Multiplicative Loss for Enhancing Semantic Segmentation in Medical and Cellular Images

TL;DR

The paper tackles loss-function design for semantic segmentation under data scarcity by introducing Multiplicative Loss (ML), which multiplies Dice and Cross Entropy losses to stabilize optimization, and Confidence-Adaptive Multiplicative Loss (CAML), which applies a confidence-driven exponent to emphasize hard samples. ML and CAML show consistent improvements over tuned additive losses across medical and cellular segmentation benchmarks and architectures, with CAML particularly advantageous in extreme data-scarcity scenarios. The methods avoid manual hyperparameter tuning and promote robust convergence, though they exhibit reduced gains on some Transformer-based models, suggesting architecture-aware calibration. Overall, the work offers simple, effective loss designs that enhance generalization in data-limited medical imaging tasks and related cellular imaging problems.

Abstract

We propose two novel loss functions, Multiplicative Loss and Confidence-Adaptive Multiplicative Loss, for semantic segmentation in medical and cellular images. Although Cross Entropy and Dice Loss are widely used, their additive combination is sensitive to hyperparameters and often performs suboptimally, especially with limited data. Medical images suffer from data scarcity due to privacy, ethics, and costly annotations, requiring robust and efficient training objectives. Our Multiplicative Loss combines Cross Entropy and Dice losses multiplicatively, dynamically modulating gradients based on prediction confidence. This reduces penalties for confident correct predictions and amplifies gradients for incorrect overconfident ones, stabilizing optimization. Building on this, Confidence-Adaptive Multiplicative Loss applies a confidence-driven exponential scaling inspired by Focal Loss, integrating predicted probabilities and Dice coefficients to emphasize difficult samples. This enhances learning under extreme data scarcity by strengthening gradients when confidence is low. Experiments on cellular and medical segmentation benchmarks show our framework consistently outperforms tuned additive and existing loss functions, offering a simple, effective, and hyperparameter-free mechanism for robust segmentation under challenging data limitations.

Figures (5)

• Figure 1: Visualization of loss values and gradient magnitudes with respect to predicted probability $p$. The proposed Multiplicative Loss amplifies gradients for uncertain predictions and suppresses gradients for confident predictions, thus promoting stable and efficient optimization.
• Figure 2: Comparison of gradient magnitudes between CAML and ML with respect to the predicted probability $p$. CAML adaptively adjusts gradient strength based on instance-level confidence, emphasizing hard samples while suppressing excessive updates for high-confidence predictions.
• Figure 3: Qualitative comparison between our ML and a dataset-tuned additive loss function. Both methods used U-Net. The results are shown on three datasets: COVID-19 (row 1), CHASE (row 2), and Drosophila (row 3). Yellow boxes highlight regions where ML improved the missed or misclassified areas by additive loss.
• Figure 4: Qualitative comparison between the proposed CAML and a dataset-tuned additive loss function. Both methods used U-Net under a low-data regime (1/8 training samples). The results are shown on COVID-19 (row 1), CHASE (row 2), and Drosophila (row 3). Yellow boxes highlight regions where CAML outperforms the baseline in under- and over-segmented areas.
• Figure 5: Comparison of gradient magnitudes between CAML and ML with respect to the predicted probability $p$. CAML adaptively adjusts gradient magnitudes based on instance-level confidence, giving higher gradient updates to hard samples while suppressing excessive updates for high-confidence predictions.