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|
## morphology.R
##
## Morphological transformations with R
## (c) 2004 Vincent Zoonekynd
##
## Distributed under the GPL v2 or later
##
## (This work was mainly written before my arrival at BioRet,
## <a href="http://www.bioret.com/" target="_blank">http://www.bioret.com/</a>)
##
############################################################
# Translation
# Translates the image "x" by "i" units horizontally and "j" units
# vertically. The pixels that leave the image limits are discarded.
# The newly exposed pixels are set to "zero".
translate <- function (x,i,j,zero=0) {
n <- dim(x)[1]
m <- dim(x)[2]
while (i>0) {
x <- rbind( rep(zero,m), x[-n,] )
i <- i - 1
}
while (i<0) {
x <- rbind( x[-1,], rep(zero,m) )
i <- i + 1
}
while (j>0) {
x <- cbind( rep(zero,n), x[,-m] )
j <- j - 1
}
while (j<0) {
x <- cbind( x[,-1], rep(zero,n) )
j <- j + 1
}
x
}
############################################################
# Structuring elements
new.structuring.element <- function (m, xmin, xmax, ymin, ymax) {
m <- t(m)
stopifnot( dim(m)[1] == xmax - xmin + 1 )
stopifnot( dim(m)[2] == ymax - ymin + 1 )
r <- list()
r$xrange <- seq(xmin,xmax)
r$yrange <- seq(ymin,ymax)
r$value <- function (i,j) { m[1+i-xmin,1+j-ymin] }
r$m <- m # useless...
class(r) <- "structuring.element"
r
}
structuring.element.plus <-
new.structuring.element( matrix(c(F,T,F,T,T,T,F,T,F),nr=3,nc=3), -1, 1, -1, 1)
structuring.element.times <-
new.structuring.element( matrix(c(T,F,T,F,T,F,T,F,T),nr=3,nc=3), -1, 1, -1, 1)
structuring.element.square <-
new.structuring.element( matrix(T,nr=3,nc=3), -1, 1, -1, 1)
structuring.element.disc <- function (radius) {
r <- ceiling(radius)
n <- 2*r+1
m <- matrix(F, nr=n, nc=n)
x <- (n+1)/2
m <- (col(m)-x)^2 + (row(m)-x)^2 <= radius^2
new.structuring.element(m, -r,r,-r,r)
}
structuring.element.square <- function (radius=1) {
r <- ceiling(radius)
n <- 2*r+1
m <- matrix(F, nr=n, nc=n)
x <- (n+1)/2
m <- sup(abs(col(m)-x), abs(row(m)-x)) <= radius
new.structuring.element(m, -r,r,-r,r)
}
############################################################
# Hit-and-Miss Transform (French: transformation tout-ou-rien)
TTR <- function (x, s) {
res <- matrix(T, nr=dim(x)[1], nc=dim(x)[2])
for (i in s$xrange) {
for (j in s$yrange) {
if(!is.na(s$value(i,j))) {
if(s$value(i,j)) {
res <- res & translate(x,i,j)
} else {
res <- res & !translate(x,i,j)
}
}
}
}
res
}
se.rotation <- function (s) {
M <- s$m
n <- dim(M)[1]
m <- dim(M)[2]
y <- range(s$xrange)
x <- range(-s$yrange)
new.structuring.element(t(M)[m:1,], x[1],x[2],y[1],y[2])
}
rotations <- function (s) {
res <- list()
res <- append(res, list(s))
s <- se.rotation(s)
res <- append(res, list(s))
s <- se.rotation(s)
res <- append(res, list(s))
s <- se.rotation(s)
res <- append(res, list(s))
res
}
TTRr <- function (x,s) {
res <- matrix(F, nr=dim(x)[1], nc=dim(x)[2])
for (ss in rotations(s)) {
res <- res | TTR(x,ss)
}
res
}
iTTRr <- function (x,s) { x & ! TTRr(x,s) }
############################################################
# The "sup" and "inf" operations are the equivalent, for grayscale
# images, of the "union" and "intersection" operations for binary
# images.
sup <- function (x,y) {
ifelse(x>y,x,y)
}
inf <- function (x,y) {
ifelse(x>y,y,x)
}
complementaire <- function (image) {
max(image) - image
}
prive.de <- function (a,b) {
inf(a, complementaire(b))
