TABLE OF CONTENTS Section 4.5.2 focused on using the median filter to enhance images corrupted by shot noise. It was shown that low-pass filters do not perform as well as median filters in removing impulse noise, because the spatial smoothing mixes any image-independent noisy outliers with the signal content. The median filter, on the other hand, was found to be well-suited for removing such signal-independent statistical outliers, while at the same time preserving the edges of the image. But what if the noise is not completely independent of the signal content, for example additive or multiplicative noise corrupting an image such that the noisy pixels are a mixture of original pixel intensities and noise levels? Might it be possible to construct an intelligent filter that somehow adapts itself to this behavior?
Adaptive filters are designed to address this question, and are the third and final class of spatial image filters we shall explore. The premise behind adaptive image filtering is that by varying the filtering method as the kernel slides across the image (in the same manner as the convolution operation), they are able to tailor themselves to the local properties and structures of an image. In essence, they can be thought of as self-adjusting digital filters. While certain types of adaptive filters may perform better than median filters at removing impulse noise (these are mostly variations on the basic median filtering scheme), they are most often used for denoising non-stationary images, which tend to exhibit abrupt intensity changes.
