Based On The Image Analysis Of Krawtchouk Moments

In general, moments describe numeric quantities at some distance from a reference point or axis. The use of moments for image analysis is straightforward if we consider a binary or gray level image segment as a two-dimensional density distribution function. Moments are commonly used in statistics to characterize the distribution of random variables and similarly in mechanics to characterize bodies by their spatial distribution of mass. The set of moments derived from images provide mass of geometrical features. In this way, applications of moments and its invariants in fields of image processing refer to pattern recognition, image reconstruction, watermarking and so on.In this paper, definition and properties of some common moments will be first introduced, these moments include Hu moments, Legendre, Zernike, Tchebichef moments and so on. Then we put an emphasis on Krawtchouk moments, taking its properties and fast computing as the base knowledge, research is focused on using Krawtchouk moments in image reconstructing and watermarking.The research work of this paper can be classified in the following respects:1. First, we put forward a new symmetry property of Krawtchouk polynomials on the diagonal based on the pre-research of other scientists. For calculating Krawtchouk moments of images, the use of symmetry properties does not only mean savings of computation time and storage space for Krawtchouk polynomials, but also the reducing of accumulation of numerical errors. Further more, the symmetry properties free the choosing of the parameter (p1, p2), it is possible to reconstruct any region-of-interest of images with any sets of parameters during the range of [0,1].2. A near optimum local image watermarking using Krawtchouk moments is put forward in chapter4. In order to find the best parameters set (p1,p2),(p1,p2) defining the local behavior of the Krawtchouk polynomials, the proposed technique uses a simple genetic algorithm as optimization procedure. The results near optimum parameters are used to construct the corresponding image’s moments where the watermark information is inserted. The PSNR of the resulted watermarked image and the NC between the original and reconstructed watermark consist of the fitness function. Appropriate experiments have taken place and results have proved that the proposed technique can improve the quality of the watermarked image, and watermark is robust to some processing attacks.3. We put emphasis on the research of the method for recognition graphic pattern which bases on Krawtchouk moment invariants. The Krawtchouk moment invariants are obtained through normalization with respects to scaling, translation and rotation for original image and combing Krawtchouk discrete orthogonal moment. Object recognition experiments show Krawtchouk moment invariants perform significantly better than Hu’s moment invariants or Zernike’s moment invariants in both noise-free and noisy condition.