Measuring Small - Scale Water Surface Waves : Nonlinear Interpolation & Integration Techniques for Slope - Image Data

(b) (c) (e) (d) (f) Figure 3. Results. (a) 128 × 128 Pixel Slope Image. (b) Reconstructed Topography. (c) Surface Plot. (d) 128 × 128 Pixel Slope Image. (e) Reconstructed Topography. (f) Surface Plot. Figure 2. Density Plot of Slope Data: Breaking Wave Case. This slope image is associated with the data shown in Figure 1. The plot measures 500 × 240 pixels, which corresponds to an area of 80 mm × 62 mm of water surface. Black areas depict signal dropouts (i.e., slopes corresponding to such areas have exceeded instrument measurement capability). This data is typical of slope imagery of breaking waves. Figure 1.Surface Plot of Slope Data. Note that bubbles have a distinctive signature and represent a physical discontinuity either below or at the water's surface. Note also that signal dropouts (flagged as pixels with slope-2.0 rad) have rounded corners associated with them. Many of the new enhancements involve the genetic algorithm portion of the hybrid. Genetic algorithms belong to the class of domain-independent algorithms (which includes neural nets) and represents one of the few probabilistic techniques that exploit com-binatorial search for optimization. In our case, a genetic algorithm optimizes for a set of Fourier coefficients along a row (or column) vector from a slope image that describes a curve that contains those portions of the vector data that are unaffected by either bubbles or drop-outs. The search space is substantial, but can be highly constrained. For constraining, we have used bootstrapping and an index-mediated hybridization scheme that is described in [2]. We have implemented our system prototype on a parallel machine (i.e., an IBM SP-2). 3. RESULTS AND CONCLUSION The data set featured in this paper is from a custom built, single-gradient direction Jähne-type instrument [4]. Measured were small-scale waves in the context of a steady spilling breaking wave, which were generated in a specialized wave tank facility at U-M. (This facility features a recirculating flow with an extremely low turbulence level across a wide cross section, so that breaking waves can be observed fairly undisturbed from the flow.) Over three gigabytes of data have been collected that represent various breaking and non-breaking conditions. Figure 3 shows examples of our method for nonlinear interpolation and integration along the gradient direction imaged by the instrument. The results were obtained with our parallel system prototype on an IBM SP-2 and used four processing nodes. The results indicate that the …