METHODS AND PROCESSES FOR INTERACTIVE DISPLAY OF THREE DIMENSIONAL COVARIANCE

• US 20140354647A1
• Filed: 05/22/2014
• Published: 12/04/2014
• Est. Priority Date: 05/29/2013
• Status: Active Grant

• Current Assignee: Raytheon Company (Rtx Corporation)
• Original Assignee: Raytheon Company (Rtx Corporation)
• Inventors: Verret, Jody D.
• Granted Patent: US 9,646,424 B2
• Time in Patent Office: Days
• US Class Current: 345/427
• CPC Class Codes: G01S 5/16 using electromagnetic waves other than radio waves
• CPC Class Codes: G06T 19/20 Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
• CPC Class Codes: G06T 2219/2004 Aligning objects, relative positioning of parts
• CPC Class Codes: G06T 2219/2016 Rotation, translation, scaling

Abstract

A system and method for displaying a three-dimensional surface along with ellipsoids representing covariances. In one embodiment, at a point on a three dimensional surface, an ellipsoid is formed having principal axes proportional to the eigenvalues of a covariance matrix. The ellipsoid and the three-dimensional surface are projected onto a two-dimensional plane for display on a two-dimensional screen to a user. The covariance matrix may be an estimated error covariance or a sample covariance.

Claims

1. A method for displaying a three-dimensional surface, the method comprising:

associating a covariance matrix with a first point on the surface;

forming an ellipsoid, the ellipsoid comprising three major axes, each major axis having a length proportional to the square root of an eigenvalue of the covariance matrix, and being parallel to an eigenvector of the covariance matrix;

displaying a two-dimensional projection of the surface; and

displaying a two-dimensional projection of the ellipsoid at the first point.

2. The method of claim 1, wherein the covariance matrix is an estimated error covariance provided by a photogrammetric bundle adjustment algorithm.

3. The method of claim 1, wherein the covariance matrix is the sample covariance of points on the surface in a region around the first point.

4. The method of claim 1, further comprising:

receiving, through a user interface, a selection of a point of interest on the surface,

wherein the covariance matrix is an estimated error covariance provided by a photogrammetric bundle adjustment algorithm at the point of interest.

5. The method of claim 4, wherein:

the receiving of a selection of a point of interest on the surface, the forming of an ellipsoid, and the displaying of a two-dimensional projection of the ellipsoid at the point on the surface comprise;

receiving a selection of a point of interest on the surface in real time;

forming an ellipsoid in real time; and

displaying a two-dimensional projection of the ellipsoid in real time.

6. The method of claim 4, further comprising:

receiving an ellipsoid scale change command; and

displaying an ellipsoid with a scale adjusted according to the received ellipsoid scale change command.

7. The method of claim 1, further comprising:

receiving, through a user interface, a selection of a point of interest,

wherein the covariance matrix is the sample covariance of points on the surface in a region around the point of interest.

8. The method of claim 7, wherein:

the receiving of a selection of a point of interest on the surface, the forming of an ellipsoid, and the displaying of a two-dimensional projection of the ellipsoid at the point on the surface comprise;

receiving a selection of a point of interest on the surface in real time;

forming an ellipsoid in real time; and

displaying a two-dimensional projection of the ellipsoid in real time.

9. The method of claim 8, further comprising:

receiving an ellipsoid scale change command; and

displaying an ellipsoid with a scale adjusted according to the received ellipsoid scale change command.

10. The method of claim 1, wherein the covariance matrix is an estimated error covariance corresponding to a distance between the first point and a second point on the surface.

11. A system for displaying a three-dimensional surface, the system comprising a processing unit configured to:

associate a covariance matrix with a first point on the surface;

form an ellipsoid, the ellipsoid comprising three major axes, each major axis having a length proportional to the square root of an eigenvalue of the covariance matrix, and being parallel to an eigenvector of the covariance matrix;

display a two-dimensional projection of the surface; and

display a two-dimensional projection of the ellipsoid at the first point.

12. The system of claim 11, wherein the covariance matrix is an estimated error covariance provided by a photogrammetric bundle adjustment algorithm.

13. The system of claim 11, wherein the covariance matrix is the sample covariance of points on the surface in a region around the first point.

14. The system of claim 11, wherein the processing unit is further configured to receive, through a user interface, a selection of a point of interest on the surface, and

wherein the covariance matrix is an estimated error covariance provided by a photogrammetric bundle adjustment algorithm at the point of interest.

15. The system of claim 14, wherein:

the receiving of a selection of a point of interest on the surface, the forming of an ellipsoid, and the displaying of a two-dimensional projection of the ellipsoid at the first point comprise;

receiving a selection of a point of interest on the surface in real time;

forming an ellipsoid in real time; and

displaying a two-dimensional projection of the ellipsoid in real time.

16. The system of claim 14, wherein the processing unit is further configured to:

receive an ellipsoid scale change command; and

display an ellipsoid with a scale adjusted according to the received ellipsoid scale change command.

17. The system of claim 11, wherein the processing unit is further configured to receive, through a user interface, a selection of a point of interest, and

wherein the covariance matrix is the sample covariance of points on the surface in a region around the point of interest.

18. The system of claim 17, wherein:

the receiving of a selection of a point of interest on the surface, the forming of an ellipsoid, and the displaying of a two-dimensional projection of the ellipsoid at the point on the surface comprise;

receiving a selection of a point of interest on the surface in real time;

forming an ellipsoid in real time; and

displaying a two-dimensional projection of the ellipsoid in real time.

19. The system of claim 18, wherein the processing unit is further configured to:

receive an ellipsoid scale change command; and

display an ellipsoid with a scale adjusted according to the received ellipsoid scale change command.

20. The system of claim 11, wherein the covariance matrix is an estimated error covariance corresponding to a distance between the first point and a second point on the surface.