K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the decomposition of the special symmetric matrix s = 1 2 ( v v ) is numerically less accurate when and v coincide with each other. 3. Both algorithms give much better estimates when translation along Z axis is present. This is consistent to the sensitivity analysis done in Daniilidis [3]. In the case of translation in X Y plane, our algorithm gives better rotation estimates than the subspace method [4] especially when the noise levels are high. This is due to the fact that in our algorithm the rotation is estimated simultaneously with the translation, so that its bias is only ....

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

....estimate may suddenly change direction by roughly 90 o , especially in the case 8 when translation is parallel to the image plane. We will refer to such estimates as the second eigenmotion. A similar situation for the di#erential case and small field of view has previously been reported in [3]. Figure 2 and 3 demonstrate such a sudden appearance of the second eigenmotion. They are the simulation results of the proposed nonlinear algorithm of minimizing the function F s for a cloud of 40 randomly generated pairs of image correspondences (in a field of view 90 o , depth varying from ....

K. Danilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

....Similar to detecting local minima in the differential case (see [22] the second eigenmotion ambiguity can usually be detected by checking the positive depth constraints. A similar situation of the 90 o flip in the motion estimates for the differential case has previously been reported in [4]. Figure 4 and 5 demonstrate such a sudden appearance of the second eigenmotion. They are the simulation results of the proposed nonlinear algorithm of minimizing the function F s for a cloud of 40 randomly generated pairs of image correspondences (in a field of view 90 o , depth varying from ....

K. Danilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990. 32

....flow. However, this technique sacrifices the accuracy for the computational ease. Some researchers formulated the problem in the form of the least squares minimization and solved it by a numerical search algorithm. However, it has been pointed out that the resulting solution has a systematic bias [2]. An unbiased solution can be obtained by computing the maximum likelihood solution, but the computational burden is heavy [1] 3] 9] In order to avoid this difficulty, several researchers have devised simplified methods for obtaining an unbiased estimator [5] 10] In this report, we modify ....

Daniilidis K., and Nagel, H.H., Analytical results on error sensitivity of motion estimation from two views, Image Vis. Comput., 8, 1990, pp.287--303.

....an error analysis needs to be performed. The problem of determining the epipolar geometry of a stereo rig is also known as the structure from motion problem in the motion analysis literature. A significant research effort has been devoted to the analysis of errors in structure from motion, e.g. [1, 18, 17, 52, 19, 31, 20], to cite just a few examples. One common characteristic of these approaches is that their error models are linear. The main reason for this is the mathematical and computational tractability of the linear model. A secondary reason is the lack of an adequate non linear error model. In this ....

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

....depth minimization from normal flow, given a rotational error the obtained solution will have no error in the translation. In other cases ambiguities remain. In the spherical eye case the analysis is simply performed for noiseless flow. A large number of error analyses have been carried out [2, 12, 13, 15, 29, 41, 43, 44] in the past for a camera type eye, while there is no published research of this kind for the full field of view case. None of the existing studies, however, has attempted a topographic characterization of the function to be minimized for the purpose of analyzing different motion techniques. All ....

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

.... computations for this motion is that, with noise, there is an ambiguity between rotations in depth and translations parallel to the image plane [3] Note that this ambiguity is entirely different from the bias in the coplanarity constraint based two frame algorithms that was analyzed in [11, 26]. This bias leads to a local minimum solution for the motion parameters in which the translation direction is approximately along the optical axis (z axis) irrespective of the true direction. In our experiments, this solution was observed but was not used for the results reported here. The ....

K. Daniilidis and H. H. Nagel. Analytical results on error sensitivity of motion estimation from two views. In Proc. 1st European Conference on Computer Vision, pages 199--208, 1990.

....the image center) ffl pure translation (the fundamental matrix is antisymmetric) In the two last cases, the nature of the (Euclidean) motion can be characterized from fundamental matrices. Note that whereas the two first cases are known in the context of motion analysis ( 12, 79, 31, 71, 80] [12, 53, 1, 79, 29, 8]) the last one is specific to our problem, and comes from the fact that the fundamental matrix in the case of a pure translation depends only on two independent parameters, instead of seven. We present briefly some experimental results in figure 22 and refer the interested reader to [46] for more ....

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

....i BR component. 21 Recall that Step 2a1 neglects the constraints on the form of the Fa . 2.3.4 The Bas Relief Ambiguity: Step 2c A few inverse depth components are intrinsically more difficult to recover accurately than the rest. This is due to the well known bas relief ambiguity 22 [32, 1, 8, 24, 27, 58, 31, 57, 38, 40, 53, 7]. Any bias in an algorithm degrades the reconstructions of these components much more than that of the rest of the structure, so it is especially important to minimize the bias in computing them. The bas relief ambiguity reflects the fact that the image effects of rotating and translating are ....

K. Daniilidis and H.--H. Nagel, "Analytical results on error sensitivity of motion estimation from two view," Image and Vision Computing, vol 8. no. 4, 297--303, 1990.

