Image-Based Quantification of Boundary Uncertainty for Reliable Soymilk Solid Content Measurement

Soymilk solid content (%) is a critical quality indicator that is directly related to product classification and regulatory compliance in food manufacturing. However, conventional optical refractometer-based measurements often suffer from blurred scale boundaries and subjective reading errors, leading to poor reproducibility under varying illumination conditions. This study proposes an image-based signal analysis framework that quantitatively interprets blurred liquid-scale boundaries by analyzing pixel intensity profiles, their gradients, and effective boundary widths. Instead of relying on human visual judgment, the proposed method characterizes boundary uncertainty using Gaussian-smoothed intensity signals and derivative-based feature extraction. Quantitative validation against ground-truth concentration values over 150 images demonstrates an overall mean absolute error (MAE) of 1.90 and a root mean squared error (RMSE) of 3.85. Illumination conditions yielding stable, single-peak derivative responses achieve an overall MAE of 0.23, whereas severe illumination conditions associated with unstable or distorted derivative patterns result in substantially higher errors (MAE = 8.57, RMSE = 8.60). These results quantitatively confirm that derivative-based boundary signal stability is directly linked to measurement accuracy. By transforming visual ambiguity into quantifiable signal features, this work provides a practical and reproducible alternative to subjective refractometer readings and offers a foundation for reliability-aware optical concentration measurement systems in industrial environments.