T-measure: A Topology-Consistent Metric for Binary Segmentation

Evaluation metrics establish a standard assessment framework for models, playing a pivotal role in model optimization and advancement. However, widely adopted pixel-wise metrics (e.g., IoU, Dice) rely heavily on pixel-level statistics, often failing to capture the structural integrity of predictions. While the S-measure ($S_m$) incorporates structural perception to some extent, it struggles to differentiate critical structural violations and remains insensitive to background false positives and small objects. To address these limitations, we propose the Topology-aware measure ($T_m$), a novel metric designed to explicitly quantify topological consistency. $T_m$ employs the Fuzzy Jaccard Index as a foundational score, integrates a Topological Integrity term ($I_{topo}$) to penalize critical structural fragmentation, and utilizes a Boundary Alignment term ($\mathcal{A}_{bdy}$) to evaluate boundary alignment. These three components synergize to achieve robust evaluation of prediction maps at the topological level. We establish a rigorous Meta-Measure validation framework and benchmark our method against nine mainstream metrics across diverse complex scenarios. Extensive experiments demonstrate that $T_m$ performs exceptionally in downstream tasks and maintains high consistency with human visual perception.