Medical procedures have become a critical application area that makes substantial use of image processing. Medical image processing tasks mainly deal with image restoration, image segmentation that bring out medical image details, measure quantitatively medical conditions etc. The diagnosis of a health problem is now highly dependent on the quality and the credibility of the image analysis. The practical contributions of this thesis can be considered in many directions for medical domain. This manuscript addresses a 3D image analysis with variational methods and wavelet transform in the context of medical image processing. We first survey the second-order variational minimization model, which was proved that better than the classical Rudin-Osher-Fatemi model. This method is considered in problems associated to image denoising, image segmentation, that makes a short state of the art on medical imaging processing techniques. Then we introduce the concept of wavelet transform and present some algorithms that also used in this domain. Experimental results show that these tools are very useful and competitive. The core of this research is the development of new 3D representations, which are well adapted to representing complicated medical data, and filament structures in 3D volumes: the cerebellum and mice vessels network. Each of these two based methods has advantages and disadvantages, we then propose a new modified model that combines these schemes in the rest of the thesis. In this situation we propose a new modified model that combines these schemes. With the new decomposition model, in the reconstructed image, noise can be removed successfully and contours, textures are well preserved. This leads to further improvements in denoising performance. Finally, the further part of the thesis is devoted to the description of contribution to extend some classical contour closing methods, namely hysteresis thresholding and contour closing based on chamfer distance transform, in the 3D context. The thesis concludes with a review of our main results and with a discussion of a few of many open problems and promising directions for further research and application.
