conv_fft: Convolution of 3D Arrays using the Fourier Transform
In dcemriS4: A Package for Medical Image Analysis (S4 implementation)

Description Usage Arguments Details Value Author(s) References See Also Examples

Convolve a

1	conv.fft(A, B, C, FFTA=NULL)

`A`	is a three-dimensional array (“the template”).
`B`	is a three-dimensional array (“the target”).
`C`	is a vector of length three (the center of “the template”).
`FFTA`	is the three-dimensional Fourier transform of `A`, this may save time when looping over multiple “targets”.

The arrays A and B are transformed into the Fourier domain and multiplied together (equivalent to a convolution in the image domain across all spatial locations simultaneously).

A three-dimensional array, the same dimension as the input arrays, that is the convolution of the “target” to the “template” at all spatial locations.

Brandon Whitcher

Briggs, W.L. and Henson, V.E. (1995) The DFT: An Owner's Manual for the Discrete Fourier Transform, SIAM: Philadelphia.

fft, ftm, shift3D

cube <- array(0, c(20,20,1))
cube[9:12,9:12,1] <- 1
tkernel <- array(0, c(20,20,1))
tkernel[,,1] <- c(.5, 1, .5, rep(0,20-3)) 
tcenter <- find.center(ifelse(tkernel > 0, TRUE, FALSE))
out <- conv.fft(tkernel, cube, tcenter)
out[8:13,8:13,1]  ## text output

par(mfrow=c(2,2))  ## graphic output
image(drop(tkernel), col=tim.colors(), main="Template")
image(drop(cube), col=tim.colors(), main="Target")
image(drop(out), col=tim.colors(), main="Output")