Multi-fractal analysis of SAR ocean wave imagery

The exact relationship between fractal dimension and landscape patterns or development is not fully understood. The multi-fractal dimensionality of an ocean wave data set was investigated in an attempt to determine its relationship with fractal dimension. Airborne CV-580 SAR imagery from the Canada Centre for Remote Sensing (C.C.R.S) of an area of ocean over the Grand Banks, Newfoundland, has provided for this research. No radiometric or geometric corrections were applied to the data. Peleg's blanket method was used to calculate the fractal dimension of both the SAR imagery and a data set simulated to respond like ocean waves. The fractal dimension of actual waves was analyzed visually, graphically, and statistically by comparison to simulated wave data. Regression of SAR imagery digital values and fractal dimension imagery digital values indicated that a significant relationship existed between the variates. The results of the regression imply that a relationship exists between Bragg resonant scattering and fractal dimension, although most of the variance between the variates can be explained by speckle. Regressions indicate that relationships between the mean fractal dimension and geophysical parameters, such as significant wave height, mean zero-crossing period and wind speed, were less significant than the relationships with the change in mean fractal dimension. Correlations of change in mean fractal dimension with wave height and wave period appear to be in agreement with SAR ocean wave imaging models which use the variation in speckle intensity as a means of measuring ocean waves. Variation in mean fractal dimension with respect to scale change was attributed to artifacts of sampling. This research found that the fractal dimension is correlated with image texture in SAR ocean wave imagery and is fairly constant with mean values in a range of 2.08 to 2.20. A significant and strong correlation coefficient was found between variance of SAR digital values within the sample window used to calculate the fractal dimension and the fractal dimension. This result indicated that the fractal dimension is a measure of image texture.