Robust Maximum Likelihood estimation by sparse bundle adjustment using the L1 norm

Sparse bundle adjustment is widely used in many computer vision applications. In this paper, we propose a method for performing bundle adjustments using the L₁ norm. After linearizing the mapping function in bundle adjustment on its first order, the kernel step is to compute the L₁ norm equations. Considering the sparsity of the Jacobian matrix in linearizing, we find two practical methods to solve the L₁ norm equations. The first one is an interior-point method, which transfer the original problem to a problem of solving a sequence of L₂ norm equations, and the second one is a decomposition method which uses the differentiability of linear programs and represents the optimal updating of parameters of 3D points by the updating variables of camera parameters. The experiments show that the method performs better for both synthetically generated and real data sets in the presence of outliers or Laplacian noise compared with the L₂ norm bundle adjustment, and the method is efficient among the state of the art L₁ minimization methods.