An iterative morphological decomposition algorithm for reduction of skeleton points

International Journal of Computer Science & Information Technology (IJCSIT) Vol 7, No 1, February 2015
DOI:10.5121/ijcsit.2015.7110 93
AN ITERATIVE MORPHOLOGICAL DECOMPOSITION
ALGORITHM FOR REDUCTION OF SKELETON
POINTS
1
Dr. A. Sri Krishna, 2
G. L. K. Vasista, 3
N. Neelima.
1,3
Dept. of IT, R.V.R& J.C College of Eng. Guntur, India.
2
Dept. of CSE, AMRITA School of Eng., Coimbatore, India.
ABSTRACT
Shape representation is an important aspect in image processing and computer vision. There are
several skeleton transforms that lead to morphological shape representation algorithm. One of the main
problems with these algorithms is in selecting the skeleton points that represent the shape component. If the
numbers of skeleton subsets are reduced then the reconstruction process will be easy and time consuming.
The present paper proposes a skeleton scheme that selects skeleton points based on the largest shape
element. By this, overall skeleton subsets will be reduced. The present method is applied on various images
and is compared with generalized skeleton transform and octagon-generating decomposition algorithm.
KEYWORDS
Skeleton subsets, Reconstruction, Shape component, Structuring element, Shape representation.
1. INTRODUCTION
Shape description and analysis is a fundamental problem in image processing and pattern
recognition [1][2]. Good shape representation or description schemes not only are important in
developing shape analysis algorithms for shape matching and recognition tasks[6], they also are
important in developing efficient coding schemes for data compression purposes[8] and
developing video compression and image data retrieval algorithms. Certain properties of a shape
representation scheme are desirable. A good shape representation should have well defined
mathematical characterizations. The representation should be generated according to simple,
precise, and meaningful rules, instead of depending on some arbitrary decisions. A well-defined
representation is more likely to capture the intrinsic characteristics of a given shape explicitly. A
good shape representation should provide an accurate and complete description of the given
shape. The original shape should be allowed to be easily reconstructed or approximated. A good
shape representation should be compact. Efficient manipulation of the shape representation
should be possible. A good shape representation should be easily computed. Computational
efficiency is always a desirable feature in a computer imaging system.
A number of shape representation schemes have been developed over the years. Structural
shape description is one of them. In a structural shape description, a shape is first decomposed
into a number of shape components or primitives. The given shape is represented in terms of
these simpler components and the relationships among them. In recent years, a number of
morphological shape representation and decomposition algorithms have been proposed [8]-[14].
Mathematical morphology is a shape-based approach to image processing [5] [6]. One advantage
of mathematical morphology is that basic morphological operations can be implemented very
efficiently on many parallel image computers [7]. Another advantage of mathematical

94
morphology is that it has a well-developed mathematical structure, which provides a foundation
for the analysis of morphological image processing algorithms.
In a recent paper [15], a generalized skeleton transform (GST) was introduced that derives
generalized skeleton points for a given shape image. Each skeleton point represents a generalized
maximal “disk,” which, in general, is an octagon. The main advantage of the generalized skeleton
transform is that iteads to an efficient shape decomposition scheme. In this scheme, a given shape
is decomposed into a collection of modestly overlapping octagonal shape components. These
octagonal components are more primitive than the components obtained from the morphological
shape decomposition (MSD) or overlapped morphological shape decomposition (OMSD) [9].
Each octagonal component is represented by a single center point and the overlapping level is
reduced. However, one problem with this decomposition scheme is that the GST needs to be
applied multiple times. Another problem is that although it is easier to compare two octagons than
to compare two shape components from the MSD or OMSD, it is still not a trivial task to define a
meaningful similarity measure for such octagonal components. In the recent paper [16], octagon-
fitting algorithm (OFA) is defined that finds a special maximal octagon for each image point of a
given shape. The OFA has allowed us to develop two new shape decomposition algorithms. The
first decomposition algorithm will use octagonal shape components octagon-generating
decomposition (OGD) algorithm and the second disk-generating decomposition (DGD)
algorithm. However, the OFA will only need to be applied once. Recently new algorithms for
skeletonization and thinning, for 2D images based on primitive concept approach were proposed
[17]-[19].
The paper is organized as follows: The methodology is introduced in section 2. Section 3 contains
experimental results and some discussions. Concluding remarks are given in section 4.
2. METHODOLOGY
The skeleton points that participate in the reconstruction of the image are called the skeleton
subset. One needs to store skeleton subsets for reconstruction of the image. The present paper
aims to remove redundant skeleton subsets. Any shape reconstruction algorithm can be
represented as the Block Diagram shown in Figure 1.The skeleton points are generated using
skeleton point generation algorithm. However all these skeleton points are not required for the
reconstruction of the image. The present paper proposes an efficient algorithm for the selection of
skeleton subsets for reconstruction of the image. The algorithm uses the sequence of eight
structuring elements in the following order: ,...,,,...,,,..., 10710710 BBBBBBBB
.
.The structuring element is in
Figure 2.
Fig. 1.Block diagram of Shape reconstruction
Fig.2 Structuring Elements.
Original
shape
element
skelet
on
point
gener
ation
Select
ion of
skelet
on
points
Recon
structi
on of
shape

