Many useful image processing operations may be implemented by filtering the image with a selected FIR filter. This is known as linear filtering and finds application in edge detection, image sharpening, noise reduction, and image matching. According to Equations (5.2.2), (5.2.3), (5.2.4), and (5.2.5) the output image is obtained by a convolution/correlation operation. The choice of filter depends on the desired outcome. A number of standard FIR filters have been predefined for use in these applications. The following presents the most commonly used smoothing and sharpening FIR filters. Additional filters, such as those used in edge detection, are described in Section 7.3. Arbitrary FIR 1D and 2D filters may be designed using the functions and methods described in Sections 9.3 and 9.4.

BoxFilter, DiskFilter, GaussianFilter, ExponentialFilter and SmoothingFilter are all variants of so-called smoothing filters. They produce a response that is the local average of the samples of a signal. Such an operation tends to reduce the local variability of sample values and thus decreases signal noise and smooths the signal. However, averaging also smears image edges resulting in a blurred picture. BoxFilter returns a matrix with constant coefficients equal to the inverse of the filter's dimensions. This FIR filter is commonly known as a moving-average filter.

The Savitzky-Golay FIR smoothing filters, also known as polynomial smoothing or least-squares smoothing filters, are generalizations of the FIR moving-average filter. These are filters that optimally (in the sense of least squares) fit a set of data points to polynomials of different degrees. These filters preserve edges far better than a moving-average filter at the expense of not removing as much noise. For additional noise reduction techniques, see Section 5.5. The length N of a Savitzky-Golay filter must be odd and at least two greater than the desired polynomial order k (i.e., N>k+1). For any given length N, filters of order k and k+1, where k is even, return the same result. Here we show the coefficients of a Savitzky-Golay filter of order three and dimensions 5 × 5.

A standard technique to improve image quality is to enhance the visibility of edges by a technique called unsharp masking. Unsharp masking introduces overshoots in the vicinity of an edge, effectively simulating a well-documented human visual phenomenon known as the Mach band effect. Mach bands are nonexistent overshoots that we tend to perceive in the vicinity of sharp brightness transitions in a picture. This linear operation may be implemented by convolving an image with UnsharpFilter. The degree of edge enhancement may be controlled using the option UnsharpRatio.

A different technique for increasing the visibility of edges is to diminish all flat or constant areas of an image. As a result, the only nonzero samples are those in the vicinity of an edge. Such an effect may be obtained by applying HighpassFilter to an image. (A detailed discussion of edge detection may be found in Section 8.1.) A typical highpass filter is shown here.