K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... number of studies have given rise to three crisp results regarding noise sensitivity in structure from motion [7] These are: a) A translation can be easily confounded with a rotation in the case of a small field of view under the assumption of lateral motion and insufficient variation of depth [1, 6]. Intuitively, translation along the x axis can be confused with rotation around the y axis and translation along the y axis with rotation around the x axis. Evidence for this result can be obtained intuitively from the flow equation (1) As can be seen, if the scene in view is a plane, then the ....

....As can be seen, if the scene in view is a plane, then the flow becomes a polynomial in the retinal coordinates x; y with the terms t 1 2 , t 2 Gamma 1 representing the zero order terms. An elegant proof of this fact using techniques from estimation theory has been presented by Daniilidis [6] for the case of unbiased estimators. b) Usually an error metric is developed whose minimization provides a solution for 3D motion and subsequently for structure. If this metric is not appropriately normalized, in the case of a small field of view the translation estimate is biased toward the ....

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K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992, in German.

.... the case of stereo, the 3D transformation amounting to the extrinsic calibration parameters of the stereo rig cannot be accurately estimated, only approximated [4] In the case of motion, the three dimensional motion parameters describing rotation and translation are estimated within error bounds [3, 5, 20, 26]. Finally, visual correspondence itself cannot be obtained perfectly; errors are always present. Thus, because of errors in both visual correspondence and 3D transformation, the recovered depth of the scene is always a distorted version of the scene structure. The fundamental contribution of this ....

K. Daniilidis. On the error sensitivity in the recovery of object descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992, in German.

....problem becomes well posed and stable [7] although still nonlinear. The basic understanding of the influence of the field of view has attracted a few investigators over the years. In this paper we will not study this question in more detail and only refer to the literature for more information [3, 6, 10]. Thus, in conclusion, there are two principles relating camera design to performance in structure from motion the field of view and the linearity of the estimation. These principles are summarized in Fig. 1. A polydioptric spherical camera is therefore the ultimate camera since it combines ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

....is a geometric problem and it exists for both small and large baselines between the views, that is, for the case of continuous motion as well as in the case of discrete displacements of the cameras. The basic understanding of these difficulties has attracted only a few investigators over the years [3, 9, 14, 16]. a) b) Figure 3. Schematic illustration of error function in the space of the direction of translation. a) A valley for a planar surface with a limited field of view. b) A clearly defined minimum for a spherical field of view. Intuitively speaking, for imaging surfaces with small ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

....is a geometric problem and it exists for both small and large baselines between the views, that is, for the case of continuous motion as well as in the case of discrete displacements of the cameras. The basic understanding of these difficulties has attracted only a few investigators over the years [3, 8, 13, 15]. Having in mind the design of an optimal sensor, we are interested in how the stability of the estimation of motion changes with the field of view. In particular, we have compared the planar small field of view camera with a spherical camera [10] Since motion estimation amounts to solving some ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

....is a geometric problem and it exists for both small and large baselines between the views, that is, for the case of continuous motion as well as in the case of discrete displacements of the cameras. The basic understanding of these difficulties has attracted only a few investigators over the years [3, 11, 12, 19, 21]. Having in mind the design of an optimal sensor, we are interested in how the stability of the estimation of motion changes with the field of view. In particular, we have compared the planar small field of view camera with a spherical camera [14] Since motion estimation amounts to solving some ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

....the y axis, and translation along the y axis can be easily confounded with rotation around the x axis, for small fields of view and insufficient depth variation. This fact has long been known from experimental observation, and has been proved for planar scene structures and unbiased estimators [11]. The orthogonality constraint found here confirms these findings, and imposes even more restrictive constraints. It shows, in addition, that the x translation and y rotation, and y translation and x rotation, are not decoupled. Furthermore, we have found that rotation around the Z axis can be ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

....translate parallel to the scene, the motion field at the center of the image is very similar in the two cases. Thus, for example, translation along the x axis is confused with rotation around the y axis. The basic understanding of this confusion has attracted few investigators over the years. See [7,8] for a review. In this paper it is shown that the confusion exists no matter what estimator is used, proving that there is an inherent limitation to the estimation of 3D motion from data of only a limited field of view. To be more precise, a statistical analysis of all the possible computational ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

.... 1996; Stark, 1968; Coombs and Brown, 1993] tracking [Ferm uller and Aloimonos, 1992; Smith and Brady, 1995; Koller et al. 1993] segmenting the scene [Nelson, 1991; Zeki et al. 1993] estimating 3D motion and reconstructing the scene in view or some representations of the third space dimension [Daniilidis, 1992; Faugeras, 1992] Fig. 1. A pattern similar to one by Ouchi [ 1977 ] For humans and other primates it is considered that two dimensional image measurements are computed which correspond to the velocity measurements of image patterns, called optical flow. The corresponding field of ....

