Curvelet Transform Applied Research In Image Processing

Wavelet analysis has been successfully applied into image processing, but it is a pity that it can not take full advantage of geometrical characteristic of image data to obtain the representation of sparse functions, such as line singularities and plane singularities. Hence, Donoho and Caneds proposed Curvelet transform which inherits the basic ideas of Wavelet transform. Structural elements in Curvelet transform not only include the parameter of dimension and location,but also provides with an orientation parameters. Therefore, Curvelet transform is superior to wavelet in case of image edge expression,such as curves, straight lines and other geometrical features.Since Curvelet transform was proposed about ten years ago, it has produced a lot of good algorithms which enriched image processing methods like image denoising, image enhancement, image fusion, etc. However, the application in image analysis is seldom reported, such as image quality assessment, texture classification or image segmentation. This thesis integrates Curvelet transform with gray theory and discusses new methods on image quality assessment and image texture classification. The main contribution can be summarized as follow:(1)In order to efficiently and objectively evaluate the quality of images, this thesis proposes a Curvelet transform and grey relational analysis based method which utilizes the global comparison mechanism of grey relation analysis theory and the analysis ability in multi-scales and multi-direction of Curvelet transform. First, the grey relational grades between the evaluating images and the reference image at different scales and directions are gained. Second, the mean of the relation grades at all angles in same scale is computed, and then, a global relation grade between the mean and the reference sequence is produced which provide us with image quality in two levels. Experimental results show that our method not only can provide image quality at different scales and angles, but also produce more reasonable conclusions than PSNR evaluate methods.(2) Since unsupervised classification is feasible even prior knowledge is absent, this thesis presents a new classification method for texture image which is based on Gray Relational Analysis (GRA) of Curvelet coefficient. During the procedure of texture feature extraction, this method not only utilizes some statistical information in spatial domain such as a gray-level co-occurrence matrix, but also employs some statistical information in frequency domain via Curvelet transform. After that, grey relational analysis was applied to classify the extracted features when any prior knowledge is not available. Experiment results show that the method is superiors to K-mean and fuzzy K-means based algorithm when the number of classification is large.