| 1. |
- Aanaes, H, et al.
(author)
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Robust factorization
- 2002
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In: IEEE Transactions on Pattern Analysis and Machine Intelligence. - 1939-3539. ; 24:9, s. 1215-1225
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Journal article (peer-reviewed)abstract
- Factorization algorithms for recovering structure and motion from an image stream have many advantages, but they usually require a set of well-tracked features. Such a set is in generally not available in practical applications. There is thus a need for making factorization algorithms deal effectively with errors in the tracked features. We propose a new and computationally efficient algorithm for applying an arbitrary errorfunction in the factorization scheme. This algorithm enables the use of robust statistical techniques and arbitrary noise models for the individual features. These techniques and models enable the factorization scheme to deal effectively with mismatched features, missing features, and noise on the individual features. The proposed approach further includes a new method for Euclidean reconstruction that significantly improves convergence of the factorization algorithms. The proposed algorithm has been implemented as a modification of the Christy-Horaud factorization scheme, which yields a perspective reconstruction. Based on this implementation, a considerable increase in error tolerance is demonstrated on real and synthetic data. The proposed scheme can, however, be applied to most other factorization algorithms.
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| 2. |
- Bigun, Josef, 1961-, et al.
(author)
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Recognition by symmetry derivatives and the generalized structure tensor
- 2004
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In: IEEE Transactions on Pattern Analysis and Machine Intelligence. - Los Alamitos, USA : IEEE Computer Society. - 0162-8828 .- 1939-3539. ; 26:12, s. 1590-1605
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Journal article (peer-reviewed)abstract
- We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: they are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications:tracking cross markers in long image sequences from vehicle crash tests andalignment of noisy fingerprints.
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| 3. |
- Björkman, Mårten, et al.
(author)
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Real-time epipolar geometry estimation of binocular stereo heads
- 2002
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In: IEEE Transactions on Pattern Analysis and Machine Intelligence. - : Institute of Electrical and Electronics Engineers (IEEE). - 0162-8828 .- 1939-3539. ; 24:3, s. 425-432
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Journal article (peer-reviewed)abstract
- Stereo is an important cue for visually guided robots. While moving around in the world, such a robot can use dynamic fixation to overcome limitations in image resolution and field of view. In this paper, a binocular stereo system capable of dynamic fixation is presented. The external calibration is performed continuously taking temporal consistency into consideration, greatly simplifying the process. The essential matrix, which is estimated in real-time, is used to describe the epipolar geometry. It will be shown, how outliers can be identified and excluded from the calculations. An iterative approach based on a differential model of the optical flow, commonly used in structure from motion, is also presented and tested towards the essential matrix. The iterative method will be shown to be superior in terms of both computational speed and robustness, when the vergence angles are less than about 15degrees. For larger angles, the differential model is insufficient and the essential matrix is preferably used instead.
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| 4. |
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| 5. |
- Zunic, Jovisa, et al.
(author)
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Efficiency of Characterizing Ellipses and Ellipsoids by Discrete Moments
- 2000
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In: IEEE Transactions on Pattern Analysis and Machine Intelligence. - : Institute of Electrical and Electronics Engineers (IEEE). - 0162-8828 .- 1939-3539. ; 22:4, s. 407-414
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Journal article (peer-reviewed)abstract
- In this paper, our studies are focused on ellipses and problems related to their representation and reconstruction from the data resulting from their digitization. The main result of the paper is that a finite number of discrete moments, corresponded to digital ellipses, is in one-to-one correspondence with digital ellipses, which enables coding of digital ellipses with an asymptotically optimal amount of memory. In addition, the problem of reconstruction, based on the same parameters, is considered. Since the digitization of real shapes causes an inherent loss of information about the original objects, the precision of the original shape estimation from the corresponding digital data is limited. We derive a sharp upper bound for the errors in reconstruction of the center position and half-axes of the ellipse, in function of the applied picture resolution (i.e., the number of pixels per unit). An extension of these results to the 3D case is also given
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