....In addition, total least squares is known to perform very poorly if outliers are present, and these are difficult to detect from few measurements. The estimation and interpretation of optical flow from a statistical point of view has received attention before in the computational literature [Daniilidis, 1992; Daniilidis and Spetsakis, 1997; Heeger, 1988; Simoncelli et al. 1991; Szeliski, 1990; Weber and Malik, 1995] It has been pointed out in [Nagel, 1995; Nagel and Haag, 1998] that optical flow estimated using gradient methods is biased. In these studies the bias is interpreted only with regard to ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

....the computation of optical flow from noisy gradient measurements has a systematic bias dependent upon the gradient distribution of the image region. The estimation and interpretation of optical flow from a statistical point of view has received attention previously in the computational literature [1, 2, 3, 11, 14, 16]. Most closely related to this paper are the studies of Nagel and Haag [7, 8] who investigate and at1 tempt to compensate for the bias in a gradient based technique; however, they interpret the bias only with respect to the underestimation of the length of the flow, and do not discuss the effects ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

.... number of studies have given rise to three crisp results regarding noise sensitivity in structure from motion [7] These are: a) A translation can be easily confounded with a rotation in the case of a small field of view under the assumption of lateral motion and insufficient variation of depth [1, 6]. Intuitively, translation along the x axis can be confused with rotation around the y axis and translation along the y axis with rotation around the x axis. Evidence for this result can be obtained intuitively from the flow equation (1) As can be seen, if the scene in view is a plane, then the ....

....As can be seen, if the scene in view is a plane, then the flow becomes a polynomial in the retinal coordinates x; y with the terms t 1 2 , t 2 Gamma 1 representing the zero order terms. An elegant proof of this fact using techniques from estimation theory has been presented by Daniilidis [6] for the case of unbiased estimators. b) Usually an error metric is developed whose minimization provides a solution for 3D motion and subsequently for structure. If this metric is not appropriately normalized, in the case of a small field of view the translation estimate is biased toward the ....

[Article contains additional citation context not shown here]

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992, in German.

....the y axis, and translation along the y axis can be easily confounded with rotation around the x axis, for small fields of view and insufficient depth variation. This fact has long been known from experimental observation, and has been proved for planar scene structures and unbiased estimators [10]. The orthogonality constraint found here confirms these findings, and imposes even more restrictive constraints. It shows, in addition, that the x translation and y rotation, and y translation and x rotation, are not decoupled. Furthermore, we have found that rotation around the Z axis can be ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

.... are further processed by the brain to perform many visual tasks, the most fundamental of which include controlling eye movement [4, 39, 2] tracking [10, 38, 25] segmenting the scene [32, 46] estimating 3D motion and reconstructing the scene or some representation of the third spatial dimension [3, 9]. For humans and primates it is believed that two dimensional image measurements are computed which correspond to velocity measurements of image patterns, called optical flow. The resulting field of measurements, the optical flow field, represents an approximation to the projection of the field of ....

....In addition, total least squares is known to perform very poorly if outliers are present, and these are difficult to detect from a few measurements. The estimation and interpretation of optical flow from a statistical point of view has received attention previously in the computational literature [3, 5, 14, 36, 40, 43]. Most closely related to this paper is the study of Nagel [29] He considers an error model slightly more complicated than ours. In particular, he assumes Gaussian noise in the gray values, linearly varying flow, and he considers the dependence of the partial derivatives in the gray value ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

.... the case of stereo, the 3D transformation amounting to the extrinsic calibration parameters of the stereo rig cannot be accurately estimated, only approximated [7] In the case of motion, the three dimensional motion parameters describing rotation and translation are estimated within error bounds [4, 5, 6, 8, 27, 33]. Finally, visual correspondence itself cannot be obtained perfectly; errors are always present. Thus, because of errors in both visual correspondence and 3D transformation, the recovered depth of the scene is always a distorted version of the scene structure. The fundamental contribution of this ....

K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992, in German.

....parameters if the points lie on a quadric with certain properties. The relation of these instability critical surfaces to the ambiguity critical surfaces has been an open problem in visual motion a . Such a relationship was first established in pure geometric terms by Hofmann [56] Following [57] we show here that an instability critical surface arises when the two optical centers take special positions on the ambiguity critical surface. Let (R; a) and (S; b) be two rotation translation pairs that yield the same point correspondences (x 1 ; x 2 ) The pair of the two ambiguity surfaces ....

K. Daniilidis. On the error sensitivity in the recovery of object descriptions and relative motions from image sequences. Doctoral dissertation, Department of Informatics, University of Karlsruhe, Germany, July 1992. in German.

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K. Daniilidis. On the Error Sensitivity in the Recovery of Object Descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992. In German.

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K. Daniilidis. On the error sensitivity in the recovery of object descriptions. PhD thesis, Department of Informatics, University of Karlsruhe, Germany, 1992, in German.

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