Appendix E - Filtering in the Image Space Domain

The digital pictures were filtered using a convolution algorithm. Mathematically, a quantized image is treated as a function f (x, y). It is filtered by convolving it with a n x n matrix filter function, h(w, v). w and v are usually some small odd number: 3,5,7.. .For every pixel in f , a multiply, shift and sum operation is conducted over the range of

l = y + v
k = x + w .

and the result stored at x,y For all x,y then, the filtered image g, is given by:

.

A filter designed to sharpen an image is the simple 3x3 shown below:

.

Unfortunately, filtering real images is seldom met with practical success with such simple schemes. The problem is that the source of the image degradations ( the blur functions) are the concatenation of camera motion, optical smearing, atmospherics, etc, and are seldom known. In theory, if one knew the blur function, one could design a filter that would remove most of the degradations. In practice, most filtering operations result in merely aesthetic improvements and no real recovery of information. The achievement of significant information recovery often entails filters, tailor made for each image being analyzed. In the course of achieving practical results, most gains in getting improvements in an image are achieved through more mundane gray shade manipulations, such as the suite of functions provided by Adobe Photoshop for contrast manipulations. Beyond this, improvements are small and tedious. The gains are usually in making subtleties noticeable. In other words, the features may seem to be suddenly "pop up" after a filtering operation. But invariably if one compares the processed image to the original, the same feature can be seen, but was overlooked due to poor contrast or smeared edges.