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A Unifying Approach to Moment-Based Shape Orientation and Symmetry Classification

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3 Author(s)
Georgios Tzimiropoulos ; Dept. of Electr. & Electron. Eng., Imperial Coll. London, London ; Nikolaos Mitianoudis ; Tania Stathaki

In this paper, the problem of moment-based shape orientation and symmetry classification is jointly considered. A generalization and modification of current state-of-the-art geometric moment-based functions is introduced. The properties of these functions are investigated thoroughly using Fourier series analysis and several observations and closed-form solutions are derived. We demonstrate the connection between the results presented in this work and symmetry detection principles suggested from previous complex moment-based formulations. The proposed analysis offers a unifying framework for shape orientation/symmetry detection. In the context of symmetry classification and matching, the second part of this work presents a frequency domain method, aiming at computing a robust moment-based feature set based on a true polar Fourier representation of image complex gradients and a novel periodicity detection scheme using subspace analysis. The proposed approach removes the requirement for accurate shape centroid estimation, which is the main limitation of moment-based methods, operating in the image spatial domain. The proposed framework demonstrated improved performance, compared to state-of-the-art methods.

Published in:

IEEE Transactions on Image Processing  (Volume:18 ,  Issue: 1 )