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 (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.

When computers are tasked with identifying and separating objects within images, we need standardized metrics to evaluate their accuracy. Currently, the most widely used evaluation methods primarily count the number of correct pixels. However, this pixel-counting approach often ignores the overall physical structure of the object. As a result, a computer model might receive a high performance score even if it incorrectly fragments a single solid object into disconnected parts, or if it completely misses very small targets and incorrectly identifies background noise. To address this limitation, we introduce a new evaluation method called the Topology-aware measure (T-m). Instead of solely relying on pixel statistics, our method explicitly calculates whether the computer's prediction maintains the correct structural completeness and accurate boundary lines of the original object. We rigorously tested our proposed metric across various complex image scenarios. The experimental results demonstrate that our new evaluation method provides a much more reliable assessment of model performance, and its scoring aligns highly with how human vision naturally judges image quality.