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| Publications:Recognition by symmetry derivatives and the generalized structure tensor |
| Abstract | <p>We suggest a set of complex diffe … <p>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:</p><ol><li>tracking cross markers in long image sequences from vehicle crash tests and</li><li>alignment of noisy fingerprints.</li></ol> noisy fingerprints.</li></ol> |
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| Author | Josef Bigun + , Tomas Bigun + , Kenneth Nilsson + |
| DOI | http://dx.doi.org/10.1109/TPAMI.2004.126 + |
| Diva | http://hh.diva-portal.org/smash/record.jsf?searchId=1&pid=diva2:237415 |
| EndPage | 1605 + |
| Issue | 12 + |
| Journal | IEEE Transaction on Pattern Analysis and Machine Intelligence + |
| PublicationType | Journal Paper + |
| Publisher | IEEE Computer Society + |
| StartPage | 1590 + |
| Title | Recognition by symmetry derivatives and the generalized structure tensor + |
| Volume | 26 + |
| Year | 2004 + |
| Has queryThis property is a special property in this wiki. | Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + , Publications:Recognition by symmetry derivatives and the generalized structure tensor + |
| Categories | Publication + |
| Modification dateThis property is a special property in this wiki. | 30 September 2016 20:42:11 + |
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