Enhanced morphological contour representation and reconstruction using line segments

Abstract

The paper proposes an enhanced morphological contour/edge representation algorithm for the representation of 2D binary shapes of digital images. The concise representation algorithm uses representative lines of different sizes and types to cover all the significant features of the binary contour/edge image. These well-characterized representative line segments, which may overlap among different types, take minimum representative points than that of most other prominent shape representation algorithms including MST and MSD. The new algorithm is computationally efficient than most other algorithms in the literature and is also capable of approximating edge images. The approximated outputs produced by the proposed algorithm by using minimal number of representative points are more natural to the original shapes than that of MST and MSD.

Full text

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Santhosh P Mathew, Philip Samuel, Justin Varghese & Saudia Subhash
International Journal of Image Processing (IJIP) Volume(3), Issue(6)
301
Enhanced Morphological Contour Representation and
Reconstruction using Line Segments


Santhosh P Mathew mathewsantosh@yahoo.com
Professor/Computer Science & Engineering
Saintgits College of Engineering
Kottayam, Kerala, India PIN 686 532

Philip Samuel philipsamu@yahoo.com
Reader & Head/Information Technology
Cochin University of Science & Technology
Cochin, Kerala, India PIN 682 022

Justin Varghese justinv@saintgits.org
Professor & Head/Computer Science & Engineering
Infant Jesus College of Engineering
Tirunelveli, Tamilnadu, India PIN 628 851

Saudia Subhash saudias@yahoo.com
Lecturer/Center for Information Technology & Engineering
Manonmaniam Sundaranar University
Tirunelveli, Tamilnadu, India PIN 627 012



Abstract
The paper proposes an enhanced morphological contour/edge
representation algorithm for the representation of 2D binary shapes of digital images.
The concise representation algorithm uses representative lines of different sizes and
types to cover all the significant features of the binary contour/edge image. These
well characterized representative line segments, which may overlap among different
types, take minimum representative points than that of most other prominent shape
representation algorithms including MST and MSD. The new algorithm is
computationally efficient than most other algorithms in the literature and is also
capable of approximating edge images. The approximated outputs produced by the
proposed algorithm by using minimal number of representative points are more
natural to the original shapes than that of MST and MSD.

Keywords: closing, dilation, erosion, opening, representation

1. INTRODUCTION
Humans recognize objects mainly on the basis of their shapes and so its representation is an
important issue of concern in image processing and computer vision to provide the foundation for
image coding [4], shape matching and object recognition [1], content-based video processing [12],
[13], image data retrieval [14], character recognition [2], automatic visual inspection and medical
diagnostics [3]. A good shape representation algorithm should be precise, well defined, accurate,
complete, easily reconstruct able and computationally efficient.
Targeting these requirements, through these years a number of representation algorithms
have evolved focusing the shape characteristics [4]-[5], [7], [9], [15]-[16]. Charif and Schonfeld [17]
made a thinning based shape representation algorithm. Multiple structuring elements and minimal
enclosing structure elements are proposed in the scheme of Pitas et. al [7]. Algorithms including
parity check [8] and chain code [18] are also proposed for representing shape images. But the
conventional parity check is not reversible unless the shapes are very simple. Maragos attempted to

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Santhosh P Mathew, Philip Samuel, Justin Varghese & Saudia Subhash
International Journal of Image Processing (IJIP) Volume(3), Issue(6)
302
represent an image as a minimal union of translated and scaled patterns from a finite basic pattern
class. Y. M. Y. Hasan and L. J. Karam [10] proposed a reversible contour representation algorithm in
which shape images is decomposed into residual and ambiguous contours but the algorithm is too
complex in its representation and reconstruction phases.
Many basic morphological shape representations have also been employed [5], [11], [16] on
binary shape images. The morphological skeleton transform (MST) [4] represents shape as a union of
all maximal disks but the disks tend to be larger in size and highly overlapping. As a variation to the
morphological skeleton transform a decomposition scheme is proposed in [16]. The morphological
shape decomposition (MSD) [5] decomposes the binary shape into non-overlapping components of
overlapping disks each, which tend to be smaller affecting the reconstruction efficiency. Though these
algorithms could meet some of the basic requirements of a typical representation algorithm, they lose
their focus in parallely meeting other vital aspects like computational efficiency, lesser bit-rate,
minimal representative points and so on.
In this paper, we propose a new representation algorithm where a given shape is represented
as a union of a number of overlapping lines contained in the given shape. The paper is organized in 6
sections. Section 2 gives an overview of the fundamental morphological operations involved in the
shape representation scheme and explains the features of MSD and MST. Section 3 explains the
features and improved characteristics of the proposed shape representation and reconstruction
algorithms. The simulation results are provided in Section 4. Further Scope is explored in section 5
and Conclusions are finally made in Section 6.
2. MORPHOLOGICAL REPRESENTATION OPERATORS
The binary shapes extracted from images are represented before being stored in the
knowledge base. The shape so represented is reconstructed and filled to be matched or recognized
later on with a suitable input as shall be the requirement. The shape representation scheme passes
the image to be represented through a morphological pre-processing set-up. It is then subjected to
the reversible shape representation algorithms. The general morphological operations involved in
these steps, the features of the top-ranking internal shape representation algorithms, MST and MSD
are highlighted in this section
2.1 Basic Morphological Operations
In the morphological analysis of binary images, a 2D image is defined as a subset of 2D Euclidean
space R R or its digital equivalent Z Z .For a digital image A Z Z and a point, b Z Z ,the
translation of A by b is defined as
 (1)
The morphological dilation of the image A by the structuring element (SE), B expands the image
while morphological erosion of A by B shrinks the image. They are defined respectively in (2) and (3).
(2)

