Forstner W., "Reliability Analysis of Parameter Estimation in Linear Models with Application to the Mensuration Problems in Computer Vision", Computer Vision, Graphics and Image Processing, vol. 40, 1987, 273--310  Home/Search   Document Not in Database   Summary   Related Articles   Check

....rely on analytic pose recovery methods and this will be reviewed first. Papers detailing the analytic, or closed form pose recovery methods also called the PnP or space resectioning problem are numerous. Authors of note are Haralick et al. Fischler and Bolles, Forstner, Horaud et al. [27,28,29,30] to name but a very select few. A rigid body can move in Euclidean space with six degrees of freedom. Each correspondence between an image and an object point (Figure 2.1) under non degenerate conditions pro vides two constraints on the motion of the object thus requiring a minimum of three ....

W. Forstner. Reliability analysis of parameter estimation in linear models and applications to mensuration problems in computer vision. Computer Vision, Graphics, and Image Processing, 1987.

....Since the third components of x ff and x 0 ff are identically 1, the matrices V 0 [x ff ] and V 0 [x 0 ff ] are singular with third columns and third rows filled with zeros. frame. The normalized covariance matrices can be estimated from Hessian of the residual surface of template matching [4, 16, 20, 21]. If the noise has the same isotropic distribution everywhere, we have V 0 [x ff ] V 0 [x 0 ff ] diag(1; 1; 0) where diag(1 1 1) is the diagonal matrix with diagonal elements 1 1 1. We use this as the default value when no information is available about the noise behavior. 4. Theoretical ....

....one. Then, each vertex was corrected with sub pixel accuracy by deformable template matching (we omit the details) The ellipses drawn in the images visualize the covariance matrices (defined up to scale) of the individual vertices estimated from the gray level variations in their neighborhoods [4, 16, 20, 21] (we omit the details) As we can see, the covariance diverges and produces a huge ellipse if the neighborhood is of almost uniform gray levels; if the point is on an edge line, the ellipse is elongated along it. From these 16 corresponding vertices we comFigure 5: Real images of an indoor scene ....

W. Forstner, Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision, Comput. Vision Graphics Image Process., 40 (1987), 273--310.

....a feature point is very close to that of the surrounding points, like a white spot in a white region, we can regard that point as having a large covariance. The magnitude of the covariance can be estimated from the curvature of the residual surface of template matching based on local correlation [5, 15, 16]. Using such a method, we obtain a small covariance in a textured region and a large covariance in a region of almost uniform gray levels; for a point on an edge (i.e. object boundary) we obtain a distribution elongated along that edge. However, the covariance measured by such a means does ....

W. Forstner, Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision, Comput. Vision Graphics Image Process., 40 (1987), 273--310.

....to verify their reliability (10) System builders should at least be aware of the basic techniques for this, even if application constraints make it difficult to use them. The extraordinary extent to which weak geometry and lack of redundancy can mask gross errors is too seldom appreciated, c.f . [34, 50, 30, 33]. Point P is reconstructed accurately : In reconstruction, just as there are no absolute references for position, there are none for uncertainty. The 3D coordinate frame is itself uncertain, as it can only be located relative to uncertain reconstructed features or cameras. All other feature ....

....self consistent consensus among many independent observations, no aspect of them should rely excessively on just a few observations. The photogrammetric literature on quality control deserves to be better known in vision, especially among researchers working on statistical issues. Forstner [33, 34] and Grun [49, 50] give introductions with some sobering examples of the effects of poor design. See also [7, 8, 21, 22] All of these papers use least squares cost functions and scalar measurements. Our treatment generalizes this to allow robust cost functions and vector measurements, and is also ....

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W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics & Image Processing, 40:273--310, 1987.

....such as homogeneity inhomogeneity and isotropy anisotropy can be relatively easily predicted. For example, if we use template matching for finding corresponding feature points, the uncertainty of matching is characterized by the variation of the matching residual around the detected point [2, 10, 12, 13]. Hence, we assume that the covariance matrices V [x ff ] and V [x 0 ff ] are known up to scale and write V [x ff ] ffl 2 V 0 [x ff ] V [x 0 ff ] ffl 2 V 0 [x 0 ff ] 5) We call the unknown magnitude ffl the noise level . The matrices V 0 [x ff ] and V 0 [x 0 ff ] which we call ....

W. Forstner, Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision, Comput. Vision Graphics Image Process., 40 (1987), 273--310.

....by [ Lucas and Kanade 1981 ] who published an iterative image registration scheme base on LSM. Among the first papers that discussed the concept of exploiting the full information of the statistical models 2 Least squares template matching 3 for robust template matching are [ Grun 1985 ] and [ Forstner 1987 ] Bergen et al. 1992 ] describe basically the same algorithm for motion estimation. It was further developed using a multi scale approach by [ Lindeberg 1995 ] Following and extending the original work of Grun, Danuser and Mazza 1996 ] achieved highly accurate results at the resolution ....

W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics, and Image Processing, 40:273--310, 1987. References 13

....in the correlation surface is greater than any spurious peak caused by noise. The model is based on the simplest noise model; additive Gaussian noise or the Gaussian Random Field (GRF) The most significant previous work on performance models for correlationbased matching is that of Forstner [3][4] on the prediction of accuracy or localisation uncertainty for the case of spatially uncorrelated Gaussian noise. However, Forstner assumes a high Signal to Noise Ratio (SNR) and does not deal directly with the question of reliability. Significantly more progress has been made in understanding ....

