PDE Based Methods For Image Denoising And Segmentation

This thesis mainly focuses on problem of image denoising and segmentation via partial differential equations, particularly, total variation (TV) model, anisotropic diffusion (PM) model and isotropic diffusion (ID) model. In the scope of the image denoising we propose a new image denoising technique. The new technique based on combination of TV, PM and ID models. The proposed technique has an ability to remove the noise and preserves the edges simultaneously, which can adapt in each region depending on the information of the image. In the scope of image segmentation we address two main approaches. The first approach concentrates on inhibit the oversegmentation that produce by the traditional watershed segmentation. To prevent the oversegmentation of traditional watershed we propose a new image segmentation algorithm. The proposed algorithm based on watershed method which we use appropriate weight function to combine the enhanced final multiscale gradient algorithm with markers algorithm to get the new algorithm. The new algorithm has a significant influence in terms of suppression oversegmentation. Consequently the locations of edges will be very accurate. The second approach concentrates on edge detection based on combination of the isotropic diffusion model and total variation model. The success of the proposed approach lies in the image has single and strong edges.The achievements that we have achieved in this thesis are lie in the following points:●A new denoising technique for images corrupted with additive salt and pepper noise and white Gaussian noise is proposed. The technique used here is to combine the anisotropic diffusion (PM) model and total variation (TV) model. The new technique utilizes both advantages of PM model and TV model, while avoiding the disadvantages of both of them.●A novel denoising algorithm based on partial differential equations variational approach is proposed. After taking into consideration the attributes of the total variation (TV) model and isotropic diffusion (ID) model, we used the polynomial interpolation method to integrate the two models in order to get a new image denoising technique. The new model has high ability to adapt and change in each region in accordance with the image’s information. In other words, the new model deals with the flat areas with more diffusion, and the edges with less diffusion. Consequently we can eliminate the noise, and at the same time maintain the edges and the other necessary features in the image. Experimental results confirm the new approach is more efficient in image denoising than both isotropic diffusion and total variation models in terms of preserving edges information and texture features.●We proposed a new de-noising technique based on combination of isotropic diffusion model, anisotropic diffusion (PM) model, and total variation model. The proposed model is able to be adaptive in each region depending on the information of the image. More precisely, the model performs more diffusion in the flat areas of the image, and less diffusion in the edges of the image. And so we can get rid of the noise, and preserve the edges of the image simultaneously. To verify that, we did several experiments, which showed that our algorithm is the best method for edge preserving and noise removing, compared with the isotropic diffusion, anisotropic diffusion, and total variation methods.●The total variation anisotropic edge detection and isotropic edge detection are presented. The total variation and isotropic diffusion models can lead to discontinuous and double edges respectively. In order to overcome these drawbacks we propose a new technique. The technique used here is the combination of the total variation (TV) model with the isotropic diffusion model. The new model is compared with total variation model and isotropic diffusion model in terms of edge detection. The experimental results show that the image filtered by the use of our model has stronger edges. The proposed algorithm has the capability of detecting the edges successfully, as well as avoiding double, thick and discontinuous edges.●A novel model of image segmentation based on watershed method is proposed in this work. To prevent the oversegmentation of traditional watershed, our proposed algorithm has five stages. Firstly, the morphological reconstruction is applied to smooth the flat area and preserve the edge of the image. Secondly, multi-scale morphological gradient is used to avoid the thickening and merging of the edges. Thirdly, for contrast enhancement the top/bottom hat transformation is used. Fourthly, the morphological gradient of an image is modified by imposing regional minima at the location of both the internal and the external markers. Finally, a weighted function is used to combine the top/bottom hat transformation algorithm and the markers algorithm to get the new algorithm. The experimental results show the superiority of the new algorithm in terms of suppression oversegmentation.