Whiten Central Projection And Generic Legendre Moments

Affine transformation is an approximate model to describe the relationship between images obtained from different viewpoints of the same object,so affine invariant feature extraction has become an important role in the field of object recognition and image registration.The methods of global invariant feature extraction can be divided into two categories: contour-based and region-based.Contour-based are of less computation but they ignore the internal information of the shape;Region-based methods can get high accuracy but the computation is expensive.Central projection can be viewed as a combination of region-based and contour-based methods,but it needs additional processes such as parametrization.The purpose of these processes is to establish the one-to-one correspondence between contours.In order to combine region-based and contour-based methods and avoid these additional processes,this paper proposes whiten central projection.On the other hand,the orthogonal moment has the advantages of excellent numerical stability and can be reconstructed conveniently.Although the fractional Legendre moment proposed recently is the extension of the traditional Legendre moment,it need to be further improved.Therefore,the generic Legendre moment is proposed.The main work of this paper is as follows:(1)The whiten central projection is proposed.In fact,it can be viewed as a combination of region-based and contour-based methods.The whiten transform can eliminate the shearing in the affine transform,and convert the affine transform into only rotation and scaling,so as to avoid additional processes such as parametrization in the central projection.Based on the proposed whiten central projection,a new affine invariant is constructed and applied to image recognition.Experiments show that the proposed invariants are more robust to noise than AMIs and MSA.A method of parametric estimation for affine transform is also designed by using whiten central projection,and it is applied to image registration.The results of experiments show that the proposed method is robust to noise,and the computational complexity is low.(2)The generic Legendre moments is proposed.Fractional Legendre moments generalize the integral order polynomials in the traditional Legendre moments to fractionalorder polynomials.In this paper,it is further extended to polynomials composed of general functions.The traditional Legendre moments and fractional Legendre moments are only special cases of the proposed orthogonal moments.The orthogonality and rotation invariance of the moment in polar coordinate system are proved.Experimental results show that the proposed method can construct orthogonal moments with better reconstruction and anti-noise performance than fractional Legendre moments.