Robust structure from motion under weak perspective

It is widely known that, for the affine camera model, both shape and motion data can be factorized directly from the measurement matrix constructed from 2D image points coordinates. However, classical algorithms for structure from motion (SfM) are not robust: measurement outliers, that is, incorrectly detected or matched feature points can destroy the result. A few methods to robustify SfM have already been proposed. Different outlier detection schemes have been used. We examine an efficient algorithm by Trajkovic et al. (1997) who use affine camera model and the least median of squares (LMedS) method to separate inliers from outliers. LMedS is only applicable when the ratio of inliers exceeds 50%. We show that the least trimmed squares (LTS) method is more efficient in robust SfM than LMedS. In particular, we demonstrate that LTS can handle inlier ratios below 50%. We also show that using the real (Euclidean) motion data results in a more precise SfM algorithm that using the affine camera model. Based on these observations, we propose a novel robust SfM algorithm and discuss its advantages and limits. The proposed method and the Trajkovic procedure are quantitatively compared on synthetic data in different simulated situations. The methods are also tested on synthesized and real video sequences.