Transcript Image Segmentation by Clustering using Moments

Image Segmentation by
Clustering
using
Moments
by,
Dhiraj Sakumalla
What is segmentation?
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It is to distinguish objects from background
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Types of segmentation
edge based
region based
In the present project we use region based
segmentation.
Region based Segmentation
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A region-based method usually proceeds as
follows: the image is partitioned into
connected regions by grouping neighboring
pixels of similar intensity levels. Adjacent
regions are then merged under some
criterion involving perhaps homogeneity or
sharpness of region boundaries.
Overstringent criteria create fragmentation;
lenient ones overlook blurred boundaries and
overmerge.
Clustering
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Clustering is a classification technique. It involves grouping
similar data together.
Given a vector of N measurements describing each
pixel or group of pixels (i.e., region) in an image, a
similarity of the measurement vectors and therefore
their clustering in the N-dimensional measurement
space implies similarity of the corresponding pixels or
pixel groups. Therefore, clustering in measurement
space is an indicator of similarity of image regions, and
is used for segmentation purposes
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Techniques used for clustering
Kmeans
Kmediods
Hierarchical
Here we use the KMeans algorithm.
Abstract
Texture segmentation is one of the early steps
towards identifying surfaces and objects in an
image. In this paper a moment based texture
segmentation algorithm is presented. The
moments in small windows of the image are
used as texture features which are then used to
segment the textures. The algorithm has
successfully segmented binary images as well
as a number of gray level texture images.
The basic algorithm.
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Step 1:
To break the image into blocks.
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Step 2:
Compute moments for each block.
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Step 3:
Obtain texture feature by applying a transformation.
.
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Step 4:
Perform an unsupervised clustering of the
image.
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Step 5:
Classify every pixel in the image according
to its features
Techniques Used
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For computing texture features
Moments
Nonlinear Transformation
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For clustering
KMeans
Computing the Moments
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Our algorithm uses the moments of an image
to compute texture features. The (p+q)th
order moments of a function of two variables
f(x,y) with respect to the origin (0,0) are
defined as :Σµ
mpq = Σx Σy f(x,y) xp yq

The central moments are defined as
µpq = Σx Σy (x-x’)p(y-y’) f(x,y)
where,
x’ = m10/m00 and y’ = m01/m00
And the normalized moments are given by
ŋpq = µpq /µ00
In this way seven 2D moments are calculated
and are applied to each block of the image.
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Thus each block now has seven values in the
output matrix.
The moments alone are not sufficient to
obtain good texture features in certain
images.
For this we apply a non-linear transformation
function on each output.
which is given by,
abs(tanh(Mk(a,b) – M’))
where
and
Mk is the kth moment of a,b
M’ is the mean of the moments
Implemantation
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First the image is broken into blocks.
The size of the block is important. As the
window size gets larger, more global features
are detected. This suggests that the choice of
window size could possibly be tied
to the contents of the image. The images with
larger texture tokens would require larger
window sizes whereas finer textures would
require smaller windows.
The size of the block taken here ranges between
3 and 8.
Kmeans
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Kmeans clustering finds a grouping of the
measurements that minimizes the within-cluster sum-ofsquares. In this method, each measurement,
represented by a vector of length N, is grouped so that it
is assigned to one of a fixed number of clusters. The
number of clusters is determined by the number of seeds
given as the second argument of KMeans.
Measurements are transferred from one cluster to
another when doing so decreases the within-cluster
distances. The algorithm stops when no more transfers
can occur. Here we will demonstrate the application of
KMeans clustering to a simple image segmentation
problem. Consider the problem of programmatically
manipulating individual red beans in a fragment of the
"beans" image.
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Matlab function used for breaking into blocks
is im2col
We use sliding window as an option
here.what this does is rather than take
distinct wiindows of size m*n it takes in each
pixel individually and and takes in the pixels
around it.
Each block thus obtained are processed by
function
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The second step is to compute the moments.
The function mention above does this.
It takes in each block and computes the
seven moments of this.
Then to this the non linear transformation is
applied.
the output of this would then be a matrix with
dimensions m*n
where,
m is the total number of pixels in the image
n is the corresponding moment values to each
pixel.
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The third step is to cluster the output matrix
from the above step.
the clustering algorithm used here is the
Kmeans algorithm.
this algorithm requires us to specify the
number of clusters required.
the distance calculations between the
centriod and the points are done using
euclidean and mahalanobis distance
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However it is observed that using Euclidean
distance yields better results than
Mahalanobis.
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The final step in this project is to classify the
pixels according to its cluster.
This is done assigning a particular graylevel
to each cluster and then remapping it to the
original image.
The matlab function used here is col2im
which reconstructs the matrix from the blocks
obtained from im2col.
Results
The segmentation has been performed on
various images both gray and color.
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original
4 clusters
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4 clusters
original
4 clusters
original
block size 5
block size 10
original
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3 clusters
2 clusters
original
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4 clusters
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original
5 clusters
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original
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4 clusters
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orignal
4 clusters
orignal
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4 clusters
diff window
Original
4 clusters
5 clusters
Conclusions
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This project dealt with segmenting an image
based on texture using moments.
From the results of this project three things
could be observed
1.
The size of the initial block of image.
The image initial block should be smaller for
images with finer textures and bigger for
images with coarse textures
2. The number of moments to be considered.
In this projects seven moments were taken
and the results were not very satisfactory.
May be fewer moments like 5 or 6 would
give a better result.
3. The output is dependent on the efficiency of
the clustering algorithm and the number of
clusters are to be given before hand.
References
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http://www.cs.iupui.edu/~tuceryan/research/C
omputerVision/moment-paper.pdf
http://documents.wolfram.com/applications/di
gitalimage/UsersGuide/7.5.html