Special Lagrangian cones with higher genus links

For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C^3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.Comment: 48 page

White Matter Lesion Segmentation from Volumetric MR Images

Abstract. White matter lesions are common pathological findings in MR tomograms of elderly subjects. These lesions are typically caused by small vessel diseases (e.g., due to hypertension, diabetes). In this paper, we introduce an automatic algorithm for segmentation of white matter lesions from volumetric MR images. In the literature, there are methods based on multi-channel MR images, which obtain good results. But they assume that the different channel images have same resolution, which is often not available. Although our method is also based on T1 and T2 weighted MR images, we do not assume that they have the same resolution (Generally, the T2 volume has much less slices than the T1 volume). Our method can be summarized as the following three steps: 1) Register the T1 image volume and the T2 image volume to find the T1 slices corresponding to those in the T2 volume; 2) Based on the T1 and T2 image slices, lesions in these slices are segmented; 3) Use deformable models to segment lesion boundaries in those T1 slices, which do not have corresponding T2 slices. Experimental results demonstrate that our algorithm performs well.