Computation of posterior covariances of object points in bundle adjustment

Abstract: Bundle adjustment (BA) is a photogrammetric method for optimal estimation of parameters from image measurements. The parameters include 3D coordinates of objects points (OP). The result of the bundle adjustment process is a vector of estimates and its covariance matrix, C. The elements of this matrix contain quality indicators of the estimation. By looking for the elements with the highest values, the most problematic parameter can be removed. The matrix C is created by inversion of the systems normal matrix, N, which is sparse. However, inverting N directly is intractable since the inverse is generally dense. In many cases, only the diagonal blocks of C are needed. This thesis evaluates algorithms that compute only the 3-by-3 blocks of C that correspond to the OPs. The algorithms utilize the Cholesky factor for efficiency. The results show that if N is permuted into an arrowhead shape and the sparsity of the Cholesky factor is properly exploited, then it is possible to efficiently compute the 3-by-3 diagonal blocks of the posterior covariance matrix.