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Image Segmentation by

using K-MeansClustering

Language- C++

Platform- GNU/LINUX

Compiler GNU G++Libraries-

IM-3.6 - for Digital imaging

NEWMAT11 Matrix library 1

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ORGANIZATION

Defense Research & Development

Organization (DRDO)

DRDO has a network of 52 laboratories

eg.

SAG, LASTEC, DTRL

Defense Terrain Research Laboratory2

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CONTENTS

Introduction

Image

Image Processing

Image Segmentation

K-Means Clustering

Results

Libraries Conclusion

Refrences

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INTRODUCTION

The goal is to change the representation of an

image into something that is more meaningful

and easier to analyze i.e. to segment the image

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20 40 60 80 100 120

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40

60

80

100

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Digital Image

A digital image is a representation of a two-dimensional image using ones and zeros

Digital imaging is the art ofmaking digital

images

Each image is compiled of a certain amount of

pixels, which are then mapped onto a grid and

stored in a sequence by a computer. Every pixel

in an image is given a tonal value to determineits hue or color.

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PIXELS

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Each pixel's color sam

ple has three num

erical RGB com

ponents(Red, Green, Blue) to represent the color.

These three RGB components are three 8-bit numbers for each

pixel.

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Image Processing

Analog Image Processing

Digital Image Processing

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Output the result

Analyze or

Manipulate the

Image

Import anImage

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Image Magnification, Reduction

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Noise Removal, Mosaic

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Image Segmentation

(one of the vital steps used in Image processing)

segmentation refers to the process of partitioning a digital

image into multiple segments (sets of pixels, also known

as superpixels).

The goal of segmentation is to simplify and/or change the

representation of an image into something that is more

meaningful and easier to analyze.

Image segmentation is typically used to locate objects

and boundaries (lines, curves, etc.) in images

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Below is the Original data, on

which the K-Means steps will

be implemented

March 10, 2004 11

8 1 0 1 2 1 4 1 6 1 8 2 0 7

8

9

1 0

1 1

1 2

1 3

1 4

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Placing K points as the initial

centroids.

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8

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1 0

1 1

1 2

1 3

1 4

I n i t i a l C l u s t e r C e n t e r s a t I t e r a t i o n 1

Here, the no. of Clusters in which the pixels of image

is to be divided is 2. hence, k=2

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Assigning each object to the group

that has the closest centroid.

In this step, we calculate the distance of each object (pixel)

with the centroids & on comparing, the pixel with shortest

distance resides in the cluster of that centroid.

Euclidean Distance

. If the two pixels that we are considering have

coordinates (x1,y1) and (x2,y2) , then the Euclidean

distance is given by:

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we got two clusters & the objects in

that cluster are nearer to it as compare

to that of other cluster

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8

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1 0

1 1

1 2

1 3

1 4U p d a t e d M e m b e r s h i p s a n d B o u n d a r y a t I t e r a t i o n 1

X V a r i a b l e

Y

V

a

ria

b

le

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At 3rd step, we need to re-calculate k new centroids as

barycenters of the clusters resulting from the previous step

i.e., just take the mean of every cluster that will be new

centroid as-

we got new centroids after taking the mean of objects of

both clusters.

(Now again the 2nd step is repeated for dividing the objects

in two clusters according to the new centroids) 15

8 1 0 1 2 1 4 1 6 1 8 2 0 7

8

9

1 0

1 1

1 2

1 3

1 4

p d a te d C l u s te r C e n te r s a t I te r a t i o n 2

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(Below is the final result, convergence has been achieved

i.e., centroids dont shift any more)

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1 0

1 1

1 2

1 3

1 4U p d a t d

ip s a n d

n d a r y a t I t r a t i n 4

X a r ia b l

a

riab

l

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K-MEANS CLUSTERING

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.

The algorithm is composed of the following steps :

1). Place K points into the space represented by the

objects that are being clustered. These points

represent initial group centroids.

2). Assign each object to the group that has the closestcentroid.

3). When all objects have been assigned, recalculate

the positions of the K centroids.

4). Repeat Steps 2 and 3 until the centroids no longermove. This produces a separation of the objects into

groups from which the metric to be minimized can

be calculated.

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RESULTSIM Info File Name: ./flower.jpg

File Size: 1

7.50 Kb

Format: JPEG - JPEG File Interchange Format

Image Count: 1

Width: 184

Height: 148

Color Space: RGB

Data Type: byte

Data Size: 79.78 Kb

FileFormat: JPEG

ResolutionUnit: DPI

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Image Orientation:

Top-down

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Is Packed: Yes

Is Top Down: Yes

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Red Plane123 54 0 25 78 245 54 76 125 245 23 175 129

254 234 21 54 36 87

23 65 92 145 23474 190

165 34 26 86 187 165 136 134 176 153 12 9 0

Green Plane

23 0 12 7 34 243 65 1 48 21 76 34 87 27 142 163134 1 98 0 34 234 176 19 1 231 1175 123 32 95

94 36 37 83 95 28 29 83 73 85 93 56 0 124 234

Blue Plane43 2 65 3 34 243 65 1 48 21 76 34 87 27 142 163

239 0 83 0 31 232 172 10 19 233 1 75 223 62 75

44 66 57 88 55 88 59 73 43 75 93 46 2 224 134 20

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K= 6

k=8

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Gray images

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K = 5

K = 8

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MATRIX LIB-NEWMAT11

To construct an m x n matrix, A, (m and n are

integers) use Matrix A(m,n);

SquareMatrix SQ(n);

UpperTriangularMatrix UT(n);

SymmetricMatrix S(n);

DiagonalMatrix D(n);

IdentityMatrix I(n);

A.swap(B);

swap(A,B);23

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CONCLUSIONfor smaller values of k the algorithms give good results. For larger

values of k, the segmentation is very coarse, many clusters appear in the

images at discrete places.

Further, the computational time complexity of the algorithm is O

(nkl), where n is the total number of objects in the dataset, k is the

required number of clusters we identified and l is the number of

iterations.

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THANK YOU

QUERIES ?

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