Carlos Platero

Javier Sanguino, Carlos Platero, Olga Velasco

This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, we propose a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. We also prove that our filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edge-preserving process. Under the conditions established for the diffusivity and using a stopping criterion for the diffusion time, we get piecewise constant images with a low computational effort. Finally, we test our filter with real images and we illustrate the effects of our diffusivity function as a method to get piecewise constant images. The code is available at https://github.com/cplatero/NonlinearDiffusion.

Carlos Platero, M. Carmen Tobar

The objective of this study is to develop a patch-based labeling method that cooperates with a label fusion using non-rigid registrations. We present a novel patch-based label fusion method, whose selected patches and their weights are calculated from a combination of similarity measures between patches using intensity-based distances and labeling-based distances, where a previous labeling of the target image is inferred through a label fusion method using non-rigid registrations. These combined similarity measures result in better selection of the patches, and their weights are more robust, which improves the segmentation results compared to other label fusion methods, including the conventional patch-based labeling method. To evaluate the performance and the robustness of the proposed label fusion method, we employ two available databases of T1-weighted (T1W) magnetic resonance imaging (MRI) of human brains. We compare our approach with other label fusion methods in the automatic hippocampal segmentation from T1W-MRI. Our label fusion method yields mean Dice coefficients of 0.847 and 0.798 for the two databases used with mean times of approximately 180 and 320 seconds, respectively. The collaboration between the patch-based labeling method and the label fusion using non-rigid registrations is given in the several levels: (a) The pre-selection of the patches in the atlases are improved, (b) The weights of our selected patches are also more robust, (c) our approach imposes geometrical restrictions, such as shape priors, and (d) the work-flow is very efficient. We show that the proposed approach is very competitive with respect to recently reported methods.