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Adjust collection of 3-D points and camera poses



[xyzRefinedPoints,refinedPoses] = bundleAdjustment(xyzPoints,pointTracks,cameraPoses,intrinsics) refines 3-D points and camera poses to minimize reprojection errors. The refinement procedure is a variant of the Levenberg-Marquardt algorithm. The function uses the same global reference coordinate system to return both the 3-D points and camera poses.

[wpSetRefined,vSetRefined,pointIndex] = bundleAdjustment(wpSet,vSet,viewIDs,intrinsics) refines 3-D points from the world point set, wpSet, and refines camera poses from the image view set, vSet. viewIDs specify the camera poses in vSet to refine.

[___,reprojectionErrors] = bundleAdjustment(___) returns the mean reprojection error for each 3-D world point, in addition to the arguments from the previous syntax.

[___] = bundleAdjustment(___,Name=Value) specifies options using one or more name-value arguments in addition to any combination of arguments from previous syntaxes. For example, MaxIterations=50 sets the number of iterations to 50. Unspecified arguments have default values.


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Load data for initialization.

data = load("globeBA.mat");

Refine the camera poses and points.

[xyzRefinedPoints,refinedPoses] = ...

Display the 3-D points and camera poses before and after the refinement.

pcshowpair(pointCloud(data.xyzPoints), pointCloud(xyzRefinedPoints), ...
    AxesVisibility="on", VerticalAxis="y", VerticalAxisDir="down", MarkerSize=40);
hold on
plotCamera(data.cameraPoses, Size=0.1, Color="m");
plotCamera(refinedPoses, Size=0.1, Color="g");
legend("Before refinement", "After refinement", color="w");

Input Arguments

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Unrefined 3-D points, specified as an M-by-3 matrix of [x y z] locations.

Matching points across multiple images, specified as an N-element array of pointTrack objects. Each element contains two or more matching points across multiple images.

Camera pose information, specified as a two-column table with columns ViewId and AbsolutePose. The view IDs relate to the IDs of the objects in the pointTracks argument. You can use the poses object function to obtain the cameraPoses table.

Camera intrinsics, specified as a cameraIntrinsics object or an N-element array of cameraIntrinsics objects. N is the number of camera poses or the number of IDs in viewIDs. Use a single cameraIntrinsics object when images are captured using the same camera. Use a vector cameraIntrinsics objects when images are captured by different cameras.

3-D world points, specified as a worldpointset object.

Camera poses, specified as an imageviewset object.

View identifiers, specified as an N-element array. The viewIDs represent which camera poses to refine specifying their related views in imageviewset.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: MaxIterations=50 sets the number of iterations to 50.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Maximum number of iterations before the Levenberg-Marquardt algorithm stops, specified as a positive integer.

Absolute termination tolerance of the mean squared reprojection error in pixels, specified as positive scalar.

Relative termination tolerance of the reduction in reprojection error between iterations, specified as positive scalar.

Flag to indicate lens distortion, specified as false or true. When you set PointsUndistorted to false, the 2-D points in pointTracks or in vSetmust be from images with lens distortion. To use undistorted points, first use the undistortImage function to remove distortions from the images, then set PointsUndistorted.

View IDs for fixed camera pose, specified as a vector of nonnegative integers. Each ID corresponds to the ViewId of a fixed camera pose in cameraPoses. An empty value for FixedViewIDs means that all camera poses are optimized.

Solver, specified as "sparse-linear-algebra" or "preconditioned-conjugate-gradient". Use the "sparse-linear-algebra" solver for low sparsity images. Low sparsity indicates that many camera views observe some of the same world points. Use the "preconditioned-conjugate-gradient" (PCG) solver, from the general graphic optimization (g2o) library, for high sparsity images. High sparsity indicates that each camera view observes, only a small portion of the world points, specified by xyzPoints.

Display progress information, specified as false or true.

Output Arguments

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3-D locations of refined world points, returned as an M-by-3 matrix of [x y z] locations.

Data Types: single | double

Refined camera poses, returned as a two-column table. The table contains columns for ViewId and AbsolutePose.

Refined 3-D world points, returned as a worldpointset object.

Refined camera poses, specified as an imageviewset object.

Indices to wpSetRefined of refined 3-D world points, returned as an M-element array.

Reprojection errors, returned as an M-element vector. The function projects each world point back into each camera. Then, in each image, the function calculates the reprojection error as the distance between the detected and the reprojected point. The reprojectionErrors vector contains the average reprojection error for each world point.

Detected point and reprojected point next to each other, with reprojection error as the distance between them


[1] Lourakis, Manolis I. A., and Antonis A. Argyros. "SBA: A Software Package for Generic Sparse Bundle Adjustment." ACM Transactions on Mathematical Software 36, no. 1 (March 2009): 2:1–2:30.

[2] Hartley, Richard, and Andrew Zisserman. Multiple View Geometry in Computer Vision. 2nd ed. Cambridge, UK ; New York: Cambridge University Press, 2003.

[3] Triggs, Bill, Philip F. McLauchlan, Richard I. Hartley, and Andrew W. Fitzgibbon. "Bundle Adjustment — A Modern Synthesis." In Proceedings of the International Workshop on Vision Algorithms, 298–372. Springer-Verlag, 1999.

Extended Capabilities

Version History

Introduced in R2016a

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