The binary segmentation of whiteboard strokes is hindered by extreme class imbalance, caused by stroke pixels that constitute only $1.79%$ of the image on average, and in addition, the thin-stroke subset averages $1.14% \pm 0.41%$ in the foreground. Standard region metrics (F1, IoU) can mask thin-stroke failures because the vast majority of the background dominates the score. In contrast, adding boundary-aware metrics and a thin-subset equity analysis changes how loss functions rank and exposes hidden trade-offs. We contribute an evaluation protocol that jointly examines region metrics, boundary metrics (BF1, B-IoU), a core/thin-subset equity analysis, and per-image robustness statistics (median, IQR, worst-case) under seeded, multi-run training with non-parametric significance testing. Five losses -- cross-entropy, focal, Dice, Dice+focal, and Tversky -- are trained three times each on a DeepLabV3-MobileNetV3 model and evaluated on 12 held-out images split into core and thin subsets. Overlap-based losses improve F1 by more than 20 points over cross-entropy ($0.663$ vs $0.438$, $p < 0.001$). In addition, the boundary metrics confirm that the gain extends to the precision of the contour. Adaptive thresholding and Sauvola binarization at native resolution achieve a higher mean F1 ($0.787$ for Sauvola) but with substantially worse worst-case performance (F1 $= 0.452$ vs $0.565$ for Tversky), exposing a consistency-accuracy trade-off: classical baselines lead on mean F1 while the learned model delivers higher worst-case reliability. Doubling training resolution further increases F1 by 12.7 points.