Convolution of 3D Arrays using the Fourier Transform

Description

Convolve a

Usage

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

Arguments

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”.

Details

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).

Value

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.

Author(s)

Brandon Whitcher

References

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

See Also

fft, ftm, shift3D

Examples

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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")