Fourier Transform is a widely used and known tool in image synthesis and analysis. A less used class of transforms are the Hadamard, Paley, Walsh and Haar Transforms, also known as Binary Fourier Transforms, since the transformation kernel is +1/-1.
From a computer point of view, all these transforms can be implemented by a Cooley-Tukey algorithm, or a modified Cooley-Tukey algorithm. Thus, computation of Fourier, Paley, Walsh, Hadamard and Haar transforms is fast and simple. Consequently all these transforms find applications in signal and image processing, speech processing, pattern recognition, holographic synthesis ...ect. Integrated in Vinci, they provide a powerful and complementary tool for image analysis.
We present here examples of Fourier, Walsh, Paley, Hadamard and Haar Transforms,computed on a Sun SparcStation 20 / 50 Mhz. The original image is a 1024x1024 black and white image ( 1 byte per pixel ) and transforms are processed in "Double" ( 8 bytes ).
For suggestions about this page, please contact: guillermo.ciscar@jrc.it
Original
FOURIER (Elapsed time: 41s)
HAAR (Elapsed time: 5s)
HADAMARD (Elapsed time: 6). PALEY (9s). WALSH (9s).
Other projects
Image & Hologram. Dynamic compression
Holographic synthesis
For further information, please contact:
Jean-Claude Grossetie, Stéphane Morucci
