Mathematical Definition
Bundle adjustment amounts to jointly refining a set of initial camera and structure parameter estimates for finding the set of parameters that most accurately predict the locations of the observed points in the set of available images. More formally, assume that 3D points are seen in views and let be the projection of the th point on image . Let denote the binary variables that equal 1 if point is visible in image and 0 otherwise. Assume also that each camera is parameterized by a vector and each 3D point by a vector . Bundle adjustment minimizes the total reprojection error with respect to all 3D point and camera parameters, specifically
where is the predicted projection of point on image and denotes the Euclidean distance between the image points represented by vectors and . Clearly, bundle adjustment is by definition tolerant to missing image projections and minimizes a physically meaningful criterion.
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