Segmenting individual trophectoderm (TE) cells is essential for developing quantitative metrics to assess the developmental potential of human blastocysts. The elongated shape and circular arrangement of TE cells lead to continuously varying orientations across the image, posing challenges for existing cell instance segmentation methods that assume uniformly oriented cells. As a result, most methods segment the TE as a single region, and the development of quantitative, cell-level metrics predictive of live birth potential remains unexplored. In this work, we propose an instance segmentation model that represents elongate, circularly arranged TE cells using elliptical distance maps, with which superior performance in both segmentation accuracy and metric extraction was achieved, compared with state-of-the-art methods. The extracted metrics, including TE cell number, the mean and standard deviation of cell length, width, area, and mean inter-cell distance, serve as effective predictors of a blastocyst’s live birth potential. When used to predict live birth, these metrics achieved a significantly higher area under the receiver operating characteristic curve (AUC = 0.693) than traditional TE morphological grades (AUC = 0.585). The source code is publicly available at https://github.com/robotVisionHang/TESeg.

Quantitative analysis of cleavage-stage embryos is a critical step for embryo evaluation in in vitro fertilization (IVF) treatment. Deep learning-based instance segmentation methods have emerged as a promising solution. However, existing methods, typically designed for opaque instances in nature scenes, face challenges when applied to segmenting overlapping cells in cleavage-stage embryos. The semi-transparency of the cells in cleavage-stage embryos leads to vague boundaries and complex overlaps between cells, making it difficult for existing models to segment these cells without merging or missing cells. In this work, we propose a novel instance segmentation network for segmenting overlapping, semi-transparent cleavage-stage embryo cells. Specifically, the network introduces two specialized branches that learn complementary representations: an overlap branch for addressing inter-instance overlaps and a boundary branch for dealing with intra-instance shapes. Then, an attention-based feature fusion module is designed to integrate learned overlap and boundary features to enhance the instance representation for the segmentation branch. Finally, an overlap-aware post-processing module leverages the outputs from the overlap and boundary branches to adaptively adjust suppression thresholds, ensuring the preservation of distinct yet highly overlapping cells. Experiments on two cleavage-stage embryo datasets demonstrate that our method outperformed state-of-the-art methods in both segmentation accuracy and recall, highlighting its potential for quantitative embryo evaluation in clinical IVF.

Deep Equilibrium Model (DEQ), which serves as a typical implicit neural network, emphasizes their memory efficiency and competitive performance compared to explicit neural networks. However, there has been relatively limited theoretical analysis on the representation of DEQ. In this paper, we utilize the Neural Collapse ($\mathcal{NC}$) as a tool to systematically analyze the representation of DEQ under both balanced and imbalanced conditions. $\mathcal{NC}$ is an interesting phenomenon in the neural network training process that characterizes the geometry of class features and classifier weights. While extensively studied in traditional explicit neural networks, the $\mathcal{NC}$ phenomenon has not received substantial attention in the context of implicit neural networks. We theoretically show that $\mathcal{NC}$ exists in DEQ under balanced conditions. Moreover, in imbalanced settings, despite the presence of minority collapse, DEQ demonstrated advantages over explicit neural networks. These advantages include the convergence of extracted features to the vertices of a simplex equiangular tight frame and self-duality properties under mild conditions, highlighting DEQ's superiority in handling imbalanced datasets. Finally, we validate our theoretical analyses through experiments in both balanced and imbalanced scenarios.