Showing papers by "Jana Kosecka published in 2000"
TL;DR: A precise characterization of the space of differential essential matrices gives rise to a novel eigenvalue-decomposition-based 3D velocity estimation algorithm from the optical flow measurements that gives a unique solution to the motion estimation problem and serves as a differential counterpart of the well-known SVD- based 3D displacement estimation algorithm for the discrete case.
Abstract: The aim of this paper is to explore a linear geometric algorithm for recovering the three dimensional motion of a moving camera from image velocities. Generic similarities and differences between the discrete approach and the differential approach are clearly revealed through a parallel development of an analogous motion estimation theory previously explored in Vieville, T. and Faugeras, O.D. 1995. In Proceedings of Fifth International Conference on Computer Vision, pp. 750–756s Zhuang, X. and Haralick, R.M. 1984. In Proceedings of the First International Conference on Artificial Intelligence Applications, pp. 366–375. We present a precise characterization of the space of differential essential matrices, which gives rise to a novel eigenvalue-decomposition-based 3D velocity estimation algorithm from the optical flow measurements. This algorithm gives a unique solution to the motion estimation problem and serves as a differential counterpart of the well-known SVD-based 3D displacement estimation algorithm for the discrete case. Since the proposed algorithm only involves linear algebra techniques, it may be used to provide a fast initial guess for more sophisticated nonlinear algorithms (Ma et al., 1998c. Electronic Research Laboratory Memorandum, UC Berkeley, UCB/ERL(M98/37)). Extensive simulation results are presented for evaluating the performance of our algorithm in terms of bias and sensitivity of the estimates with respect to different noise levels in image velocity measurements.
76 citations
TL;DR: This paper characterize explicitly all the vantage points that give rise to a valid Euclidean reprojection regardless of the ambiguity in the reconstruction of the reconstructed scene, motion and calibration.
Abstract: The necessary and sufficient conditions for being able to estimate scene structure, motion and camera calibration from a sequence of images are very rarely satisfied in practice. What exactly can be estimated in sequences of practical importance, when such conditions are not satisfied? In this paper we give a complete answer to this question. For every camera motion that fails to meet the conditions, we give explicit formulas for the ambiguities in the reconstructed scene, motion and calibration. Such a characterization is crucial both for designing robust estimation algorithms (that do not try to recover parameters that cannot be recovered), and for generating novel views of the scene by controlling the vantage point. To this end, we characterize explicitly all the vantage points that give rise to a valid Euclidean reprojection regardless of the ambiguity in the reconstruction. We also characterize vantage points that generate views that are altogether invariant to the ambiguity. All the results are presented using simple notation that involves no tensors nor complex projective geometry, and should be accessible with basic background in linear algebra.
36 citations
26 Jun 2000
TL;DR: It is shown that, in several special cases, the Kruppa equations can be renormalized and become linear and, in particular, for cases when the camera motion is such that its rotation axis is parallel or perpendicular to translation, linear algorithms for self-calibration are obtained.
Abstract: In this paper, we study general questions about the solvability of the Kruppa equations and show that, in several special cases, the Kruppa equations can be renormalized and become linear. In particular, for cases when the camera motion is such that its rotation axis is parallel or perpendicular to translation, we can obtain linear algorithms for self-calibration. A further study of these cases not only reveals generic difficulties with degeneracy in conventional self-calibration methods based on the nonlinear Kruppa equations, but also clarifies some incomplete discussion in the literature about the solutions of the Kruppa equations. We demonstrate that Kruppa equations do not provide sufficient constraints on camera calibration and give a complete account of exactly what is missing in Kruppa equations. In particular, a clear relationship between the Kruppa equations and chirality is revealed. The results then resolve the discrepancy between the Kruppa equations and the necessary and sufficient condition for a unique calibration. Simulation results are presented for evaluation of the sensitivity and robustness of the proposed linear algorithms.
29 citations
25 Nov 2000
TL;DR: This article reviews some techniques as well as challenges shared by many applications which use visual sensing to guide the action of the robotic agent and require coordination between multiple agents to support hierarchical view of such systems sensing.
Abstract: The capability of perceiving the environment is crucial for advancing the level of autonomy and sophistication of (semi) autonomous robotic systems and determines the complexity of the tasks robotics agents can achieve. This article reviews some techniques as well as challenges shared by many applications which use visual sensing to guide the action of the robotic agent and require coordination between multiple agents. In order to support hierarchical view of such systems sensing both in the context of low-level control as well as planning and coordination between multiple mobile agents will be considered. Several examples of the design and analysis of these hierarchical hybrid systems will be outlined in the context of Intelligent Highways, namely autonomous driving and coordination between multiple vehicles and mobile robot navigation in indoors man made environments.