}
############################################################
# Dilatation and erosion (here, for grayscale images) are the basic
# operations, from which you can define all the others.
dilatation <- function (image, kernel) {
n <- dim(image)[1]
m <- dim(image)[2]
result <- image
for (k in kernel$xrange)
for (l in kernel$yrange)
if (!is.na(kernel$value(k,l)) && kernel$value(k,l))
result <- sup(result,translate(image,k,l))
result
}
erosion <- function (image, kernel) {
complementaire(dilatation(complementaire(image), kernel))
}
############################################################
# Opening and closing
ouverture <- function (image, kernel) {
dilatation( erosion(image, kernel), kernel )
}
fermeture <- function (image, kernel) {
erosion( dilatation(image, kernel), kernel )
}
gradient <- function (image, kernel) {
dilatation(image,kernel) & ! erosion(image,kernel)
}
gradient.interne <- function (image, kernel) {
prive.de(image, erosion(image,kernel))
}
gradient.externe <- function (image, kernel) {
prive.de(dilatation(image,kernel), image)
}
laplacien <- function (image) {
n <- dim(image)[1]
m <- dim(image)[2]
result <- matrix(FALSE, nr=n, nc=m)
for (i in 2:(n-1)) {
for (j in 2:(m-1)) {
result[i,j] <- (
4*image[i,j]
- image[i-1,j] - image[i,j-1] - image[i+1,j] - image[i,j+1]
) != 0
}
}
result
}
# Top hat
chapeau.haut.de.forme <- function (image, kernel) {
prive.de( fermeture(image, kernel), image)
}
chapeau.haut.de.forme.conjugue <- function (image, kernel) {
prive.de( image, ouverture(image, kernel) )
}
reconstruction <- function (x,y) { # x is binary, y need not be
xx <- x*y
repeat {
x <- xx
xx <- inf( dilatation(x,structuring.element.plus), y )
if(all(x==xx)) break
}
x
}
# Hysteresis threshold
seuillage.par.hysteresis <- function (image,a,b) {
reconstruction( image >= b, image >= a )
}
# Hole filling
bouchage.de.trous <- function (x) {
n <- dim(x)[1]
m <- dim(x)[2]
M <- matrix(F, nr=n, nc=m)
M[1,] <- T
M[,1] <- T
M[n,] <- T
M[,m] <- T
!reconstruction(M,!x)
}
# Local maxima
maxima.locaux.4 <- function (d) {
n <- dim(d)[1]
m <- dim(d)[2]
d.N <- rbind( d[-1,], rep(0,m) )
d.S <- rbind( rep(0,m), d[-n,] )
d.W <- cbind( d[,-1], rep(0,n) )
d.E <- cbind( rep(0,n), d[,-m] )
(d>d.N) & (d>d.E) & (d>d.W) & (d>d.S)
}
maxima.locaux.8 <- function (d) {
n <- dim(d)[1]
m <- dim(d)[2]
t.N <- function (d) rbind( d[-1,], rep(0,dim(d)[2]) )
t.S <- function (d) rbind( rep(0,dim(d)[2]), d[-dim(d)[1],] )
t.W <- function (d) cbind( d[,-1], rep(0,dim(d)[1]) )
t.E <- function (d) cbind( rep(0,dim(d)[1]), d[,-dim(d)[2]] )
(d>t.N(d)) & (d>t.S(d)) & (d>t.E(d)) & (d>t.W(d)) &
(d>t.N(t.E(d))) & (d>t.N(t.W(d))) &
(d>t.S(t.E(d))) & (d>t.S(t.W(d)))
}
max.loc.hys <- function (x, r, h) {
res <- matrix(T, nr=dim(x)[1], nc=dim(x)[2])
for (k in r$xrange) {
for (l in r$yrange) {
res <- res & (translate(x,k,l)<x+h)
}
}
res
}
# Regional maxima
dilatation.geodesique <- function (x, y, r) {
for (i in 1:r) {
# On prend la 4-distance et la 8-distance une fois sur deux :
# ça correspond a une boule octogonale.
if ( i %% 2 == 0 ) {
x <- dilatation(x, structuring.element.plus) & y
} else {
x <- dilatation(x, structuring.element.square()) & y
}
}
x
}
r.h.maxima <- function (x,r,h) {
res <- matrix(F, nr=dim(x)[1], nc=dim(x)[2])
for (n in 1:255) {
res <- res | (
(x>n) & ! dilatation.geodesique(x>n+h, x>n, r)
)
}
res
} |
Algorithme du RH maxima
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