TABLE OF CONTENTS Chapter written by Yannick BERTHOUMIEU.
Finite impulse response or FIR filters are currently used in image processing. As well as improving the visual quality of images, these digital filters help with contour detection and the motion estimation between two consecutive images. Quite often they are dedicated to estimating the components of the gradient or of the Laplacian.
In order not return to topics we have already presented, and in keeping with the rest of this text, in this chapter we will discuss frequency response of 2-D digital filters that are used in applications such as signal and noise separation.
As we saw in Chapter 5, there are many design techniques dedicated to FIR filters. Each of these techniques can be applied to the domain of images.
In order to limit our discussion to a two-dimensional context, we have focused on the isotropic feature of the designed filter. Isotropy means that the effect of filtering is identical with all orientations. We will discuss two filters that have this characteristic: circular and Gaussian filters. For design, we have chosen the windowing method because, as we show in section 9.4, it is based on concepts used in two-dimensional spectrum analysis. In order for our presentation to be as clear as possible, whenever possible we will provide examples of how the techniques are used.
The most basic digital forms of the impulse responses of 2-D FIR filters are given by squared matrices of small size [3 3]...