....minimization techniques were developed [Spetsakis and Aloimonos, 1988; Horn, 1990; Aisbett, 1990; Philip, 1991] These techniques address the minimization in two steps; in one step they solve for the translational and in the other for the rotational components. In [Spetsakis and Aloimonos, 1989; Daniilidis and Nagel, 1990] the linearization technique has been analyzed statistically. Spetsakis and Aloimonos [1989] proved that under the assumption of Gaussian noise the best result for the E matrix is obtained by weighted least mean square minimization, where the weight factors are dependent on the motion parameters ....

K. Daniilidis and H.H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297-- 303, 1990.

....errors due to possible translational residuals. These errors are functions of the scene, so the parallel and orthogonal cross sections cannot completely separate structure and motion. Therefore, our analysis also requires consideration of the effects of scene structure. For similar purposes in [3] the authors restrict their study to a specific scene structure, the plane, to simplify their analysis of errors in motion estimation. In our approach, in order to achieve more general results, we instead introduce a noise source G into the model (Figure 24a) to account for the effects of this ....

K. Daniilidis and H.H. Nagel. Analytical results on error sensitivity of motion estimation from two views. In Proceedings of the European Conference on Computer Vision, pages 199--208, 1990.

....ffl x 0 , fi ffl = fl ffl y 0 . This means that the function has its global minimum along a line from which the FOE can be derived exactly, but the rotational component parallel to the translational component (x 0 ; y 0 ) cannot be determined. A large number of error analyses have been carried out [2, 11, 12, 14, 25, 39, 41, 44] in the past. None of the existing studies, however, has attempted a topographic characterization of the function to be minimized for the purpose of analyzing different motion techniques. All the studies consider optical flow or correspondence as image measurements and investigate minimizations ....

K. Daniilidis and H. H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

....of images are central topics in computer vision, with applications e.g. in robotics and navigation. Several algorithms exist, in general based on iterative numerical techniques. A survey, as well as a new algorithm, can be found in [5] The problem is ill posed, both what concerns stability ( 2] [1]) and non uniqueness ( 3] 9] The purpose of the present article is to develop some new theoretical tools, which may contribute to the understanding of the stability and ambiguity problems, and to develop new algorithms. The basic ideas are to study the imaging of point con gurations instead ....

....problem were computed. The image data have then been subjected to noise. As is witnessed by many authors, cf. e.g. 2] small disturbances in image location may give rise to large deviations in the reconstruction. Progressing eoeorts are devoted to the explanation of these observations, cf. e.g. [1]. It turns out that relative depth is relativly insensitive to disturbances; typically a random error of one pixel in each of the image point coordinates causes an error in each component of the normalized relative depth vector q of about 0.02. As also can be expected, by using con gurations ....

Daniilidis, K. and Nagel, H-H, Analytical Results on Error Sensitivity of Motion Estimation from Two Views, in Computer Vision ECCV90, ed. O. Faugeras, Springer Lect. Notes Comp. Sc., 427, pp 199-208, 1989.

....Vision In the previous section, it has been shown that the continuous approach exploiting camera velocity is an attractive solution to cope with the 3D reconstruction of a static scene. However, structure estimation from a monocular image sequence is very sensitive to the measurement errors [13] and to the nature of the camera movements [15] The experimental results reported in the next section will confirm that important errors on the structure estimation appear when no particular strategy concerning camera motion is defined. We have also pointed out that some given motions are not ....

K. Daniilidis and H.H. Nagel: "Analytical results on error sensitivity of motion estimation from two views," Proc. 1 st ECCV, pp. 199-208, Antibes, France, Apr. 1990.

.... 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 and H. H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

.... between the ground truth and the estimate) One approach to the problem is to design algorithms to minimize the effects of noise by using a form of constrained minimization [6, 7] use statistical estimation [8, 9, 10] analyze the behavior of the error in a wide variety of configurations [11, 12, 13], analyze the Cramer Rao Lower Bound (CRLB) of the estimation [14] study the effects of bias and devising tools to reduce it [15] etc. Most of this work has been collected and presented in a recent book by Kanatani [16] Other approaches include the direct methods [17, 18] that avoid the first ....

....with statistical measures or bounds the error in the motion and depth estimates. These error measures may be computed in closed form or numerically with an algorithm. They express the error in the computed parameters as a function of the true parameters and the measurement noise. Studies like [13, 11, 14, 38, 39] belong to the first category because they contain explicit expressions with respect to the problem parameters. Analyses like those in [10, 40, 41] comprise a second category because they establish bounds or approximations of the estimate error which are computed by sampling the parameter space. ....

[Article contains additional citation context not shown here]

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

No context found.

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

No context found.

K. Daniilidis and H.-H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

No context found.

K. Daniilidis and H. Nagel. Analytical results on error sensitivity of motion estimation from two views. Image and Vision Computing, 8:297--303, 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC