FHT 3D

3D Fast Hartley Transform

Author: Bob Dougherty (rpd@optinav.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.

License:
Copyright (c) 2005, OptiNav, Inc.
All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

Neither the name of OptiNav, Inc. nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

ImageJ: ImageJ can be freely downloaded from the ImageJ web site.

Author:	Bob Dougherty (rpd@optinav.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.
License:	Copyright (c) 2005, OptiNav, Inc. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of OptiNav, Inc. nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
ImageJ:	ImageJ can be freely downloaded from the ImageJ web site.