Image Analysis: Is the Fourier Transform Becoming Obsolete?

We show that, despite its great usefulness in image processing and analysis, the Fourier transform may also suffer from certain drawbacks and limitations. We show how several limitations of a technical nature can be overcome. More importantly, we show that the fundamental limitation of the Fourier transform, its lack of spatial localization, has favored the development of alternative tools for the local analysis of one-dimensional signals and images. The spectrogram technique, Gabor filters and wavelets are introduced with some examples of applications. Also, the importance of the spectrum phase is emphasized.