Two-stage robust surface detection algorithm for continuous casting mold water models using smooth surface-wave priors

We propose a two-stage method that enables the accurate detection of water-surfaces from low-contrast images, aiming to quantify the water-surface dynamics in the water model of a continuous casting mold used in the steel manufacturing industry. In the first stage, the initial water-surface positions are estimated using Canny edge detection combined with dynamic programming. In the second stage, the surface estimation is refined by removing outliers through mathematical programming, which includes an -loss function and a regularization term based on the sum of squared first/second-order differences. By explicitly considering the prior physical information of the smooth temporal and spatial variations of the water-surface, the method is robust against outliers and accurately detects water-surfaces even in cases where conventional approaches previously misidentified the surface. The proposed two-stage method—formulated with especially second-order difference regularization-is analyzed theoretically and validated through experiments conducted on an industrial-scale water model. It achieves near-real-time throughput and meets the practical accuracy requirement of mm, making it suitable for industrial deployment.