Unsupervised segmentation of micro-CT scans of polyurethane structures by combining hidden markov random fields and a U-Net

Extracting a digital representation of a material from images is a prerequisite for any quantitative structure-property analysis. Supervised convolutional neural networks (CNNs) now deliver state-of-the-art segmentation accuracy, but their performance depends on large, manually annotated training sets—an impractical requirement for most bulk micro-computed-tomography ( μ CT) studies. Classical unsupervised techniques such as Hidden-Markov Random Fields (HMRF) avoid the need for ground-truth labels, yet they are typically slow and yield lower-quality segmentations. Here, we introduce HMRF-UNet, a hybrid framework that embeds the probabilistic neighborhood model of HMRF directly into the U-Net’s loss function. The loss simultaneously (i) enforces spatial smoothness through higher-order neighborhood terms, (ii) respects class-wise intensity distributions, and (iii) benefits from data-driven feature learning. By combining HMRF’s label-free regularization with the fast inference of CNNs, the method delivers unsupervised segmentation at a speed comparable to that of supervised networks. We evaluate the approach on a μ CT dataset of polyurethane (PU) foam. An ablation study quantifies the contribution of each neighborhood term, and the HMRF-UNet attains a Dice similarity coefficient of 0.957 ± 0.017 , while processing a 256 × 256 slice in 200 ms on a single GPU; performance that rivals supervised baselines. To further diminish the reliance on annotated data, we propose a two-stage pre-training strategy: the network is first optimized with the HMRF loss on unlabeled data and subsequently fine-tuned on a minimal labeled subset. This approach recovers 98.4% of the fully supervised performance while using only 1% of ground-truth annotations. The proposed framework provides accurate, high-throughput segmentation without extensive manual labeling, enabling rapid, data-driven characterization of complex porous architectures across a broad range of material systems.