Author: Bob Dougherty (email@example.com) Installation: Download FHT_3D.java or FHT_3D.class and place it in the Plugins folder. Description: ImageJ plugin to compute the 3D Fast Hartley Transform of a 32-bit image stack. The width and height of the stack must be powers of 2, but they need not match. The number of slices is not restricted, but the plugin runs much faster if the number of slices is a power of 2 because the slow version of the transform in the depth direction is used otherwise. The Hartley coefficients replace the image data. Running the plugin a second time restores the original images (apart from round-off error, which should be very small) because symmetrical normalization is applied. The order of the coefficents in the output is the native form of the Hartley transform, so the lower spatial frequencies are near the edges of the images and the first and last slices of the stack. The plugin Swap_Quadrants_3D can be used to switch to the alternate form with the higher frequencies near the edges, but be sure to run Swap_Quadrants_3D again before inverting the transform. References: The code is a result of generalizing the FHT routines in ImageJ and Joachim Walter's FFT Filter plugin. The comments in the ImageJ code include:
"[FFT] is based on Arlo Reeves' Pascal implementation of the Fast Hartley Transform from NIH Image (http://rsb.info.nih.gov/ij/docs/ImageFFT/). The Fast Hartley Transform was restricted by U.S. Patent No. 4,646,256, but was placed in the public domain by Stanford University in 1995 and is now freely available."
Versions: 0: 4/24/2005
0.1: 4/25/2005 The image is explicitly redrawn upon completion.
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