Abstract
The objective of the work is to model the shape of the sinusoidal shape of regular water waves generated in a laboratory flume. The waves are traveling in time and render a smooth surface, with no white caps or foam. Two methods are proposed, treating the water as a diffuse and specular surface, respectively. In either case, the water is presumed to take the shape of a traveling sine wave, reducing the task of the 3D reconstruction to resolve the wave parameters. The first conceived method performs the modeling part purely in 3D space. Having triangulated the points in a separate phase via bundle adjustment, a sine wave is fitted into the data in a least squares manner. The second method presents a more complete approach for the entire calculation workflow beginning in the image space. The water is perceived as a specular surface, and the traveling specularities are the only observations visible to the cameras, observations that are notably single image. The depth ambiguity is removed given additional constraints encoded within the law of reflection and the modeled parametric surface. The observation and constraint equations compose a single system of equations that is solved with the method of least squares adjustment. The devised approaches are validated against the data coming from a capacitive level sensor and on physical targets floating on the surface. The outcomes agree to a high degree.
Highlights
Attempts to characterize the water surface with optical methods date back to the beginning of the 20th century [1,2]
The capacitive level sensor was mounted on a rod-like probe and sensed the variations in electrical capacity within the sensor
Given the dielectric constant of the liquid, this information can be directly transformed to the changes in the water level, in which the probe is normally immersed
Summary
Attempts to characterize the water surface with optical methods date back to the beginning of the 20th century [1,2]. The interest in a quantitative description of the surface with light came from the field of oceanography and the use of photography to map the coastlines. This prompted further applications, namely the use of photography to quantify ocean waves and to exploit these parameters in, e.g., shipbuilding, to engineer structures of the appropriate strength [3,4,5]. The same drivers disseminated optical methods among other applications, in river engineering and the oceanographic domain. The knowledge of the dispersive processes gives an insight into the way pollution and sediments are transported [6,7,8,9]
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