Medical image segmentation is often considered as the task of labelling each pixel or voxel as being inside or outside a given anatomy. Processing the images at their original size and resolution often result in insuperable memory requirements, but downsampling the images leads to a loss of important details. Instead of aiming to represent a smooth and continuous surface in a binary voxel-grid, we propose to learn a Neural Unsigned Distance Field (NUDF) directly from the image. The small memory requirements of NUDF allow for high resolution processing, while the continuous nature of the distance field allows us to create high resolution 3D mesh models of shapes of any topology (i.e. open surfaces). We evaluate our method on the task of left atrial appendage (LAA) segmentation from Computed Tomography (CT) images. The LAA is a complex and highly variable shape, being thus difficult to represent with traditional segmentation methods using discrete labelmaps. With our proposed method, we are able to predict 3D mesh models that capture the details of the LAA and achieve accuracy in the order of the voxel spacing in the CT images.