  Surface reconstruction from magnetic resonance (MR) imaging data is
indispensable in medical image analysis and clinical research. A reliable and
effective reconstruction tool should: be fast in prediction of accurate well
localised and high resolution models, evaluate prediction uncertainty, work
with as little input data as possible. Current deep learning state of the art
(SOTA) 3D reconstruction methods, however, often only produce shapes of limited
variability positioned in a canonical position or lack uncertainty evaluation.
In this paper, we present a novel probabilistic deep learning approach for
concurrent 3D surface reconstruction from sparse 2D MR image data and aleatoric
uncertainty prediction. Our method is capable of reconstructing large surface
meshes from three quasi-orthogonal MR imaging slices from limited training sets
whilst modelling the location of each mesh vertex through a Gaussian
distribution. Prior shape information is encoded using a built-in linear
principal component analysis (PCA) model. Extensive experiments on cardiac MR
data show that our probabilistic approach successfully assesses prediction
uncertainty while at the same time qualitatively and quantitatively outperforms
SOTA methods in shape prediction. Compared to SOTA, we are capable of properly
localising and orientating the prediction via the use of a spatially aware
neural network.
