Weak-perspective structure from motion for strongly contaminated data

It is widely known that, for the affine camera model, both shape and motion data can be factorised directly from the measurement matrix containing the image coordinates of the tracked feature points. 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 Trajković et al. [1] who use the 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 more precise SfM than using the affine motion data. Based on these observations, we propose a novel robust SfM algorithm and discuss its advantages and limits. Furthermore, we introduce a RANSAC based outlier detector that also provides robust results. The proposed methods and the Trajković procedure are quantitatively compared on synthetic data in different simulated situations. The methods are also tested on synthesised and real video sequences.