Introductory remarks

In considering image processing problems, it is commonly required that certain types of basic patterns be extracted from a noisy and/or complex scene. For digital image processing techniques considered in this book, one generally implies the processing of two-dimensional data that leads to applications in such a broad spectrum of problems as picture processing, medical data interpretation, underwater and earth sounding, trajectory detection, radargram enhancement, etc. If the noise conditions are favorable, involving high signal-to-noise ratios (SNR), and the corrupting noise is Gaussian with independent identically distributed (i.i.d.) samples (pixels), the classical techniques based on the matched filter theory are applicable. On the other hand, even a small deviation from the Gaussian assumption or the variability of SNR in various parts of the image will severely deteriorate the performance of the matched filter. In image formation by certain optical systems, such as infrared sensors and detectors, unfavorable noise conditions will prevail. As a matter of fact, the distribution function of the image pixels contaminated by noise is seldom known in imaging problems.

Another difficulty associated with processing of large two-dimensional images is that the SNR may vary significantly from region to region. In the latter situation the use of a simple thresholded matched filter will yield false alarm rates and probabilities of detection that will vary unpredictably over the scene.