filt3d {imagefx}

Filter Image (Matrix) with Mask via Convolution

Description

Apply a filter mask to smooth, sharpen, shift, or otherwise modify an image (matrix)

Usage

filt3d(x, mask)

Arguments

x

Image (matrix) to be filtered

mask

Filter mask (matrix) with same dimensions as x

Details

x and mask are convolved in the frequency domain via multiplication and returned to the spatial domain using the fast Fourier transform.

Value

Filtered matrix with same dimensions as x.

Author(s)

Alex J.C. Witsil

See Also

fft fftshift

Examples

##########
## EG 1 ##
##########
## example of a low pass filter

## generate test data
data <- matrix(0,nrow=256,ncol=256)

box.width = 100
box.height = 100
box.mid=c(nrow(data)/2,ncol(data)/2)

## define where the box indices are
box.row.inds <- (box.mid[1]-box.width/2):(box.mid[1]+box.width/2)
box.col.inds <- (box.mid[2]-box.height/2):(box.mid[2]+box.height/2)

## create the box in the data matrix
data[box.row.inds,box.col.inds] = 1

## define the sigma in the low pass Gaussian filter
sig=5

## create a low pass Gaussian filter
gaus <- build.gaus(nrow(data),ncol(data),sig)

## filter the data matrix with the Gaussian filter mask
data.lp <- filt3d(data,gaus)


## PLOTTING EG1 ##

dev.new()
close.screen(all.screens=TRUE)
split.screen(c(1,3))

## set up some grid lines
grid.xs <- 1:nrow(data)
grid.ys <- 1:ncol(data)

screen(1)
image(grid.xs,grid.ys,data,col=gray.colors(200),useRaster=TRUE,main="Data")

screen(2)
image(grid.xs,grid.ys,gaus,col=gray.colors(200),useRaster=TRUE,main="Low Pass Gaussian Mask")

screen(3)
image(grid.xs,grid.ys,data.lp,col=gray.colors(200),useRaster=TRUE,main='Filtered Data')

## close screens
close.screen(all.screens=TRUE)


##########
## EG 2 ##
##########
## example of a high pass filter

## generate test data
data <- matrix(0,nrow=256,ncol=256)

box.width = 100
box.height = 100
box.mid=c(nrow(data)/2,ncol(data)/2)

## define where the box indices are
box.row.inds <- (box.mid[1]-box.width/2):(box.mid[1]+box.width/2)
box.col.inds <- (box.mid[2]-box.height/2):(box.mid[2]+box.height/2)

## create the box in the data matrix
data[box.row.inds,box.col.inds] = 1

## find the middle of the data matrix
mid <- c(nrow(data)/2,ncol(data)/2)

## create a 5-point Laplacian high pass filter
lap <- matrix(0,nrow=nrow(data),ncol=ncol(data))
lap[(mid[1]-1):(mid[1]+1),mid[2]] = c(1,-4,1)
lap[mid[1],(mid[2]-1):(mid[2]+1)] = c(1,-4,1)

## perform  high pass filter on the data using the Laplacian mask
data.hp <- filt3d(data,lap)


## PLOTTING EG2 ##

## set up some grid lines
grid.xs <- 1:nrow(data)
grid.ys <- 1:ncol(data)

dev.new()
close.screen(all.screens=TRUE)
split.screen(c(1,3))

screen(1)
image(grid.xs,grid.ys,data,col=gray.colors(200),useRaster=TRUE,main="Data")

screen(2)
image(grid.xs,grid.ys,lap,col=gray.colors(200),useRaster=TRUE,main="High Pass Laplacian Mask")

screen(3)
image(grid.xs,grid.ys,data.hp,col=gray.colors(200),useRaster=TRUE,main='Filtered Data')

## close screens
close.screen(all.screens=TRUE)


##########
## EG 3 ##
##########
## example of a shift transform filter

## generate test data
data <- matrix(0,nrow=256,ncol=256)

box.width = 100
box.height = 100
box.mid=c(nrow(data)/2,ncol(data)/2)

## define where the box indices are
box.row.inds <- (box.mid[1]-box.width/2):(box.mid[1]+box.width/2)
box.col.inds <- (box.mid[2]-box.height/2):(box.mid[2]+box.height/2)

## create the box in the data matrix
data[box.row.inds,box.col.inds] = 1

## create a delta function at some (x,y) location
delta.x = 80
delta.y = 180
delta <- matrix(0,nrow=nrow(data),ncol=ncol(data))
delta[delta.x,delta.y] = 1

## perform the shift transform filter
data.shift <- filt3d(data,delta)


## PLOTTING EG3 ##

## set up some grid lines
grid.xs <- 1:nrow(data)
grid.ys <- 1:ncol(data)

dev.new()
close.screen(all.screens=TRUE)
split.screen(c(1,3))

screen(1)
image(grid.xs,grid.ys,data,col=gray.colors(200),useRaster=TRUE,main="Data")

screen(2)
image(grid.xs,grid.ys,delta,col=gray.colors(200),useRaster=TRUE,main="Shift Delta Mask")

screen(3)
image(grid.xs,grid.ys,data.shift,col=gray.colors(200),useRaster=TRUE,main='Filtered Data')

## close screens
close.screen(all.screens=TRUE)