Anil Kumar

Image Segmentation

in image segmentaion, we divide image into cluster according to the some feature of image like color, pixel intensity Here we Restrict ourselves to gray-scale images

load the data

flower = read.csv("flower.csv", header=FALSE)
str(flower)

## 'data.frame':    50 obs. of  50 variables:
##  $ V1 : num  0.0991 0.0991 0.1034 0.1034 0.1034 ...
##  $ V2 : num  0.112 0.108 0.112 0.116 0.108 ...
##  $ V3 : num  0.134 0.116 0.121 0.116 0.112 ...
##  $ V4 : num  0.138 0.138 0.121 0.121 0.112 ...
##  $ V5 : num  0.138 0.134 0.125 0.116 0.112 ...
##  $ V6 : num  0.138 0.129 0.121 0.108 0.112 ...
##  $ V7 : num  0.129 0.116 0.103 0.108 0.112 ...
##  $ V8 : num  0.116 0.103 0.103 0.103 0.116 ...
##  $ V9 : num  0.1121 0.0991 0.1078 0.1121 0.1164 ...
##  $ V10: num  0.121 0.108 0.112 0.116 0.125 ...
##  $ V11: num  0.134 0.125 0.129 0.134 0.129 ...
##  $ V12: num  0.147 0.134 0.138 0.129 0.138 ...
##  $ V13: num  0.000862 0.146552 0.142241 0.142241 0.133621 ...
##  $ V14: num  0.000862 0.000862 0.142241 0.133621 0.12931 ...
##  $ V15: num  0.142 0.142 0.134 0.121 0.116 ...
##  $ V16: num  0.125 0.125 0.116 0.108 0.108 ...
##  $ V17: num  0.1121 0.1164 0.1078 0.0991 0.0991 ...
##  $ V18: num  0.108 0.112 0.108 0.108 0.108 ...
##  $ V19: num  0.121 0.129 0.125 0.116 0.116 ...
##  $ V20: num  0.138 0.129 0.125 0.116 0.116 ...
##  $ V21: num  0.138 0.134 0.121 0.125 0.125 ...
##  $ V22: num  0.134 0.129 0.125 0.121 0.103 ...
##  $ V23: num  0.125 0.1207 0.1164 0.1164 0.0819 ...
##  $ V24: num  0.1034 0.1034 0.0991 0.0991 0.1034 ...
##  $ V25: num  0.0948 0.0905 0.0905 0.1034 0.125 ...
##  $ V26: num  0.0862 0.0862 0.0991 0.125 0.1422 ...
##  $ V27: num  0.086207 0.086207 0.103448 0.12931 0.000862 ...
##  $ V28: num  0.0991 0.1078 0.1164 0.1293 0.1466 ...
##  $ V29: num  0.116 0.134 0.134 0.121 0.142 ...
##  $ V30: num  0.121 0.138 0.142 0.129 0.138 ...
##  $ V31: num  0.121 0.134 0.142 0.134 0.129 ...
##  $ V32: num  0.116 0.134 0.129 0.116 0.112 ...
##  $ V33: num  0.108 0.112 0.116 0.108 0.108 ...
##  $ V34: num  0.1078 0.1078 0.1034 0.0991 0.1034 ...
##  $ V35: num  0.1078 0.1034 0.0991 0.0991 0.0991 ...
##  $ V36: num  0.1078 0.1034 0.1034 0.0905 0.0862 ...
##  $ V37: num  0.1078 0.1078 0.1034 0.0819 0.0733 ...
##  $ V38: num  0.0948 0.0991 0.0776 0.069 0.0733 ...
##  $ V39: num  0.0733 0.056 0.0474 0.0474 0.056 ...
##  $ V40: num  0.0474 0.0388 0.0431 0.0474 0.0603 ...
##  $ V41: num  0.0345 0.0345 0.0388 0.0474 0.0647 ...
##  $ V42: num  0.0259 0.0259 0.0345 0.0431 0.056 ...
##  $ V43: num  0.0259 0.0259 0.0388 0.0517 0.0603 ...
##  $ V44: num  0.0302 0.0302 0.0345 0.0517 0.0603 ...
##  $ V45: num  0.0259 0.0259 0.0259 0.0388 0.0474 ...
##  $ V46: num  0.0259 0.0172 0.0172 0.0259 0.0345 ...
##  $ V47: num  0.01724 0.01724 0.00862 0.02155 0.02586 ...
##  $ V48: num  0.0216 0.0129 0.0129 0.0172 0.0302 ...
##  $ V49: num  0.0216 0.0216 0.0216 0.0345 0.0603 ...
##  $ V50: num  0.0302 0.0345 0.0388 0.0603 0.0776 ...

gray-scale image is represented as a matrix of pixel intensity values ranging from 0 (black) to 1 (white) so let's convert our dataframe into matrix

flowerMatrix = as.matrix(flower)
str(flowerMatrix)

##  num [1:50, 1:50] 0.0991 0.0991 0.1034 0.1034 0.1034 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:50] "V1" "V2" "V3" "V4" ...

