An Introduction to Remotely Sensed Data Analysis - Sampling Spatial Units for Agricultural Surveys - page 75

For a discussion on the nature of errors and their propagation see Haining and
Arbia ( 1993 ). Equation ( 4.7 ) can be simplified to the linear form (Geman and
Geman 1984 ; Ripley 1988 )

Y ¼ HX þ ε: ð 4 : 8 Þ

We can consider the following multiplicative model as an alternative to the additive
model in Eq. ( 4.8 ) (Geman and Geman 1984 )

Y ¼ HX ε: ð 4 : 9 Þ

In essence, the statistical approach to image restoration estimates the true scene
from the RS image. One of the most common methods for this is the maximum a
posteriori (MAP) technique (Ripley 1988 ). Using Bayes theorem we have

'

Pr X ð = Y Þ p Y ð = X Þ Pr X ðÞ; ð 4 : 10 Þ

where Pr(X) is the a priori probability of the true scene, and p (Y/X) is the
likelihood. The MAP estimate is the solution that maximizes the a posteriori
probability Pr(X/Y), and is an example of an empirical Bayesian technique. This
method largely depends on the choice of the distributional form of the a priori
probability Pr(X). The most common choices for Pr(X) are the spatial Markovian
model or Gibbs stochastic processes (Besag 1986 ; Ripley 1988 ).

4.4 Image Enhancement

The main aim of enhancement is to improve the interpretability of images for
human analysts, or to provide a better input for other automated image processing
techniques. To help the image interpretation, the visual appearance of the scene can
be improved using image enhancement techniques in the frequency domain (for
example, gray level stretching to increase the contrast), and filtering in the spatial
domain to enhance the edges.
Contrast stretching is typically the first enhancement method applied to an
image. Consider an image where each pixel is examined and its brightness value
noted. Then, we can construct a graph of the number of pixels with a given
brightness versus the brightness value. This graph is known as the histogram of
the image. Only one histogram can be defined for an image, but the same histogram
may represent many images. In fact, a histogram includes only radiometric and not
spatial information. Most digital images have 256 color levels, which results in a
good contrast. Conversely, some digital images have poor contrast. For example,
consider an image that has an original histogram with values between 30 and 90. In
this case, the analyst might wish to expand the range to the maximum possible to
improve the contrast and make interpretation easier. This method involves