95
Algorithm1: Skeleton Points Generation.
1. Read an Input image X1 of size a x b.
2. Define Eight Structuring elements S1,S2……S8.
3. Initialize an array SK[1:8] to zero, and b1 to 1.
4. Convert the Input image X1 to a binary image X.
5. Erode the binary image X with S1 Structuring element and store it in an array T.
6. If T is Empty go to step10.
7. Sk[b1]=SK[b1]+1.
8. If T does consists of Isolated points Push the array Ton to the stack and go to step 10
9. Store the Isolated points in an 3D array Y and it corresponding Structuring element in an
array S
10. Find the difference between X array and T array and store in array Z.
11. If Z is Empty go to step 14.
12. If Z does consists of Isolated points Push the array Ton to the stack and go to step 14.
13. Store the Isolated points in an array 3D Y and it corresponding Structuring element in an
array S
14. If stack empty go to 19.
15. Pop the image from Top of the stack and store it in X.
16. Calculate b1=mod(b1+1,8)
17. Switch(b1)
Case 1: Erode X with S1 and store it in array T
Break;
Break;
Break;
Break;
Break;
Break;
Break;
Break;
18. Go to step 6.
19. End.
The present paper selects the skeleton points from above algorithm.To reduce overlapped
skeleton points , the proposed paper outlines a new algorithm called Skeleton point reduction
decomposition(SRD). The present algorithm defines a size relation between any two final shape
elements represented by two skeleton points in the following way. If the two skeleton points
belong to the same final subset, then they represent two final shape elements of the same shape.
Obviously, they have the same size and the two image points cannot be adjacent to each other. If
they belong to two different final subsets, then there must be an erosion step. The eroded subset is
called Y set and the other will be called as the Z set. The Y set defines the larger shape element
than the other. This is due to the erosion step of the reduction process.
The proposed algorithm takes each skeleton point and does the summation of corresponding
structuring elements and takes largest value as the first shape element. The first shape component
in the structural representation is the largest final shape element. The second shape component is

96
the largest shape element with its center outside the first shape component. This condition ensures
that each shape component covers a significant new area of the given shape and only modest
overlapping is allowed. The same selection process is repeated until all the image points are
covered. The complete process of selecting the final shape element is given in the Algorithm2 as
skeleton point reduction decomposition (SRD) algorithm.
Algorithm2: Skeleton point reduction decomposition (SRD).
1. Read N i.e. Number of skeleton point subsets from the Algorithm to generate skeleton points.
2.
  

N
i j
N
i
jiSEiSum
1
8
11
),()(
3. Arrange the Array Sum in decreasing order.
4. Arrange the skeleton point subsets and corresponding structuring elements in the decreasing
order of their Sums.
5. Select the first skeleton point subset and initialize I=1 and K=1.
6. Take an Array A and store the x and y coordinate of the skeleton points and corresponding
eight structuring elements by incrementing index K.
7. Initialize Array X with zeros of size of the image to store shape component. Place 1 at the x
and y coordinate of the skeleton points and dilate with corresponding structuring element.
8. Increment I=I+1, Take the skeleton point subset with index I and check the position of first
isolated points from the set of skeleton points.
9. If (position (x, y) is with in shape X) go to step 8.
10. Increment K=K+1, store the x and y coordinate of the skeleton points and corresponding
eight structuring element by incrementing index of K.
11. Initialize Array B with zeros of the size of image to store temporary shape component. Place
1 at the x and y coordinate positions of the skeleton points and dilate with corresponding
structuring element.
12. Add Array B to Array X i.e. (X contains shape components).
13. )( NIIf  Go to 8.
14. Array A consists of selected skeleton point subsets and the corresponding structuring element.
Algorithm3: Reconstruction of image.
A given shape is reconstructed using the following formula:
DCX i
N
i  1 (3)
Where N is the number of skeleton points subsets selected from the skeleton point reduction
decomposition (SRD) algorithm Ci is the set of centers of the representative disks and
D(i.e. .......... 0710 BBBB  )is the combination of the basic structuring elements used to derive X.
3. RESULTS AND DISCUSSIONS
The present method is applied on different images i.e.(a) teapot;(b) lamp; (c) telephone; (d)
dog; (e) digits; (f) letters;(g) fish; (h) butterfly; (i) Telugu character which represent different
shapes as shown in Figure 3. The reconstructed images using generalized skeleton transform
(GST), octagon-generating decomposition (OGD) and present skeleton point reduction
decomposition (SRD) algorithms are shown in Figure 4, 5 and 6 respectively. One problem with
any generalized morphological skeleton transform is after decomposition they generate noise. To
overcome this single noise removal algorithm “Median Filter” of size 3X3 is applied on the
reconstructed images of GST, OGD and SRD and they are shown in Figure 7, 8, and 9
respectively. Sometimes by reversing the background color there will be a change in
reconstructed images due to overlapping of dilation operation. To estimate this effect the present

