# Filter Image (Matrix) with Mask via Convolution Apply a filter mask to smooth, sharpen, shift, or otherwise modify an image (matrix) ```r 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. ## Returns Filtered matrix with same dimensions as `x`. ## Author(s) Alex J.C. Witsil ## See Also `fft` `fftshift` ## Examples ```r ########## ## 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) ```

filt3d function