A Geometrically-Constrained Deep Network For Ct Image Segmentation

• Main Authors: Lambert, Zoe, Guyader, Carole Le, Petitjean, Caroline
• Format: Conference Proceeding
• Language: English
• Subjects: ADMM algorithm; Computed tomography; CT scans; deep learning; Douglas-Rachford algorithm; Image segmentation; Mathematical model; Measurement; Minimization; Planning; proximal operator; Training
• ISSN: 1945-8452
• DOI: 10.1109/ISBI48211.2021.9434088

Incorporating prior knowledge into a segmentation process, whether it be geometrical constraints such as volume penalisation, (partial) convexity enforcement, or topological prescriptions to preserve the contextual relations between objects, proves to improve accuracy in medical image segmentation, in particular when addressing the issue of weak boundary definition. Motivated by this observation, the proposed contribution aims to include geometrical constraints in the training of convolutional neural networks in the form of a penalty in the loss function. These geometrical constraints take several forms and encompass level curve alignment through the weighted total variation component, an area penalisation phrased as a hard constraint in the modelling, and an intensity homogeneity criterion based on a combination of the standard Dice loss with the piecewise constant Mumford-Shah model. The mathematical formulation yields a non-smooth non-convex optimisation problem, which rules out conventional smooth optimisation techniques and leads us to adopt a Lagrangian setting. The application falls within the scope of organ-at-risk segmentation in CT (Computed Tomography) images, in the context of radiotherapy planning. Experiments demonstrate that our method provides significant improvements over existing non-constrained approaches.