97
paper generated all nine images by reversing the background color as shown in Figure 10. The
GST, OGD and SRD algorithms are applied on all nine images and the reconstructed images are
shown in Figure 11, 12 and 13 respectively. A noise filter is applied on the Figure 11, 12 and 13
images to reduce the noise effect and resultant reconstructed images for GST, OGD, and SRD are
shown in Figure 14, 15 and 16 respectively. The generalized skeleton transform, failed in
reconstructing the images as shown in the Figure 4 and Figure 11.
The size of the reduced skeleton point subsets for all the three methods GST, OGD and SRD
algorithms in foreground and background intensities are shown in Table 1 and 2 respectively. The
tables clearly indicate the strength of the proposed SRD algorithm over GST and OGD algorithm.
After applying noise removal algorithm lot of noise is reduced in all the three methods. Although
skeleton subsets are reduced drastically in GST, it failed in reconstruction stage of several images.
The some of the reconstructed images by GST are difficult to recognize. This is clearly evident
from Figure 11(a), 11(e) and 11(f) and also from Figure 14(a), 14(e) and 14(f). Moreover GST
has completely failed in reconstruction of the images when background intensity is reversed. This
fact is evident from Figure 4 and Figure 7. This is due to an abnormality caused by the discrete
nature of the algorithm. And the aim of any algorithm in reducing skeleton subsets must be to
obtain a good reconstructed image component. Though in few cases (roughly 10%) the OGD
algorithm produces good reconstructed image than the SRD algorithm but the numbers of
skeleton subsets of OGD are higher than the proposed SRD algorithm. This clearly indicates the
SRD algorithm can be used in applications like Broadcast TV, Video conferencing and Facsimile
transmission where the error rate is tolerated.
Fig. 3.Shape images used in the experiments: (a) teapot;(c) telephone;(d) dog; (e) digits; (f) letters;(g)
fish;(h) butterfly; (i) telugu character
Fig. 4.Shape images after reconstruction using GST Algorithm (a)teapot; (b)lamp; (c)telephone; (d)dog;
(e)digits; (f)letters; (g)fish; (h)butterfly; (i)telugucharacter

98
Fig. 5.Shape images after reconstruction using OGD Algorithm (a)teapot; (b) lamp;(c)telephone; (d) dog;
(e) digits; (f) letters; (g) fish; (h) butterfly; (i) telugu character.
Fig. 6.Shape images after reconstruction using SRD Algorithm (a)teapot; (b)lamp; (c)telephone; (d)dog;
(e)digits; (f)letters; (g)fish; (h)butterfly; (i)telugu character.
Fig. 7.Shape images after reconstruction using GST Algorithm and application of median filter (a)teapot;
(b)lamp; (c)telephone; (d)dog; (e)digits; (f)letters; (g)fish; (h)butterfly; (i)telugu character

99
Fig.8. Shape images after reconstruction using OGD Algorithm and application of median filter(a) teapot;
(b)lamp; (c)telephone; (d)dog; (e)digits; (f)letters; (g)fish; (h)butterfly; (i) telugu character
Fig. 9.Shape images after reconstruction using SRD Algorithm and application of median filter (a)teapot;
(b)lamp; (c)telephone; (d)dog; (e)digits; (f)letters; (g)fish; (h)butterfly; (i)telugu character.
Fig.10.Shape images used in the experiments(with foreground and background reversed)a) teapot; (b)lamp;
(c)telephone;(d) dog;(e) digits; (f) letters;(g) fish; (h) butterfly; (i) telugu character.

