The Research On The Application Of V-system In Digital Geometry

V-system is a class of complete orthogonal function system and is just the generalization of the Haar function system. The V-system consists of not only smooth functions but also discontinuous functions at multi-levels, thus it can be utilized to express the complex geometry group finitely and precisely. What is more, the V-system also has the characteristics of multi-resolution and is a class of practical wavelet. Based on these characteristics of V-system above, this paper shows the successful applications of V-system in the geometric signal reconstruction, characters recognition and image denoising, which provide useful explorations to develop V-system and the area of its applications.This paper includes four main results as following,(1)To reconstruct the geometric group based on V-system. As the function systems such as Fourier system, Chebvshev polynomial etc. are in high smooth, their finite items cannot exactly express those geometric group, because the phenomenon of Gibbs will appear then. But we can obtain the finite expression using the characteristics of V-system. Its result of reconstructing the geometric group is compared with the Fourier function system's. Both the theory and the experimental result show that the phenomenon of Gibbs can be eliminated by using V-system to reconstruct geometric signals. So V-system has obvious advantageous over Fourier function in this aspect.(2)To classify and recognize the Chinese characters, letters and numbers based on the V-descriptor. We compared the experimental results of V-system with the classical method of Fourier descriptor. Our experimental results show that the normalized V-descriptor can recognize some geometric group efficiently and exactly. To some extent, V-descriptor has better recognition rate than Fourier descriptor.(3)We obtain the discrete linear V-system and use it in the image transform and get a new method for image compression. The experimental results show that it gets higher PSNR than classical slant transform, slantlet transform and DCT in reserving the same rate of the image in dealing with some images.(4)A new method of image denoising is obtained in the last chapter based on V-system. By comparing with the classical Discrete Wave Transform(DWT)(such as sym4,db4), the results show that V-system are better than classical wavelets transform in dealing with the noises such as gaussian and salt&pepper. In condition, we also summarized the experimental results for different values of k, the conclusion is that the denoising result of V-system of degree 3 is the best.