UPThèses

English

Cooperation of the wavelet transform and the partial differential equations methods for multispectral image processing

In this work, the Wavelet Transform (WT) and Partial Differential Equations (PDE)-based methods are merged together towards an efficient color and multispectral image processing paradigm that integrates denoising, segmentation, inpainting and video mosaicing. The proposed denoising models make use of multiscale multistructure tensors that are based on wavelet and bandelet transforms. These structure tensors allow for accumulating multiscale gradient information of local regions. Thus, averaging properties are maintained while preserving edge structure. These structure tensors are used in anisotropic diffusion processes of multispectral images. Therefore, a more efficient and accurate formulation for edge-preserving diffusion is obtained. In the segmentation domain, the wavelet-based structure tensor is used to detect the edges that are then modeled by level set functions. A functional is defined on these level sets whose minimizers define the optimal classification of objects. In a second step, foveal wavelets are used to guide the curve flow in an active contour segmentation process. The proposed approach is capable of driving the snake curve to the real edges of different regions in a noisy image. In the inpainting domain, we propose a two-steps image inpainting algorithm that relies on geometrical grouplets. The grouplets are used to represent the complex geometry of the image. Then, missing data are synthesized by propagating the geometrical information from outside to the inside of the inpainting zone. In the video processing domain we propose two models for mosaicing and inpainting that are based on the bandelet transform. In these models, the geometrical flow of each frame in the video sequence is determined by using the Bandelet transform. Then, mosaicing and inpainting are performed by searching for pairs of dyadic squares in the successive frames quadtrees that are valid neighbors. This is accomplished by the minimization of a cost measure that studies the geometrical similarity of each pair of squares. Then, bivariate orthogonal polynomials are used to define a 2D non-separable wavelet decomposition and a multi-resolution analysis. Finally, the 2D non-separable wavelet functions are used to define a multiscale edge detector

Keywords : wavelet transform, bandelet transform, denoising, segmentation, inpainting, mosaicing, orthogonal polynomials., signal and image processing.