100
Fig. 11.Shape images after reconstruction using GST Algorithm (a)teapot; (b)lamp; (c)telephone; (d)dog;
(e)digits; (f)letters; (g)fish; (h)butterfly; (i)telugu character
Table 1. Numbers of Components Used by Different Decomposition Algorithms to Represent Nine 7070
Shape Images
Generalized-
Skeleton
Algorithm
Octagonal-
Generating
Decomposition
Algorithm
Skeleton point
Reduction
Decomposition
Algorithm
Teapot 38 190 103
Lamp 29 203 101
Telephone 40 165 101
Dog 39 235 116
Digits - 193 115
Letters 35 227 132
Fish 41 173 92
Butterfly 39 257 119
Telugu
characters 47 146 110
Fig. 12.Shape images after reconstruction using OGD Algorithm (a)teapot; (b)lamp; (c)telephone; (d) dog;
(e) digits; (f) letters; (g) fish; (h) butterfly; (i) telugu character

101
Fig. 13.Shape images after reconstruction using SRD Algorithm (a)teapot; (b)lamp; (c)telephone; (d)dog;
(e)digits; (f)letters; (g)fish; (h)butterfly; (i)telugu character
Fig. 14..Shape images after reconstruction using GST Algorithm and application of median filter (a)teapot;
Fig. 15. Shape images after reconstruction using OGD Algorithm and application of median filter (a)
teapot; (b)lamp; (c)telephone; (d)dog; (e)digits; (f)letters; (g)fish; (h)butterfly; (i) telugu character.

102
Fig. 16.Shape images after reconstruction using SRD Algorithm and application of median filter (a)teapot;
Table.2. Numbers of Components Used by Different Decomposition Algorithms to Represent Nine 7070
Shape Images (with foreground and background inverted).
Generalized-
Skeleton
Algorithm
Octagonal-
Generating
Decomposition
Algorithm
Skeleton point
Reduction
Decomposition
Algorithm
Teapot 26 78 74
Lamp 31 110 87
Telephone 38 173 137
Dog 31 114 86
Digits 36 82 52
Letters 31 77 73
Fish 38 133 121
Butterfly 38 105 106
Telugu
characters 39 115 89
4. CONCLUSIONS
In this paper we have introduced a Skeleton point Reduction Decomposition (SRD)
algorithm. Using this method, the numbers of skeleton subsets are reduced. However, by
comparing GST, the numbers of skeleton subsets are more. But GST failed completely in
representing some of the images. The present paper concludes that GST fails in reconstruction of
some shapes and fails completely if we reverse the background color. The number of skeleton
subsets is reduced by the proposed algorithm when compared with OGD. Hence the present paper
concludes that the proposed SRD algorithm is better than GST and OGD. The extra noise
generated in reconstruction of the image can easily be removed by applying simple noise filters.

103
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Authors
Dr. A. Sri Krishna received the PhD degree from JNTUK, Kakinada in 2010,
M.Tech degree in Computer Science from Jawaharlal Nehru Technological
University (JNTU) in 2003, M.S degree in software systems from Birla Institute
of Technology and Science, Pilani in 1994, AMIE degree in Electronics &
communication Engineering from Institution of Engineers, Kolkata in 1990. She
has 23 years of teaching experience as Assistant Professor, Associate Professor,
Professor and presently she is working as a Professor and Head, Dept of
Information Technology at RVR&JC College of Engineering, Guntur. She has
published 15 papers in International/ National Journals and Conferences. Her research interest includes
Image Processing and Pattern Recognition. She is member of IE(I) and member of CSI.

104
G L K Vasista Pursuing his B.Tech Graduation in computer science and
engineering in Amrita School of Engineering, Coimbatore, India. He has been
actively participating and presenting papers in student technical Symposium
seminars at National Level. His area of interest includes Image Processing, Data
Structures and Algorithms, Networks and Web Technology.
.
N.Neelima received masters degree M.Tech(CSE) from Acharya Nagarjuna
University in the year 2007, Guntur. She has 7 years of teaching experience.
Presently she is working as an Assistant Professor in Department of IT, RVR & JC
College of Engineering and she is pursuing Ph.D from JNTUH, Hyderabad. Her
research interest includes Image and Signal Processing and computer vision. She is
a member of IAENG.

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