Abstract
Uncertainty modeling in 3D Computer Vision typically relies on propagating the uncertainty of measured feature positions through the modeling equations to obtain the uncertainty of the 3D shape being estimated. It is widely believed that this adequately captures the uncertainties of estimated geometric properties when there are no large errors due to mismatching. However, we identify another source of error which we call feature localization error. This captures how well a feature corresponds to the true 3D point, rather than how well features correspond over multiple images. We model this error as independent of the tracking error, and when combined as part of the total error, we show that it is significant and may even dominate the 3D reconstruction error.
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References
Daniilidis, K. and Spetsakis, M. E. (1996). Visual Navigation. Lawrence Erl-baum Associates, Hillsdale, NJ. Chapter in book edited by Y. Aloimonos.
Haralick, R. M. (1996). Propagating covariance in computer vision, Int. J. of Patt. Recog. and AI., 10(5):561–572.
Kanatani, K. (1993). Unbiased estimation and statistical analysis of 3-D rigid motion from two views. IEEE Trans. Patt. Anal Mach. Intell., 15(1):37–50.
Kanatani, K. and Morris, D. D. (2001). Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy. IEEE Transactions on Information Theory, 47(5):2017–2028.
Matties, L. and Shafer, S. A. (1987). Error modeling in stereo navigation. IEEE   Journal of Robotics and Automation, RA-3(3):239–48.
Morris, D. D. (2001). Gauge Freedoms and Uncertainty Modeling for 3D Computer Vision. PhD thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA. (see also: CMU-RI-TR-01-15).
Morris, D. D. and Kanade, T. (1998). A unified factorization algorithm for points, line segments and planes with uncertainty models. In Proc. Sixth Int. Conf Comp. Vision, pages 696–702, Bombay, India.
Morris, D. D., Kanatani, K., and Kanade, T. (2000). Uncertainty modeling for optimal structure from motion. In Vision Algorithms: Theory and Practice, pages 200–217, Berlin. Springer.
Shi, J. and Tomasi, C. (1994). Good features to track. In Proc. Comp. Vision Patt. Recog., pages 593–600, Seattle.
Szeliski, R. and Kang S. B. (1994). Recovering 3D shape and motion From image streams using non-linear least squares. In  J. of Visual Comm. and Image Rep., 5(1), pages 10–28.
Thomas, J. I., Hanson, A., and Oliensis, J. (1994). Refining 3D reconstructions: A theoretical and experimental study of the effect of cross-correlations. CVGIP, 60(3):359–370.
Weng, J., Huang, T., and Ahuja, N. (1989). Motion and structure from two perspective views: Algorithms, error analysis, and error estimation. IEEE Trans. Patt. Anal. Mach. Intell., 11(2):451–476.
Young, G.-S. J. and Chellappa, R. (1992). Statistical analysis of inherent ambiguities in recovering 3-D motion from a noisy flow field. IEEE Trans. Patt. Anal. Mach. Intell., 14(10):995–1013.
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Morris, D.D., Kanade, T. (2002). Feature Localization Error in 3D Computer Vision. In: Winkler, J., Niranjan, M. (eds) Uncertainty in Geometric Computations. The Springer International Series in Engineering and Computer Science, vol 704. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0813-7_9
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DOI: https://doi.org/10.1007/978-1-4615-0813-7_9
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