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.

[1]  Patrice Duval,et al.  Observation of Coherent Bremstrahlung by EDX Analysis in a Transmission Electron Microscope. Case of the Martensites of Cu-Al System , 1996 .

[2]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  J. Spence.  Uniqueness and the inversion problem of incoherent multiple scattering , 1979 .

[4]  M. Hÿtch,et al.  Quantitative criteria for the detection and characterization of nanocrystals from high-resolution electron microscopy images , 1995 .

[5]  Sankar K. Pal,et al.  Smoothing of digital images using the concept of diffusion process , 1996, Pattern Recognit..

[6]  E. Anguiano,et al.  Fractal characterization by frequency analysis. II. A new method , 1993 .

[7]  Peter Hawkes.  The STEM forms templates , 1995 .

[8]  John D. Austin,et al.  Adaptive histogram equalization and its variations , 1987 .

[9]  Harry Wechsler,et al.  Segmentation of Textured Images and Gestalt Organization Using Spatial/Spatial-Frequency Representations , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Azeddine Beghdadi,et al.  An image enhancement technique and its evaluation through bimodality analysis , 1992, CVGIP Graph. Model. Image Process..

[11]  Guido Gerig,et al.  Nonlinear anisotropic filtering of MRI data , 1992, IEEE Trans. Medical Imaging.

[12]  Rangaraj M. Rangayyan,et al.  Adaptive-neighborhood histogram equalization for image enhancement , 1992, CVGIP Graph. Model. Image Process..

[13]  Azeddine Beghdadi,et al.  Contrast enhancement technique based on local detection of edges , 1989, Comput. Vis. Graph. Image Process..

[14]  M. Hytch,et al.  Analysis of Variations in Structure from High Resolution Electron Microscope Images by Combining Real Space and Fourier Space Information , 1997 .

[15]  Peter Hawkes,et al.  Review paper Image Algebra for Electron Images , 1995 .

[16]  P. Flandrin,et al.  Detection of changes of signal structure by using the Wigner-Ville spectrum , 1985 .

[17]  Wilson S. Geisler,et al.  Multichannel Texture Analysis Using Localized Spatial Filters , 1990, IEEE Trans. Pattern Anal. Mach. Intell..