Wavelet Theory In Image Technology

Wavelets function and transformation are becoming more and more popular by scientists and engineers in many fielde because of its almost perfect mathematical characteristic. Since the 1980s, wavelet theory has already become a new research method for image technique. During afterward ten more years, the application of wavelets theory is more and more common with its developing and perfection and has solved many problems. Based on the foundation of the former research achievements and combining their research works, this thesis expatiates several applicable algorithms on image technique, mainly include:1, The algorithm of edge detection and the Canny Optimization Rule which based on the multi-resolution analysis are studied. The author developed a method of using Dual Wavelets for the sake of edge detection through detecting the bizarre degree (Lipschitz index) of the edge curve and also put forward the way of detecting the edge of the image by using directional derivative rather than partial derivative. It points out that if the wavelet transformation just transforming at a vertical and horizontal orientation that can not reflect correctly the edge information with various directional texture image. It is verified that the first directional derivative and second directional derivative of gaussian function are concessional wavelets and has the character of symmetry and dissymmetry. A sufficient condition is given for that a directional derivative of separable function may be as an edge detective operator. The result of the simulation indicates its good effection.2, The thesis expounded three basic facts of geometric transformation of image: geometric space transformation; geometric position transformation and gray scale interpolation. In order to apply the wavelet to image grey level interpolation, the first is to illustrate that the inverse transformation formula of dualistic wavelet is the formula of gray scale interpolation, the second is to deduce the gray scale interpolation formula by using the method of multi-resolution analysis and it also deduces the general expression of the gray scale interpolation which isf(x,y) = s(δ_x)~T As(δ_y) (see Chapter 4) on the condition that the scale function is separable,orthometric and has limited carried set. The simulation experiments with DB2 wavelet showed that this algorithm is better than the bilinearity algorithm and is as good as the third faltung method.3, The thesis analyzed several common method for movement object segmentation. The method of texture analysis based on the wavelet transformation is developed for object segmentation; and the author also developed an illumination model for background image: the model with local even illumination, as well as to prove that the scope of the wavelet transformation is stable by using the model except at the edge region. This result shows that the algorithm of background estimate based on the wavelet transformation is reliable to the variation of illumination and environment and also shows the advantages of carrying on texture analysis and...