Identification of the Free Surface for Unidirectional Nonbreaking Water Waves From Side-View Digital Images

Abstract

We present a semi-automated image processing method, the continuous maximum gradient (CMG) method, for identifying the air–water interface in side-view digital images of unidirectional water waves in a glass-walled laboratory wave flume. In a manner similar to Canny edge detection, CMG exploits gradients in pixel intensity to identify the free surface, but also enforces an additional streamline constraint. This latter step is necessary to exclude signals from other features, such as wave gauges and water droplets on the glass, which also exhibit large intensity gradients. To demonstrate the performance and accuracy of CMG, we first compare its detection results with independent wave gauge measurements. The maximum difference in total spectral variance was found to be approximately 4%, while quantitative error metrics from a regression analysis yielded an $R^{2}$ value of 0.997 for the surface elevation time-series. We also compare the CMG detection results with imagery data from existing literature where excellent visual agreement is observed, confirming the broad applicability of the CMG method. The employment of CMG facilitates free surface measurements at a very high resolution (order of millimeters) which is essential for capturing the spatio-temporal wave-field evolution and obtaining instantaneous measurement of local wave shape.