Bundle adjustment using epipolar constraints
Methods, systems, and apparatus for performing bundling adjustment using epipolar constraints. A method includes receiving image data from a headset for a particular pose. The image data includes a first image from a first camera of the headset and a second image from a second camera of the headset. The method includes identifying at least one key point in a three-dimensional model of an environment at least partly represented in the first image and the second image and performing bundle adjustment. Bundle adjustment is performed by jointly optimizing a reprojection error for the at least one key point and an epipolar error for the at least one key point. Results of the bundle adjustment are used to perform at least one of (i) updating the three-dimensional model, (ii) determining a position of the headset at the particular pose, or (iii) determining extrinsic parameters of the first camera and second camera.
1 . A method comprising:
receiving, from a headset, image data for a particular pose of the headset, the image data comprising (i) a first image from a first camera of the headset and (ii) a second image from a second camera of the headset;
identifying a set of key points in a three-dimensional model of an environment at least partly represented in the first image and the second image;
performing bundle adjustment using the first image and second image by jointly optimizing (i) a reprojection error for the key points of the set of key points (ii) an epipolar error for the key points of the set of key points; and (iii) a factory calibration error, wherein the factory calibration error comprises a change in relative position between the first camera and a reference position on the headset, wherein jointly optimizing comprises:
calculating a total error, wherein calculating the total error comprises summing together:
a first summation of reprojection errors for the set of key points,
a second summation of epipolar errors for the set of key points, and
a third summation of factory calibration errors for the set of key points; and
using results of the bundle adjustment to perform at least one of (i) updating, as an updated three-dimensional model, the three-dimensional model, (ii) determining a position of the headset at the particular pose, or (iii) determining extrinsic parameters of the first camera and second camera.
2 . The method of claim 1 , comprising providing an output for display by the headset based on the updated three-dimensional model.
3 . The method of claim 1 , wherein the epipolar error is a result of deformation of the headset causing a difference from a calibration of the headset.
4 . The method of claim 1 , comprising determining a set of extrinsic parameters for the first camera and the second camera based on the first image and the second image.
5 . The method of claim 1 , wherein the extrinsic parameters include a translation and rotation that together indicate a relationship of the first camera or the second camera with respect to a reference position on the headset.
6 . The method of claim 1 , comprising:
receiving images from the first and second cameras at each of a plurality of different poses along a path of movement of the headset; and
determining different extrinsic parameters for the first and second cameras for at least some of the plurality of different poses using results of the jointly optimizing involving the epipolar error.
7 . The method of claim 1 , wherein jointly optimizing the error comprises minimizing the total error across each of the multiple key points.
8 . The method of claim 1 , comprising:
receiving, from the headset, second image data for multiple poses of the headset;
identifying at least one second key point in the three-dimensional model of the environment at least partly represented in the second image data;
performing bundle adjustment for each of the multiple poses by jointly optimizing (i) a reprojection error for the at least one key point based on the second image data and (ii) an epipolar error for the at least one key point based on the second image data; and
using results of the bundle adjustment for each of the multiple poses to perform at least one of (i) updating the three-dimensional model, (ii) determining another position of the headset at each of the multiple poses, or (iii) determining other extrinsic parameters of the first camera and the second camera at each of the multiple poses.
9 . The method of claim 1 , comprising:
receiving, from the headset, first image data for a first pose of the headset and second image data for a second pose of the headset, wherein a deformation of the headset occurs between the first pose of the headset and the second pose of the headset;
identifying at least one second key point in the three-dimensional model of the environment at least partly represented in the first image data and in the second image data;
performing the bundle adjustment using the first image data and the second image data by jointly optimizing at least the epipolar error (a) for the at least second one key point (b) that represents the deformation of the headset that occurred between the first pose and the second pose of the headset; and
using results of the bundle adjustment to perform at least one of (i) updating the three-dimensional model, (ii) determining a first position of the headset at the first pose or a second position of the headset at the second pose, or (iii) determining first extrinsic parameters of the first camera and the second camera at the first pose, or second extrinsic parameters of the first camera and the second camera at the second pose.
10 . The method of claim 1 , comprising updating a series of poses of the headset using the results of the bundle adjustment.
11 . The method of claim 1 , wherein using the results of the bundle adjustment comprises updating the three-dimensional model comprising updating positions of one or more key points in the three-dimensional model.
12 . The method of claim 1 , wherein using the results of the bundle adjustment comprises determining the position of the headset at the particular pose with respect to the three-dimensional model.
13 . The method of claim 1 , wherein the first image and the second image were captured at approximately a same time.
14 . A non-transitory computer storage medium encoded with instructions that, when executed by one or more computers, cause the one or more computers to perform operations including:
receiving, from a headset, image data for a particular pose of the headset, the image data comprising (i) a first image from a first camera of the headset and (ii) a second image from a second camera of the headset;
identifying a set of key points in a three-dimensional model of an environment at least partly represented in the first image and the second image;
performing bundle adjustment using the first image and second image by jointly optimizing (i) a reprojection error for the key points of the set of key points (ii) an epipolar error for the key points of the set of key points; and (iii) a factory calibration error, wherein the factory calibration error comprises a change in relative position between the first camera and a reference position on the headset, wherein jointly optimizing comprises:
calculating a total error, wherein calculating the total error comprises summing together:
a first summation of reprojection errors for the set of key points,
a second summation of epipolar errors for the set of key points, and
a third summation of factory calibration errors for the set of key points; and
using results of the bundle adjustment to perform at least one of (i) updating, as an updated three-dimensional model, the three-dimensional model, (ii) determining a position of the headset at the particular pose, or (iii) determining extrinsic parameters of the first camera and second camera.
15 . The non-transitory computer storage medium of claim 14 , comprising providing an output for display by the headset based on the updated three-dimensional model.
16 . The non-transitory computer storage medium of claim 14 , wherein the epipolar error is a result of deformation of the headset causing a difference from a calibration of the headset.
17 . The non-transitory computer storage medium of claim 14 , comprising determining a set of extrinsic parameters for the first camera and the second camera based on the first image and the second image.
18 . A system comprising one or more computers and one or more storage devices on which are stored instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations including:
receiving, from a headset, image data for a particular pose of the headset, the image data comprising (i) a first image from a first camera of the headset and (ii) a second image from a second camera of the headset;
identifying a set of key points in a three-dimensional model of an environment at least partly represented in the first image and the second image;
performing bundle adjustment using the first image and second image by jointly optimizing (i) a reprojection error for the key points of the set of key points (ii) an epipolar error for the key points of the set of key points; and (iii) a factory calibration error, wherein the factory calibration error comprises a change in relative position between the first camera and a reference position on the headset, wherein jointly optimizing comprises:
calculating a total error, wherein the calculating the total error comprises summing together:
a first summation of reprojection errors for the set of key points,
a second summation of epipolar errors for the set of key points, and
a third summation of factory calibration errors for the set of key points; and
using results of the bundle adjustment to perform at least one of (i) updating, as an updated three-dimensional model, the three-dimensional model, (ii) determining a position of the headset at the particular pose, or (iii) determining extrinsic parameters of the first camera and second camera.