Fusion et recalage d'images médicales multimodales. Application à la chirurgie de l'endométriose

Endometriosis is a chronic gynecological disease affecting women of childbearing age which is characterized by the development of tissue similar to the uterine lining (the endometrium) outside the uterus, colonizing other nearby organs such as the ovaries, the fallopian tubes or, in rarer cases, the colon. This tissue is influenced by hormonal changes during subsequent menstrual cycles, leading to abdominal and pelvic pain, chronic fatigue and an increased risk of infertility. The diagnosis of endometriosis is based on two medical imaging modalities, namely ultrasound (US) and magnetic resonance imaging (MRI). Depending on the stage of the disease, laparoscopic surgery proves to be the only effective treatment for endometriosis.Besides their use for diagnosis, US and MRI images are used to identify the precise location of lesions and their depth of infiltration before surgery. The US image, performed intravaginally for this application, is a high spatial resolution modality that provides fine internal details of the imaged structures. This modality has some limitations, including a limited field of view and a low signal-to-noise ratio. On the other hand, MRI offers a large field of view of the patient's anatomy with a good signal-to-noise ratio but with relatively low spatial resolution. Therefore, precise anatomical landmarks at the millimeter scale would be undervalued when using this modality alone. In this context, producing an image bringing together the advantages of both modalities (good contrast and good signal-to-noise ratio) would be of great interest. In practical applications, US and MRI examinations are performed separately, resulting in unaligned 2D US images and 3D MRI volumes.The first aim of this PhD thesis is to propose a slice-to-volume registration algorithm of 3D MRI and 2D US images. The goal of this registration would be to extract the MRI slice that best resembles the US image, maximizing an adapted similarity criterion. The registration takes into account a global rigid transformation characterized by rotation and translation parameters which is associated with a local deformation based on B-spline functions. The latter will allow more precise matching between images, making it possible to exploit local geometric deformations within the image.Secondly, a 2D/2D fusion model is proposed for MRI and US images. The method is problem-based inverse, achieving super-resolution of the MRI image and denoising of the US image. The relationship between the gray levels of the two images has been modeled in the literature by a polynomial function. We study the potential interest of replacing this polynomial function by a non-parametric transformation constructed from the theory of Hilbert spaces with reproducing kernels. The fused image obtained with this method combines the advantages of both modalities, and presents a sharper contrast than when using a polynomial. Another significant advantage in favor of the kernel-based transformation is that it is not directly related to the propagation direction of the US scan, which is not easy to obtain in practical applications. The drawback of the proposed approach is its complexity. The model may require the estimation of a few hundred thousand parameters depending on the size of the image and the patches chosen.We propose a second fusion model based on guided filtering, which consists of separating images into base and detail layers, calculating specific weights, and then fusing them. The fused image is obtained by weighting the Base and Detail images of the MRI and the US. The weights assigned to the US image take into account the presence of speckle noise, while the weights assigned to the MRI make it possible to improve the contrast of the fused image.The interest of the proposed models is analyzed by means of quantitative and qualitative tests carried out on several datasets, including synthetic images, images of an experimental phantom and real data.