Distance estimation from image motion for moving obstacle detection
Distance from a moving image capture device to one or more points is determined. An optical flow is calculated from a first image and a second image captured by the moving image capture device. The horizontal component of the optical flow is used to generate a horizontal distance map including horizontal distances and the vertical component of the optical flow is used to generate a vertical distance map including vertical distances. Horizontal weights are applied to the horizontal distance map to generate a modified horizontal distance map where horizontal distances proximate to a vertical line intersecting a focus of expansion are attenuated. Vertical weights are applied to the vertical distance map to generate a modified vertical distance map where vertical distances proximate to a horizontal line intersecting the focus of expansion are attenuated. The modified vertical distance map and the modified horizontal distance map are then summed.
1. A system for determining distance to points from motion in captured images comprising:
a moving image capture device capturing a first image and a second image;
a processor coupled to the moving image capture device;
a memory structured to store instructions executable by the processor, the instructions, when executed, cause the processor to execute steps of:
determining a horizontal distance map including horizontal distances from the moving image capture device to a plurality of points determined from a horizontal component of an optical flow calculated from the first image and the second image;
determining a vertical distance map including vertical distances from the moving image capture device to the plurality of points determined from a vertical component of the optical flow calculated from the first image and the second image;
generating a modified horizontal distance map by applying a set of horizontal weights to the horizontal distance map, the set of horizontal weights attenuating horizontal distances associated with pixels in the horizontal distance map proximate to a vertical line intersecting a focus of expansion of the horizontal distance map;
generating a modified vertical distance map by applying a set of vertical weights to the vertical distance map, the set of vertical weights attenuating vertical distances associated with pixels in the vertical distance map proximate to a horizontal line intersecting a focus of expansion of the vertical distance map;
generating a distance map by combining the modified horizontal distance map and the modified vertical distance map; and
storing the distance map in the memory.
2. The system of claim 1 , wherein the set of horizontal weights have a minimum value at pixels located on a vertical line intersecting the focus of expansion of the horizontal distance map and have values which increase as a distance of a pixel from the vertical line intersecting the focus of expansion of the horizontal distance map increases.
3. The system of claim 2 , wherein a horizontal weight associated with a pixel, (x,y) in the horizontal distance map comprises
w
x
(
x
,
y
)
=
1
-
exp
(
-
(
x
-
e
x
)
2
σ
2
)
wherein e x comprises the focus of expansion of the horizontal distance map and σ comprises a standard deviation.
4. The system of claim 3 , wherein the standard deviation is determined from a maximum vertical range of a region of the horizontal distance map.
5. The system of claim 4 , wherein the standard deviation is one-third the maximum vertical range of the region of the horizontal distance map.
6. The system of claim 1 , wherein the set of vertical weights have a minimum value at pixels located on a horizontal line intersecting the focus of expansion of the vertical distance map and has values which increase as a distance of a pixel from the horizontal line intersecting the focus of expansion of the vertical distance map increases.
7. The system of claim 5 , wherein a vertical weight associated with a pixel, (x,y) in the vertical distance map comprises
w
y
(
x
,
y
)
=
1
-
exp
(
-
(
y
-
e
y
)
2
σ
2
)
wherein e y comprises the focus of expansion of the vertical distance map and σ comprises a standard deviation.
8. The system of claim 7 , wherein the standard deviation is determined from a maximum horizontal range of a region of the vertical distance map.
9. The system of claim 8 , wherein the standard deviation is one-third the maximum horizontal range of the region of the vertical distance map.
10. The system of claim 1 , wherein the focus of expansion of the horizontal distance map and the focus of expansion of the vertical distance map comprise a single focus of expansion.
11. A method for determining distance to points from motion in captured images comprising:
receiving a first image and a second image from a moving image capture device;
determining a horizontal distance map including horizontal distances from the moving image capture device to a plurality of points determined from a horizontal component of an optical flow calculated from the first image and the second image;
determining a vertical distance map including vertical distances from the moving image capture device to the plurality of points determined from a vertical component of the optical flow calculated from the first image and the second image;
generating a modified horizontal distance map by applying a set of horizontal weights to the horizontal distance map, the set of horizontal weights attenuating horizontal distances associated with pixels in the horizontal distance map proximate to a vertical line intersecting a focus of expansion of the horizontal distance map;
generating a modified vertical distance map by applying a set of vertical weights to the vertical distance map, the set of vertical weights attenuating vertical distances associated with pixels in the vertical distance map proximate to a horizontal line intersecting a focus of expansion of the vertical distance map;
generating a distance map by combining the modified horizontal distance map and the modified vertical distance map; and
storing the distance map in a computer-readable storage device.
12. The method of claim 11 , wherein the set of horizontal weights have a minimum value at pixels located on a vertical line intersecting the focus of expansion of the horizontal distance map and has values which increase as a distance of a pixel from the vertical line intersecting the focus of expansion of the horizontal distance map increases.
