The segmentation of the liver, lesions, and vessels from pre-operative CT scans is of major importance in hepatic surgery planning. However, large databases with reference segmentations for these regions of interest remain unavailable, a challenge often encountered in medical image segmentation. In this work, we propose the FuSe loss, a novel loss function for multi-task learning on datasets with partial annotations. By employing the nnU-Net’s 3D self-configuring pipeline to calibrate and train a deep network for the joint segmentation of the liver, lesions, and vessels, we show how the FuSe loss allows to learn from the differently annotated IRCAD and LiTS datasets, improving the overall baseline segmentation performance. With the FuSe loss, the dice scores reached up to 95.9%, 70.6% and 60.0% for the liver, lesions, and vessels respectively.

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a manifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances, and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing.