The basis for much of this text is the premise that the physical imaging process can be modeled by a mathematical representation. The models are defined by parameters, whose values must be determined in order for the model to be accurate. In this chapter, we will discuss methods for estimating many of the parameters that define an imaging system. Note that this is different from modeling the image itself, as in Section 7.4. Appendix Con stochastic images also addresses that problem. We will begin by considering a hierarchy of models, and then we will discuss the estimation of the various functions and parameters that define each model.

Image formation models

Image formation models can be written with varying degrees of accuracy and complexity. For this chapter, we will use the simplest hierarchy of models that is needed to illustrate the methods of parameter estimation. We will note the assumptions and simplifications in the following descriptions. The models presented below will be for monochrome images. The extension to multispectral and hyperspectral images requires an additional step of applying stacked notation on the wavelength bands in addition to the stacked notation on the columns in the spatial domain. The algebraic equations remain unchanged. For most parameter estimation work, dealing with a single image band is sufficient.