13. The method of claim 12 , wherein a horizontal weight associated with a pixel, (x,y) in the horizontal distance map comprises
w
x
(
x
,
y
)
=
1
-
exp
(
-
(
x
-
e
x
)
2
σ
2
)
wherein e x comprises the focus of expansion of the horizontal distance map and σ comprises a standard deviation.
14. The method of claim 13 , wherein the standard deviation is determined from a maximum vertical range of a region of the horizontal distance map.
15. The method of claim 14 , wherein the standard deviation is one-third the maximum vertical range of the region of the horizontal distance map.
16. The method of claim 11 , wherein the set of vertical weights have a minimum value at pixels located on a horizontal line intersecting the focus of expansion of the vertical distance map and has values which increase as a distance of a pixel from the horizontal line intersecting the focus of expansion of the vertical distance map increases.
17. The method of claim 15 , wherein a vertical weight associated with a pixel, (x,y) in the vertical distance map comprises
w
y
(
x
,
y
)
=
1
-
exp
(
-
(
y
-
e
y
)
2
σ
2
)
wherein e y comprises the focus of expansion of the vertical distance map and σ comprises a standard deviation.
18. The method of claim 17 , wherein the standard deviation is determined from a maximum horizontal range of a region of the vertical distance map.
19. The method of claim 18 , wherein the standard deviation is one-third the maximum horizontal range of the region of the vertical distance map.
20. The method of claim 11 , wherein the focus of expansion of the horizontal distance map and the focus of expansion of the vertical distance map comprise a single focus of expansion.
21. A non-transitory computer-readable storage medium structured to store instructions executable by a processor in a computing device, the instructions, when executed, cause the processor to execute steps of:
receiving a first image and a second image from a moving image capture device;
determining a horizontal distance map including horizontal distances from the moving image capture device to a plurality of points determined from a horizontal component of an optical flow calculated from the first image and the second image;
determining a vertical distance map including vertical distances from the moving image capture device to the plurality of points determined from a vertical component of the optical flow calculated from the first image and the second image;
generating a modified horizontal distance map by applying a set of horizontal weights to the horizontal distance map, the set of horizontal weights attenuating horizontal distances associated with pixels in the horizontal distance map proximate to a vertical line intersecting a focus of expansion of the horizontal distance map;
generating a modified vertical distance map by applying a set of vertical weights to the vertical distance map, the set of vertical weights attenuating vertical distances associated with pixels in the vertical distance map proximate to a horizontal line intersecting a focus of expansion of the vertical distance map;
generating a distance map by combining the modified horizontal distance map and the modified vertical distance map; and
storing the distance map in a computer-readable storage device.
22. The non-transitory computer-readable storage medium of claim 21 , wherein the set of horizontal weights have a minimum value at pixels located on a vertical line intersecting the focus of expansion of the horizontal distance map and have values which increase as a distance of a pixel from the vertical line intersecting the focus of expansion of the horizontal distance map increases.
23. The non-transitory computer-readable storage medium of claim 22 , wherein a horizontal weight associated with a pixel, (x,y) in the horizontal distance map comprises:
w
x
(
x
,
y
)
=
1
-
exp
(
-
(
x
-
e
x
)
2
σ
2
)
wherein e x comprises the focus of expansion of the horizontal distance map and σ comprises a standard deviation.
24. The non-transitory computer-readable storage medium of claim 23 , wherein the standard deviation is determined from a maximum vertical range of a region of the horizontal distance map.
25. The non-transitory computer-readable storage medium of claim 24 , wherein the standard deviation is one-third the maximum vertical range of the region of the horizontal distance map.
26. The non-transitory computer-readable storage medium of claim 21 , wherein the set of vertical weights have a minimum value at pixels located on a horizontal line intersecting the focus of expansion of the vertical distance map and have values which increase as a distance of a pixel from the horizontal line intersecting the focus of expansion of the vertical distance map increases.
27. The non-transitory computer-readable storage medium of claim 25 , wherein a vertical weight associated with a pixel, (x,y) in the vertical distance map comprises
w
y
(
x
,
y
)
=
1
-
exp
(
-
(
y
-
e
y
)
2
σ
2
)
wherein e y comprises the focus or expansion or the vertical distance map and σ comprises a standard deviation.
28. The non-transitory computer-readable storage medium of claim 27 , wherein the standard deviation is determined from a maximum horizontal range of a region of the vertical distance map.
29. The non-transitory computer-readable storage medium of claim 28 , wherein the standard deviation is one-third the maximum horizontal range of the region of the vertical distance map.
30. The non-transitory computer-readable storage medium of claim 21 , wherein the focus of expansion of the horizontal distance map and the focus of expansion of the vertical distance map comprise a single focus of expansion.