Multi-view height estimation from satellite images
Computing a height of a building is performed by inputting a pair of two-dimensional (2-D) aerial images of a city along with their metadata. Using the metadata, a three-dimensional (3-D) vector from each image toward the location of the camera when each image was taken is determined. A plurality of pairs of corresponding image points from the images are computed, in each pair of image points an image point of one image identifies the same physical point on the building as the second image point of the second image. Next, the images are superimposed, and for each pair of image points, determine the intersection of the 3-D vector of the first image originating at the first image point with the 3-D vector of the second image originating at the second image point. Each intersection is a 3-D position and the height is determined from the median of these 3-D positions.
1. A method of computing a height of a structure, said method comprising:
inputting a pair of first and second two-dimensional (2-D) aerial images taken from a camera from different perspectives along with metadata for each image, each image including at least said structure;
for each image, computing, using said metadata, a three-dimensional (3-D) vector from a geo-referenced location of said each image on a ground plane of the Earth toward the location of said camera when said each image was taken with said camera;
computing a plurality of pairs of coordinates of corresponding first and second image points from said geo-referenced locations of said images, wherein in each pair of image points a first image point of said first image identifies the same physical point on said structure as a second image point of said second image;
for each pair of image points, determining the intersection of said 3-D vector of said first image originating at the coordinates of said first image point with said 3-D vector of said second image originating at the coordinates of said second image point, wherein said each intersection being a 3-D position; and
determining said height by taking a median of said 3-D positions and outputting said height of said structure based upon said 3-D positions.
2. A method as recited in claim 1 , further comprising:
computing said height of said structure using only a ground-sampling distance, an azimuth angle and an off-nadir angle from said metadata of said each image.
3. A method as recited in claim 2 wherein said metadata does not include calibration data of said camera.
4. A method as recited in claim 1 wherein said camera is located in a satellite, in an aircraft, in a drone, or in a balloon.
5. A method as recited in claim 1 wherein said first image is taken with a first camera and said second image is taken with a second camera.
6. A method as recited in claim 1 , further comprising:
determining said height by multiplying said median by a ground-sampling distance of said metadata.
7. A method as recited in claim 6 , further comprising:
computing said height using only said ground-sampling distance, an azimuth angle and an off-nadir angle from said metadata of said each image.
8. A method as recited in claim 7 wherein said metadata does not include calibration data of said camera.
9. A method as recited in claim 1 , further comprising:
determining the intersection of said 3-D vector only for those pairs of images points that correspond to a building footprint of said structure.
10. A method as recited in claim 1 , further comprising:
performing said steps of claim 1 for a plurality of structures in said images.
11. A method as recited in claim 1 , further comprising:
computing said plurality of pairs of coordinates of corresponding image points for all pixels in said images.
12. A method as recited in claim 1 wherein said metadata does not include calibration data of said camera, said method further comprising:
computing said height of said structure without using said calibration data.
13. A method as recited in claim 12 wherein said metadata only includes a ground-sampling distance, an azimuth angle and an off-nadir angle for said each image.
14. A method as recited in claim 1 wherein each of said images includes the same region on earth.
15. A method as recited in claim 1 wherein said first and second images overlap.
16. A method as recited in claim 1 further comprising:
computing said three-dimensional (3-D) vector for said each image using metadata from an image pixel of said structure in said each image.
17. A system for computing a height of a structure, said system comprising:
a processing computer configured to
input a pair of first and second two-dimensional (2-D) aerial images taken from a camera from different perspectives along with metadata for each image, each image including at least said structure;
compute, for each image, using said metadata, a three-dimensional (3-D) vector from a geo-referenced location of said each image on a ground plane of the Earth toward d the location of said camera when said each image was taken with said camera;
compute a plurality of pairs of coordinates of corresponding first and second image points from said geo-referenced locations of said images, wherein in each pair of image points a first image point of said first image identifies the same physical point on said structure as a second image point of said second image;
for each pair of image points, determine the intersection of said 3-D vector of said first image originating at the coordinates of said first image point with said 3-D vector of said second image originating at the coordinates of said second image point, wherein said each intersection being a 3-D position; and
determine said height by taking a median of said 3-D positions and output a height of said structure based upon said 3-D positions.
18. A system as recited in claim 17 , wherein said processing computer being further configured to
compute said height of said structure using only a ground-sampling distance, an azimuth angle and an off-nadir angle from said metadata of said each image.
19. A system as recited in claim 18 wherein said metadata does not include calibration data of said camera.
20. A system as recited in claim 17 wherein said camera is located in a satellite, in an aircraft, in a drone, or in a balloon.
21. A system as recited in claim 17 wherein said first image is taken with a first camera and said second image is taken with a second camera.
22. A system as recited in claim 21 wherein said processing computer being further configured to
determine said height by multiplying said median by a ground-sampling distance of said metadata.
23. A system as recited in claim 17 , wherein said processing computer being further configured to
compute said height using only a ground-sampling distance, an azimuth angle and an off-nadir angle from said metadata of said each image.
24. A system as recited in claim 23 wherein said metadata does not include calibration data of said camera.
25. A system as recited in claim 17 wherein said processing computer being further configured to
determine the intersection of said 3-D vector only for those pairs of images points that correspond to a building footprint of said structure.
26. A system as recited in claim 17 , wherein said processing computer being further configured to
perform said steps of claim 16 for a plurality of structures in said images.
27. A system as recited in claim 17 , wherein said processing computer being further configured to
compute said plurality of pairs of coordinates of corresponding image points for all pixels in said images.
28. A system as recited in claim 17 wherein said metadata does not include calibration data of said camera, said processing computer being further configured to:
compute said height of said structure without using said calibration data.
29. A system as recited in claim 28 wherein said metadata only includes a ground-sampling distance, an azimuth angle and an off-nadir angle for said each image.
30. A system as recited in claim 17 wherein each of said images includes the same region on earth.
31. A system as recited in claim 17 wherein said first and second images overlap.
32. A system as recited in claim 17 wherein said processor being further configured to compute said three-dimensional (3-D) vector for said each image using metadata from an image pixel of said structure in said each image.