Ring Fourier Descriptors And Recovery Of Affine Parameters

Image classification and parameter recovery of image registration is a hot topic in the field of image processing, computer vision, pattern recognition etc, and has extensive applications. Based on this, the extraction of image invariant feature is key. The invariant feature extraction can be mainly classified into two main categories:contour-based methods and region-based methods. The contour-based methods extract features from the contour only, and its implementation is easy and it takes small calculation complexity. But,it can not reflect the internal information of image.The region-based techniques take all pixels within a shape region into account to obtain the shape representation. The derived features can reflect more image characteristics. However, these methods are usually at the expense of high computational demands and sensitive to noise in the background of the image.In this thesis, the combination of contour-based and region-based is taken into account. The contour-based method, Fourier descriptors, is converted to region-based method and classify. Region can be converted to contour by central projection transformation and recover the affine transformation parameter with the help of this contour.Main results of this thesis are as follows:(1) Propose ring Fourier descriptors:classic Fourier descriptors is based on the mature Fourier analysis theorey and its implementation is easy. However, Fourier descriptors based on the object contour coordinate sequence can only be used to objects with single boundary. Based on this, they are invalid to objects with interior holes (like the letter "A","B") or with consisting of several components (such as the Chinese characters "识"). So, the ring Fourier descriptors is proposed in this paper. The image centroid as the center of the circle, the different radius of circle to scan image, the Fourier transformation is used on the image gray value sequence, then the ring Fourier descriptors is obtained. This descriptors is invariant to shift, rotation and scaling transformation. Moreover, this method belong to region-based algorithm and are avalid to objects with consisting of several components.(2) Ring Fourier descriptors based on central projection is proposed. For extracting affine invariant feature, the central projection transformation is used to obtain generic contour. Scale the generic contour and Fourier is used on the image value sequence of expansion curve. By this, the ring Fourier descriptors based on central projection transformation and it is invariant for affine transformation.(3) Propose parameter recovery method based on central projection and cross-weighted centroid. In this thesis, the central projection is used to simplify the calculation of cross-weighted algorithm. Different points in the image can be obtained by the combination of simplied cross-weighted and affine region cutting. Through these points, linear equations can be constructed and can recover the affine parameters by these linear equations. Moreover, this method applies not only to gray image but also to binary image.