11.11 Summary

Despite the apparent complexity introduced when multichannel data are available, simple models provide a viable means of describing the information available from distributed targets. For a single frequency, physical reasoning and measurement support descriptions based on local Gaussian behavior modulated by a scalar texture, which can be interpreted as a number fluctuation effect. This interpretation cannot be pushed too far, because, for example, the differing penetration depths of H and V polarized waves into media that show preferred horizontal or vertical structures (e.g., cereals) indicate that not all scatterers receive the same incident wave. Nonetheless, distributions derived from this model appear consistent with observations, except in some cases at the longest wavelengths.

Because such simple models can be used, the information-bearing parameters in the data are readily identified. When the data are Gaussian, there is a well-developed estimation theory for these parameters. In principle, few difficulties arise in applying this theory. In practice, the complicated expressions for the sample coherence and phase difference distributions have at present prevented the development of a simple treatment for confidence intervals and moments, for example. For textured data, the estimation theory runs into the problems identified in Chapter 8, preventing analytic MLE solutions; only approximate solutions are currently available. The success of a simple tractable model for the data provides a sound basis for our investigations of filtering, classification, and segmentation in later chapters. However, it must be remarked that the empirical basis for this model is currently very incomplete. Comparatively few...