Synonyms
Optimal parameter estimation
Related Concepts
Definition
Optimal estimation in the computer vision context usually refers to estimating the parameters that describe the underlying problem from noisy observation. The estimation is done according to a given criterion of optimality, for which maximum likelihood is widely accepted. If Gaussian noise is assumed, it reduces to minimizing the Mahalanobis distance. If furthermore the Gaussian noise has a homogeneous and isotropic distribution, the procedure reduces to minimizing what is called the reprojection error.
Background
One of the central tasks of computer vision is the extraction of 2-D/3-D geometric information from noisy image data. Here, the term image data refers to values extracted from images by image processing operations such as edge filters and interest point detectors. Image data are said to be noisyin the sense that image processing operations for detecting them entail uncertainty to...
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References
Chernov N, Lesort C (2004) Statistical efficiency of curve fitting algorithms. Comput Stat Data Anal 47(4):713–728
Chojnacki W, Brooks MJ, van den Hengel A, Gawley D (2000) On the fitting of surfaces to data with covariances. IEEE Trans Pattern Anal Mach Intell 22(11): 1294–1303
Kanatani K (2008) Statistical optimization for geometric fitting: theoretical accuracy analysis and high order error analysis. Int J Comput Vis 80(2):167–188
Kanatani K, Sugaya Y (2010) Unified computation of strict maximum likelihood for geometric fitting. J Math Imaging Vis 38(1):1–13
Leedan Y, Meer P (2000) Heteroscedastic regression in computer vision: Problems with bilinear constraint. Int J Comput Vis 37(2):127–150
Neyman J, Scott EL (1948) Consistent estimates based on partially consistent observations. Econometrica 16(1): 1–32
Rangarajan P, Kanatani K, Niitsuma H, Sugaya Y (2010) Hyper least squares and its applications. In: Proceedings of the 20th international conference on pattern recognition, August 2010, Istanbul, Turkey
Sampson PD (1982) Fitting conic sections to “very scattered” data: An iterative refinement of the Bookstein algorithm. Comput Graph Image Process 18(1): 97–108
Taubin G (1991) Estimation of planar curves, surfaces, and non-planar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans Pattern Anal Mach Intell 13(11):1115–1138
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Kanatani, K. (2014). Optimal Estimation. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_714
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DOI: https://doi.org/10.1007/978-0-387-31439-6_714
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