Methods and processes for interactive display of three dimensional covariance
First Claim
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1. A method for displaying a three-dimensional surface, the method comprising:
- using an electro-optical sensor to generate a plurality of images of a physical surface;
generating the three-dimensional surface from the plurality of images, using a multiray intersection of image coordinates on the physical surface and a photogrammetric bundle adjustment algorithm;
associating a covariance matrix with a first point on the three-dimensional 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 plane projection of the three-dimensional surface, a brightness of each point of the two-dimensional plane projection of the three-dimensional surface corresponding to an average intensity of corresponding points in the images; and
displaying a two-dimensional plane projection of the ellipsoid at the first point,wherein the covariance matrix is a sample covariance of points on the three-dimensional surface in a region around the first point, the sample covariance C being given by
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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.
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8 Claims
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1. A method for displaying a three-dimensional surface, the method comprising:
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using an electro-optical sensor to generate a plurality of images of a physical surface; generating the three-dimensional surface from the plurality of images, using a multiray intersection of image coordinates on the physical surface and a photogrammetric bundle adjustment algorithm; associating a covariance matrix with a first point on the three-dimensional 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 plane projection of the three-dimensional surface, a brightness of each point of the two-dimensional plane projection of the three-dimensional surface corresponding to an average intensity of corresponding points in the images; and displaying a two-dimensional plane projection of the ellipsoid at the first point, wherein the covariance matrix is a sample covariance of points on the three-dimensional surface in a region around the first point, the sample covariance C being given by - View Dependent Claims (2, 3, 4)
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5. A system for displaying a three-dimensional surface, the system comprising a processing unit configured to:
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receive a plurality of images of a physical surface; generate the three-dimensional surface from the plurality of images, using a multiray intersection of image coordinates on the physical surface and a photogrammetric bundle adjustment algorithm; associate a covariance matrix with a first point on the three-dimensional 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 plane projection of the three-dimensional surface, a brightness of each point of the two-dimensional plane projection of the three-dimensional surface corresponding to an average intensity of corresponding points in the images; and display a two-dimensional plane projection of the ellipsoid at the first point, wherein the covariance matrix is a sample covariance of points on the three-dimensional surface in a region around the first point, the sample covariance C being given by - View Dependent Claims (6, 7, 8)
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Specification