Convergences de structures linéaires dans les images : modélisation stochastique et applications en imagerie médicale

Abstract : This thesis deals with the detection of points of convergences in images, in an a contrario framework. This is a preliminar work which studies various alterations of the a contrario framework such as the naive model. An application in the medical field is the detection of stellate lesions in mammograms, which are highly suspicious signs of breast cancer and are characterized by a radiating pattern of spicules with a bright center. There are plenty of work regarding stellate lesions and architectural distortions. Most of them are based on the extraction of local features such as the gradient orientation, or the pixel orientation and more generally statistics of the orientation histogram. These features are then used in a classifier to assign to each pixel its probability of malignancy. The a contrario methods sets a different framework for the detection of geometric structures in images. A naïve model on line structures is defined and is often chosen as the uniform model, which is not well suited for mammograms where there is a privileged orientation of spicules. We propose in this thesis an anisotropic a contrario framework for a better description of the normal distribution of spicules in a mammogram. The designed models describe the convergence of some of the line structures to a single point. They either concern the lines or the line segments of an image wether we detect global or local convergences. In the last case we explore several definitions of the number of false alarms and several a contrario models on synthetic, natural images and mammograms. We give the a contrario models as two terms mixtures, one uniform and the other of Gaussian type. These are parametric models and we propose an algorithm to estimate their parameters (the point of convergence is estimated with an a contrario method and the other parameters are approached by maximization of the likelihood). The resulting models are used as a contrario models and the results are compared with those against the uniform model.
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Fanny Doré. Convergences de structures linéaires dans les images : modélisation stochastique et applications en imagerie médicale. Mathématiques générales [math.GM]. Université René Descartes - Paris V, 2014. Français. ⟨NNT : 2014PA05S007⟩. ⟨tel-01062135⟩

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