which distance d from the seafaring vessel to the object is given by:
d
=
(
h
cos
B
)
2
-
h
2
where B is line-of-sight angle from the camera to the object, and h is a height above sea level at which the camera is mounted on the vessel in calm water.
3. The method of claim 2 , in which the seafaring vessel includes an inertial measurement unit operable to report a roll angle θ roll and a pitch angle θ pitch of the vessel, and in which h is scaled in the equation of claim 2 by sin(θ roll )sin(θ pitch ).
4. The method of claim 1 , in which the augmented reality interface includes a real time video feed from the camera.
5. The method of claim 1 , in which the augmented reality interface includes an overhead map of a waterway showing the vessel and the object.
6. The method of claim 1 , further comprising using the identified distance to make a navigational maneuver.
7. The method of claim 6 , in which the navigational maneuver is made by the seafaring vessel.
8. The method of claim 6 , in which the navigational maneuver is made by a vessel other than the seafaring vessel.
9. A system, comprising:
a camera mounted on a seafaring vessel at a height h from sea level in calm water; and
machine-readable instructions that, when executed, cause one or more processors to:
obtain an image showing a horizon and an object from the camera;
obtain a roll angle θ roll and a pitch angle θ pitch of the vessel from an inertial measurement unit;
identify a plane passing through the camera and the horizon, the plane identified as passing through a position of the camera and a line at sea level a distance D away from the camera given by D=A sin(θ roll )sin(θ pitch )h 1/2 , where h is measured in meters and A is equal to 3.6 km/m 1/2 ;
identify a normal vector to the plane;
identify a distance from the seafaring vessel to the object using the normal vector to the plane; and
on an augmented reality interface, display an augmented reality image including the object and the distance from the seafaring vessel to the object.
10. The system of claim 9 , in which distance d from the seafaring vessel to the object is given by:
d
=
(
h
cos
B
)
2
-
h
2
where B is line-of-sight angle from the camera to the object, and h is a height above sea level at which the camera is mounted on the vessel in calm water.
11. The system of claim 10 , in which the seafaring vessel includes an inertial measurement unit operable to report a roll angle θ roll and a pitch angle θ pitch of the vessel, and in which h is scaled in the equation of claim 10 by sin(θ roll )sin(θ pitch ).
12. The system of claim 9 , in which the augmented reality interface includes a real time video feed from the camera.
13. The system of claim 9 , in which the augmented reality interface includes an overhead map of a waterway showing the vessel and the object.
14. The system of claim 9 , further comprising using the identified distance to make a navigational maneuver.
15. The system of claim 14 , in which the navigational maneuver is made by the seafaring vessel.
16. The system of claim 14 , in which the navigational maneuver is made by a vessel other than the seafaring vessel.
17. A method, comprising:
obtaining an image showing a horizon and an object from a camera mounted on a seafaring vessel at a height h from sea level in calm water;
identifying a plane passing through the camera and the horizon, the plane identified from the image using a Hough transform that only samples an area of the image corresponding to an expected location of the horizon including a distance interval centered at Ah 1/2 , where h is measured in meters and A is equal to 3.6 km/m 1/2 ;
identifying a normal vector to the plane;
identifying a distance from the seafaring vessel to the object using the normal vector to the plane; and
on an augmented reality interface, displaying an augmented reality image including the object and the distance from the seafaring vessel to the object.
18. A method, comprising:
obtaining an image showing a horizon and an object from a camera mounted on a seafaring vessel at a height h from sea level in calm water;
obtaining a roll angle θ roll and a pitch angle θ pitch of the vessel from an inertial measurement unit;
identifying a plane passing through the camera and the horizon, the plane identified from the image using a Hough transform that only samples an area of the image corresponding to an expected location of the horizon including a distance interval centered at A sin(θ roll )sin(θ pitch )h 1/2 , where h is measured in meters and A is equal to 3.6 km/m 1/2 ;
identifying a normal vector to the plane;
identifying a distance from the seafaring vessel to the object using the normal vector to the plane; and
on an augmented reality interface, displaying an augmented reality image including the object and the distance from the seafaring vessel to the object.
19. A method, comprising:
obtaining an image showing a horizon and an object from a camera mounted on a seafaring vessel;
identifying a plane passing through the camera and the horizon;
identifying a normal vector to the plane;
identifying a distance from the seafaring vessel to the object using the normal vector to the plane, the distance d given by:
d
=
(
h
cos
B
)
2
-
h
2
where B is line-of-sight angle from the camera to the object, and h is a height above sea level at which the camera is mounted on the vessel in calm water; and
on an augmented reality interface, displaying an augmented reality image including the object and the distance from the seafaring vessel to the object.
20. A system, comprising:
a camera mounted on a seafaring vessel at a height h from sea level in calm water; and
machine-readable instructions that, when executed, cause one or more processors to:
obtain an image showing a horizon and an object from the camera;
identify a plane passing through the camera and the horizon, the plane identified from the image using a Hough transform that only samples an area of the image corresponding to an expected location of the horizon including a distance interval centered at Ah 1/2 , where h is measured in meters and A is equal to 3.6 km/m 1/2 ;
identify a normal vector to the plane;
identify a distance from the seafaring vessel to the object using the normal vector to the plane; and
on an augmented reality interface, display an augmented reality image including the object and the distance from the seafaring vessel to the object.
21. A system, comprising:
a camera mounted on a seafaring vessel at a height h from sea level in calm water; and
machine-readable instructions that, when executed, cause one or more processors to:
obtain an image showing a horizon and an object from the camera;
obtain a roll angle θ roll and a pitch angle θ pitch of the vessel from an inertial measurement unit;
identify a plane passing through the camera and the horizon, the plane identified from the image using a Hough transform that only samples an area of the image corresponding to an expected location of the horizon including a distance interval centered at A sin(θ roll )sin(θ pitch )h 1/2 , where h is measured in meters and A is equal to 3.6 km/m 1/2 ;
identify a normal vector to the plane;
identify a distance from the seafaring vessel to the object using the normal vector to the plane; and
on an augmented reality interface, display an augmented reality image including the object and the distance from the seafaring vessel to the object.
22. A system, comprising:
a camera mounted on a seafaring vessel; and
machine-readable instructions that, when executed, cause one or more processors to:
obtain an image showing a horizon and an object from the camera;
identify a plane passing through the camera and the horizon;
identify a normal vector to the plane;
identify a distance from the seafaring vessel to the object using the normal vector to the plane, the distance d given by:
d
=
(
h
cos
B
)
2
-
h
2
where B is line-of-sight angle from the camera to the object, and h is a height above sea level at which the camera is mounted on the vessel in calm water; and
on an augmented reality interface, display an augmented reality image including the object and the distance from the seafaring vessel to the object.