Affine invariant for 2D image representation: a wavelet approach

The aim of this paper is to propose a method for 2D shape representation under affine transform using the discrete dyadic wavelet transform invariant to translation known as stationary wavelet transform or SWT. The main problem of this transform is its dependence to the signal starting point i.e (the same signal may have several representations depending on the starting point). The choice of the starting point is then necessary to match two descriptors. The method we propose is developed in three steps, a) the contour is first parameterized by enclosed area, b) the affine invariant feature is then calculated to finally c) determine the natural axis which enable to fix the starting point. The knowledge of the orientation of the natural axis enables to adjust the starting point on the contour between the query and the models given in the database. Furthermore, the method can select a subset of useful invariant features for the matching step. The method is tested on a database of 5000 fish species and the results are very probate.