Conclusion

Linear filtering is one of the most elementary and essential operation involved in image processing. Before such processing schemes can be implemented on a computer, the images have to be digitalized, which implies spatial sampling and luminance quantization. Spatial sampling induces periodicities in the frequency representation of the processed images, which allows limiting their description to a precise frequency domain. The spatial convolution operator is the mathematical representation associated with linear and spatially invariant filtering. Filtering computation can be implemented in the spatial or frequency domain depending on the nature and the complexity of the applied filters. In the simplest cases, the operator is fully described by a 2x2 or a 3x3 matrix. Examples of such filters and their results on real images are presented to give an idea of the application potential of the technique.