Turn matrix into a vector

flowerVector = as.vector(flowerMatrix)
str(flowerVector)

##  num [1:2500] 0.0991 0.0991 0.1034 0.1034 0.1034 ...

TO see any type of image we need to conver matrix of pixel of image into a vector, here we are use matrix.

flowerVector2 = as.vector(flowerMatrix)
str(flowerVector2)

##  num [1:2500] 0.0991 0.0991 0.1034 0.1034 0.1034 ...

Let's find the pairwase distance between all the indesity of the vector

compute distance

distance = dist(flowerVector2, method = "euclidean")

Now we can cluster the intensity for that we use hclust function,

Hierarchical clustering

clusterIntensity = hclust(distance, method="ward.D")

here method ward find minimum variance method which find compact cluster

Plot the dendrogram

plot(clusterIntensity)

plot of chunk plot we can visualize the cluster by using the rectangle to cluster

Select 3 clusters

rect.hclust(clusterIntensity, k = 3, border = "red")

## Error in rect(m[which[n]] + 0.66, par("usr")[3L], m[which[n] + 1] + 0.33, : plot.new has not been called yet

flowerClusters = cutree(clusterIntensity, k = 3)
# flowerClusters

let's split the data into these three cluster this is done by using cutree.

Select 3 clusters

rect.hclust(clusterIntensity, k = 3, border = "red")

## Error in rect(m[which[n]] + 0.66, par("usr")[3L], m[which[n] + 1] + 0.33, : plot.new has not been called yet

flowerClusters = cutree(clusterIntensity, k = 3)
# flowerClusters

Find mean intensity values

tapply(flowerVector, flowerClusters, mean)

##          1          2          3 
## 0.08574315 0.50826255 0.93147713

Let view image flowerclusters to view we need to conver this into matrix

Plot the image and the clusters

dim(flowerClusters) = c(50,50)
image(flowerClusters, axes = FALSE)

plot of chunk matricx

Original image

image(flowerMatrix,axes=FALSE,col=grey(seq(0,1,length=256)))

plot of chunk original

Let's try this with an MRI image of the brain

healthy = read.csv("healthy.csv", header=FALSE)
healthyMatrix = as.matrix(healthy)
str(healthyMatrix)

##  num [1:566, 1:646] 0.00427 0.00855 0.01282 0.01282 0.01282 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:646] "V1" "V2" "V3" "V4" ...

Plot image

image(healthyMatrix,axes=FALSE,col=grey(seq(0,1,length=256)))

plot of chunk pot

Hierarchial clustering

healthyVector = as.vector(healthyMatrix)
distance = dist(healthyVector, method = "euclidean")

## Error: cannot allocate vector of size 498.0 Gb

We have an error - why?

str(healthyVector)

##  num [1:365636] 0.00427 0.00855 0.01282 0.01282 0.01282 ...

So let's usr k-mean clustering algorithm

Specify number of clusters

k = 5

# Run k-means
set.seed(1)
KMC = kmeans(healthyVector, centers = k, iter.max = 1000)
str(KMC)

## List of 9
##  $ cluster     : int [1:365636] 3 3 3 3 3 3 3 3 3 3 ...
##  $ centers     : num [1:5, 1] 0.4818 0.1062 0.0196 0.3094 0.1842
##   ..- attr(*, "dimnames")=List of 2
##   .. ..$ : chr [1:5] "1" "2" "3" "4" ...
##   .. ..$ : NULL
##  $ totss       : num 5775
##  $ withinss    : num [1:5] 96.6 47.2 39.2 57.5 62.3
##  $ tot.withinss: num 303
##  $ betweenss   : num 5472
##  $ size        : int [1:5] 20556 101085 133162 31555 79278
##  $ iter        : int 2
##  $ ifault      : int 0
##  - attr(*, "class")= chr "kmeans"

Extract clusters

healthyClusters = KMC$cluster
KMC$centers[2]

## [1] 0.1061945

Plot the image with the clusters

dim(healthyClusters) = c(nrow(healthyMatrix), ncol(healthyMatrix))

image(healthyClusters, axes = FALSE, col=rainbow(k))

plot of chunk plot12

Apply to a test image

tumor = read.csv("tumor.csv", header=FALSE)
tumorMatrix = as.matrix(tumor)
tumorVector = as.vector(tumorMatrix)

Apply clusters from before to new image, using the flexclust package

#install.packages("flexclust")
library(flexclust)

KMC.kcca = as.kcca(KMC, healthyVector)
tumorClusters = predict(KMC.kcca, newdata = tumorVector)

Visualize the clusters

dim(tumorClusters) = c(nrow(tumorMatrix), ncol(tumorMatrix))

image(tumorClusters, axes = FALSE, col=rainbow(k))

plot of chunk viadf