Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust regression and outlier detection
Robust regression and outlier detection
Robust regression methods for computer vision: a review
International Journal of Computer Vision
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
A comparison of four algorithms for estimating 3-D rigid transformations
BMVC '95 Proceedings of the 1995 British conference on Machine vision (Vol. 1)
A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Linear and Incremental Acquisition of Invariant Shape Models From Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Robust Structure from Motion under Weak Perspective
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Consistency of robust estimators in multi-structural visual data segmentation
Pattern Recognition
Fast and precise weak-perspective factorization
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
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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 Trajkovic and Hedley [Trajkovic, M., Hedley, M., 1997. Robust recursive structure and motion recovery under affine projection. In: Proc. British Machine Vision Conference. Available from: ] 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 Trajkovic procedure are quantitatively compared on synthetic data in different simulated situations. The methods are also tested on synthesised and real video sequences.