# Re: [R] Asking Favor For the Script of Median Filter

From: David Winsemius <dwinsemius_at_comcast.net>
Date: Sun, 27 Mar 2011 17:44:50 -0400

> Hello,everybody. My name is Chuan Zun Liang. I come from Malaysia. I
> am just
> a beginner for R. Kindly to ask favor about median filter. The
> problem I
> facing as below:
>
>
>> x<-matrix(sample(1:30,25),5,5)
>> x
> [,1] [,2] [,3] [,4] [,5]
> [1,] 7 8 30 29 13
> [2,] 4 6 12 5 9
> [3,] 25 3 22 14 24
> [4,] 2 15 26 23 19
> [5,] 28 18 10 11 20
>
> This is example original matrices of an image. I want apply with
> median
> filter with window size 3X# to remove salt and pepper noise in my
> matric.
> Here are the script I attend to writing.The script and output shown as
> below:
>
>> MedFilter<-function(mat,sz)
> + {out<-matrix(0,nrow(mat),ncol(mat))
> + for(p in 1:(nrow(mat)-(sz-1)))
> + {for(q in 1:(ncol(mat)-(sz-1)))
> + {outrow<-median(as.vector(mat[p:(p+(sz-1)),q:(q+(sz-1))]))
> + out[(p+p+(sz-1))/2,(q+q+(sz-1))/2]<-outrow}}
> + out}
>

Noting that median is probably the "rate-limiting" factor, I looked for another way to get the "middle" of 9 items. Using order seem faster:

> system.time( replicate(100000, x2s <- sort(x2)))

user system elapsed
9.829 0.212 10.029
> system.time( replicate(100000, x2m <- median(x2)))

user system elapsed
7.169 0.126 7.272
> system.time( replicate(100000, x2s <-x2[order(x2)[5] ]))

user system elapsed
1.907 0.051 1.960

So see if this is any faster. On my system it's about three times faster:

x <- matrix(sample(364*364), 364,364)
out <- matrix(0, 364,364)
for(xi in 1:(nrow(x)-2)) {

```       for(yi in 1:(ncol(x)-2) ) {
xm <- x[xi+0:2, yi+0:2]
d[xi+1, yi+1] <-xm[order(xm)[5] ]}}

```

#---------tests ------
> system.time(for(xi in 1:(nrow(x)-2)) {

```+       for(yi in 1:(ncol(x)-2) ) {
+          xm <- x[xi+0:2, yi+0:2]
+           d[xi+1, yi+1] <-xm[order(xm)[5] ]}} )
```

user system elapsed
3.806 0.083 3.887

> system.time(MedFilter(x,3) )

user system elapsed
11.242 0.202 11.427

>> MedFilter(x,3)
> [,1] [,2] [,3] [,4] [,5]
> [1,] 0 0 0 0 0
> [2,] 0 8 12 14 0
> [3,] 0 12 14 19 0
> [4,] 0 18 15 20 0
> [5,] 0 0 0 0 0
>
> Example to getting value 8 and 12 as below:
>
> 7 8 30 8 30 29
> 4 6 12 (median=8) 6 12 5 (median=12)
> 25 3 22 3 22 14
>
> Even the script can give output. However, it is too slow. My image
> size is
> 364*364. It is time consumption. Is it get other ways to improving it?

David Winsemius, MD
West Hartford, CT

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