Detection of generalized principal axes is rotationally symmetric shapes
Pattern Recognition
Fold principal axis—a new tool for defining the orientations of rotationally symmetric shapes
Pattern Recognition Letters
Detecting number of folds by a simple mathematical property
Pattern Recognition Letters
Generalized Affine Invariant Image Normalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry Detection by Generalized Complex (GC) Moments: A Close-Form Solution
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Angular Difference Function and Its Application to Image Registration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Image Processing (3rd Edition)
Digital Image Processing (3rd Edition)
Notes on shape orientation where the standard method does not work
Pattern Recognition
Affine-permutation invariance of 2-D shapes
IEEE Transactions on Image Processing
A signal processing approach to symmetry detection
IEEE Transactions on Image Processing
Curvature weighted gradient based shape orientation
Pattern Recognition
Orientation and anisotropy of multi-component shapes from boundary information
Pattern Recognition
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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.