Affine Invariant Feature Extraction Based On Fractional Order Moment

Nowadays, extraction of invariant features of images is widely applied in computer vision. As we know, image moments are the important technology to describe the global feature. For example, Hu moments are used to extract the similarity features and affine invariant moments can be used to extract the affine invariant features. However, these traditional moments only can be the integer orders and the higher order moments are more sensitive to noise. To overcome these disadvantages, this paper introduces fractional order moments and uses these moments to construct the invariants, which can extract affine invariant features. Then we use this fractional order moments to define related fractional order centroid, based on that an algorithm of affine transformation parameter recovery is given. This algorithm can overcome the drawback that the extended centroid can’t recovery the binary image. Moreover, in application, we need to determine image centroid in advance in order to change Cartesian coordinates into polar coordinates. Thus, to avoid the affect of centroid, we propose integral power R-transformation, which can be used to extract similar invariant features combined with Fourier descriptors.The main contents are as follows:(1) First, we introduce the concept of fractional order moments, which are defined by the repeated integral deformation and the traditional moments are just the special case of fractional order moments. The affine invariant moments are constructed by fractional order moments, and experiments show that the low-order affine invariant moments have better anti-noise performance.(2) Second, we construct the fractional order centroid. There are three group corresponding points of affine transformation and can be constructed by image centroid and fractional order centroid. This algorithm is applicable for both binary and gray images.(3) Moreover, integral power R-transform is proposed, of which generalized R-transform is only its special case. Integral power R-transform combined with Fourier descriptors can be used to extract translation, scaling and rotation invariant features.