Wolfgang Forstner. Reliability analysis of parameter estimation in linear models with application to mensuration problems in compter vision. Computer Vision, Graphics and Image Processing, 40:273--310, 1987.

....[4] 3] 15] 18] 7] 17] and sum of squared difference (SSD) methods [2] 1] show that all the basics are in place. With small inter frame displacements, a window can be tracked by optimizing some matching criterion with respect to translation [10] 1] and linear image deformation [6], 8] 11] possibly with adaptive window size[14] Feature windows can be selected based on some measure of texturedness or cornerness, such as a high standard deviation in the spatial intensity profile [13] the presence of zero crossings of the Laplacian of the image intensity [12] and ....

W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. CVGIP, 40:273--310, 1987.

....Early work in this field was presented by [Lucas and Kanade 1981] who published an iterative image registration scheme base on LSM. Among the first papers that discussed the concept of exploiting the full information of the statistical models for robust template matching are [Gr un 1985] and [F orstner 1987] . Bergen et al. 1992] describe basically the same algorithm for motion estimation. It was further developed using a multi scale approach by [Lindeberg 1995] Following and extending the original work of Grun, Danuser and Mazza 1996] achieved highly accurate results at the resolution limit of a ....

W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics, and Image Processing, 40:273--310, 1987.

....the sum of squared differences (SSD) E(u; v) X k;l [I 1 (x u k; y v l) Gamma I 0 (x k; y l) 2 (2) These approaches have been extensively studied and used. See [Ryan et al. 1980; Burt et al. 1982; Horn, 1983; Opitz, 1983; Wood, 1983] for some comparative analyses, and [Forstner, 1987] for a review of statistical aspects of photogrammetry. To obtain sub pixel registration accuracies, a number of possible extension to the basic search technique can be used [Tian and Huhns, 1986] interpolating the correlation surface E(u; v) interpolating the intensities, the differential ....

W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics, and Image Processing, 40:273--310, 1987. 22 7 Discussion and Conclusions

....procedure, thus increasing the reliability of the estimated parameters. The Student distribution (t distribution) 8] 20] could be used to test whether a certain variable takes on a presumed value under a selected significance level (1 Gamma ff) based on the estimated variance of the variable [7]. A problem with the t test is that it provides reliable results only when the variables to be tested are not correlated. We propose here to use the F distribution (Fisher s Distribution) 2 to overcome this drawback. To sketch its use in camera model identification, two null hypotheses are ....

W. Forstner, "Reliability analysis of parameter estimation in linear models with application to mensuration problems in computer vision," Proc. Sec. Int. Workshop on Robust Computer Vision, Institut fur Photogrammetrie, Unversitat Bonn, March, 1992, pp.1-110.

....the uncorrelated nature of the feature noise compared with distortions which introduce systematic correlated noise. Another direction remains to be explored: the outliers problem in the data. Tools exist for this kind of problem and come from what is called robust estimation (see for instance [7]) this direction will be explored in the near future. ....

W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics and Image Processing, 40:273--310, 1987.

.... oe n , the threshold on T = gu =oegu to be k(ff) depending on the significance number ff of the test, and the true edge leads to a gradient magnitude being a factor ffi (non centrality parameter of the non central Normal distribution) larger than oe gu , the power of the test is given by (cf. [4]) fi(ffi; ff) P (jT j kjpixel is edge) 1 Gamma Phi(k(ff) Gamma ffi) Phi(k(ff) ffi) with the normalized Gaussian distribution Phi(x) The standard deviation oe gu of the gradient magnitude across the edge depends on the noise level oe n and the function gu = f(g) e.g. the ....

W. Forstner. Reliability Analysis of Parameter Estimation in Linear Models with Applications to Mensuration Problems in Computer Vision. Computer Vision, Graphics & Image Processing, 40:273--310, 1987.

....Early work in this field was presented by [Lucas and Kanade 1981] who published an iterative image registration scheme base on LSM. Among the first papers that discussed the concept of exploiting the full information of the statistical models for robust template matching are [Gr un 1985] and [F orstner 1987] Bergen et al. 1992] describe basically the same algorithm for motion estimation. It was further developed by [Lindeberg 1995] using a multi scale approach. Following and extending the work of Grun, Danuser and Mazza 1996] achieved highly accurate results at the resolution limit of a light ....

W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics, and Image Processing, 40:273--310, 1987.

....a nearly ubiquitous tool in early vision. In the field of statistics, notions of robustness date back over one hundred years, but the 1960 s and 1970 s saw consolidation of the field we know as robust statistics today and as characterized by the work of Huber [1981] and Hampel et al. 1986] Forstner [1987] was probably the first to apply robust statistics to computer vision problems and, since then, there has been growing interest in robust techniques. We have shown in this paper that the unifying concept underlying the line process and robuststatistical approaches is the notion of outlier ....

Forstner, W. 1987. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision Graphics and Image Processing, 40: 273--310.

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Forstner W., "Reliability Analysis of Parameter Estimation in Linear Models with Application to the Mensuration Problems in Computer Vision", Computer Vision, Graphics and Image Processing, vol. 40, 1987, 273--310

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W. Forstner. Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer vision. Computer Vision, Graphics and Image Processing, 40:273--310, 1987.

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