J. Oliensis. Rigorous bounds for two--frame structure from motion. In European Conference on Computer Vision, pages 184--195, 1996. Home/Search Document Details and Download
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Optimal Estimation of Three-Dimensional Rotation and.. - Ohta, Kanatani (1998) (6 citations) (Correct)
....Eddington epsilon, taking 1 when (ijk) is an even permutation of (123) 01 when it is an odd permutation of (123) and 0 otherwise. If the noise is isotropic and identical, we have V 0 [r ff ] V 0 [r 0 ff ] I (unit matrix) In this case, Eq. 8) corresponds to the result obtained by Oliensis [12]. 4 Optimal Estimation Applying the general theory of Kanatani [9] Sect. 14.5.2 of [9] we can obtain a computational scheme for solving Problem 1 in such a way that the resulting solution attains the accuracy bound (8) in the first order (i.e. ignoring terms of O(ffl 4 ) we minimize the ....
J. Oliensis, Rigorous bounds for two-frame structure from motion, Proc. 4th European Conf. Computer Vision, April 1996, Cambridge, Vol. 2, pp. 184--195.
Motion without Structure - Roy, Cox (Correct)
....or translation when the other component of motion is known was shown to be solvable by locating the single global minimum. This paper extends these results and considers the full motion case when both rotation and translation must be simultaneously estimated. The effect of motion ambiguity (see in [13]) on the accuracy of motion estimation is also discussed. Section 3 presents experimental results from a comprehensive evaluation based on real images of stereoscopic pairs and an indoor calibrated motion sequence. 2. Motion Estimation as a 5 D search Our goal is to determine the motion between ....
J. Oliensis. Rigorous bounds for two-frame structure from motion. Technical Report 95-155, NEC Research Institute, Princeton, NJ, 1993.
Structure from Planar Motions with Small Baselines - Vidal, Oliensis (2002) Self-citation (Oliensis) (Correct)
....) 1) Let # be the ratio between the largest translation and the smallest depth, i.e. # = Tmax Z min . We say that the baselines are small if # 1. Under this assumption, one can initialize all the translations to be zero and then solve linearly for the rotations from (1) It is shown in [6] that the errors between these rotation estimates R est and the true rotations R true are approximately proportional to # , where# is such that R true R est = exp( # SO(3) Here, u] # so(3) represents the skew symmetric matrix generating the cross product, i.e. for all ....
J. Oliensis. Rigorous bounds for two--frame structure from motion. In European Conference on Computer Vision, pages 184--195, 1996.
Three Algorithms for 2-Image and >= 2-Image Structure from Motion - Oliensis, Genc Self-citation (Oliensis) (Correct)
....this plane inaccurate. 4.2.3 Initialization We have considered two methods for providing initial estimates of the translation and rotation. The rst is the standard linear 8 point algorithm [20] as improved by Hartley [7] It can deal with motions of any size but works best for large motions [32]. The second is an improved version [28] 21] of the linear subspace technique of [14] 15] which essentially eliminates the earlier techniques s bias toward recovering e within the FOV. It can deal with translations of any size but requires small to moderate rotations. For small motions, it in ....
....should probably initialize using the 8 point algorithm for nonplanar scenes and homography computation for planar ones. Though A2 incorporates a small motion assumption, it can give accurate results even for very 17 large translations when initialized using the 8 point algorithm. As shown in [32], the 8 point algorithm gives accurate and reliable results when the translation is large and the depth range of the scene is not too small. The translation recovery step in A2 can deal with arbitrarily large translations as long as the rotation is known accurately enough: if the rotation is ....
J. Oliensis, \Rigorous Bounds for Two{Frame Structure from Motion," ECCV 184-195, 1996.
Provably Correct Algorithms for Multiframe Structure from.. - Oliensis (1996) (4 citations) Self-citation (Oliensis) (Correct)
....of this approach. It provably gives a good approximation to the ground truth within the appropriate domain. In addition to the translation direction restriction, our approach also requires that the translation not be too large compared to the depths of the feature points 3 . We have argued in [11, 9, 10] that this is not an important restriction. Experimentally, our approach is essentially always valid if the translation magnitude is less than 1=2 of the 3D depths a relatively large translation. Moreover, for translations of this large size, standard two frame algorithms, including the ....
....of this large size, standard two frame algorithms, including the notoriously unreliable 8 point algorithm [8] produce excellent estimates of structure and motion, assuming only that the 3D feature points have significant depth variation. We have verified this claim in extensive experiments in [11]. If the 3D points do not have significant depth variation, then Tomasi and Kanade s approach [18, 17] works essentially regardless of the translation size. Thus algorithms already exist which can deal with motion sequences where the translations are large. Our approach deals with the ....
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J. Oliensis, "Rigorous Bounds for Two--Frame Structure from Motion," submitted to ECCV 1996. Also http://www.neci.nj.nec.com/homepages/oliensis.html.
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