(3)
Opening of the binary image A by structuring element B denoted as A B , is defined as
(4)
Closing of the binary image A by structure element B denoted as A B , is defined as
(5)
2.2 The MST and MSD
The morphological skeleton transform (MST) [4] is a simple and efficient shape
representation scheme where a binary shape X is represented as union of all the maximal disks
contained in it. These maximal disks of different sizes may overlap with each other as can be
determined directly from the shape.
 (6)
Where
(7)
'\ ' is the logical difference operator, N is the largest integer such that X NB
iB=B B .... B i times is a disk of size i. The skeleton subset Si contains the centers of all maximal
and

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Santhosh P Mathew, Philip Samuel, Justin Varghese & Saudia Subhash
International Journal of Image Processing (IJIP) Volume(3), Issue(6)
303
inscribable disks of size i. A maximal disk cannot be contained in a representative disk of larger size
and the maximal disks of different sizes may overlap. So, in general
(8)
Another interpretation on these skeleton subsets is that Si is the set of centers of all disks of size i in
X that are not contained in any representative (maximal) disks of larger sizes, the shape can be
reconstructed as
(9)

Therefore, N dilations with B will be needed to reconstruct X from all the skeleton subsets. The MST
usually uses comparatively fewer numbers of larger, overlapping disks to represent a given shape.
There is no simple and obvious way of combining representative disks into more meaningful shape
components due to heavy overlapping.
The morphological shape decomposition (MSD) [5] decomposed a binary shape into a union of
certain non overlapping disks contained in the shape with minimum morphological operations. A
binary shape X is represented by the MSD as a union of certain disks contained in X .

Where
(10)
and

Again, N is the largest integer such that X NB
different sizes
(11)
. The sets of centers of representative disks of
are determined in the order given and then
(12)
The centers, Li of all the disks of size i contained in X that do not intersect with any representative
disks of larger sizes are determined by removing all the representative disks of larger sizes from the
given shape and then finding all the centers of representative disks of size i in the remaining areas.
Overlapping between disks of the same size still exists. Similar to the MST, the original image X can
be reconstructed using N dilations with B such that

Where some of the Li’s can be empty.
Thus shape can be easily represented by the components generated by MSD using the larger
number of smaller, non-overlapping disks. Though the level of redundancy and the reconstruction
cost when compared to MST are less, the numbers of disks used by the MSD are higher.

3. PROPOSED REPRESENTATION ALGORITHM
The proposed representation algorithm represents shape as a union of a number of representative
lines contained in its boundary extracted image. This algorithm is efficient than many other shape
representation algorithms, represents all type of images, even the edge extracted images with less
number of representative points. It is featured towards cost effective representation of shapes,
reduced representation error and least burden in pattern recognition applications. The operations
involved in representation and reconstruction of the shape of the object is schematically shown in
Figure 1.

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Santhosh P Mathew, Philip Samuel, Justin Varghese & Saudia Subhash
International Journal of Image Processing (IJIP) Volume(3), Issue(6)
304

3.1. Boundary Extraction and Smoothing
The noise manifestations in the shape of the object is smoothened by performing closing after
opening the input binary shape images and is represented as
(14)
In the proposed representation scheme, the internal boundary, K of the shape, A or the set of object
pixels that have at least one non-object neighbor is extracted from the morphological erosion gradient
(EG). K =EG (A, B) =A\ A B (15)
where B is a 3x3 4 or 8 connected flat structural element. The boundary extracted image is then
represented by proposed representation algorithm.
3.2. Proposed Representation Algorithm
The new approach uses four types of structural elements which are shown in Figure 2. These
structural elements represent the boundary extracted binary shape image, K as a union of maximal
representative lines such that
(16)
i N and j=1....4 . where 0
(17)
and

If there arise any two points such that
and if
one of them is arbitrarily selected and other is rejected. The sets of centers of representative disks of

different sizes
the order given, then
must be determined in
(18) and
(19)
This means that overlapping of representative lines is allowed only between lines of different types.



when compared with MSD and MST. The four basic structural elements when dilated twice with
themselves can be written as 3B1 , 3B2 , 3B3 , 3B4 and are shown in Figure 3.

Here, in this new approach the representative points used to represent a shape are very less

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Santhosh P Mathew, Philip Samuel, Justin Varghese & Saudia Subhash
International Journal of Image Processing (IJIP) Volume(3), Issue(6)
305

In this implementation, the unit line B1 is defined as B1 the size two line 2B1 is defined as

and the size three line 3B1 is defined as
defined
. In general, a line of size i and type j is


representative line segments of different types. A line is selected if it matches with some parts of the
given boundary image. Compared to MST and MSD, the overlapping level is much lower since the
overlapping between two lines segments is always reduced to a single point. Therefore the
redundancy level is much lower when compared to MST and MSD; the moderate overlapping reduces
the number of representative points needed. Consider the image in Figure 4. The MST uses twelve
representative points, the MSD uses a maximum number of fourteen points and the proposed method
uses the fewest number of six points to represent it. For an image X , the proposed representation
algorithm produces a sequence of center point sets:
3.3. Representation Seed Point Extraction
(20)
In this proposed representation algorithm, overlapping is allowed only between
.
If
is the four/eight neighbors of then
(21)
where SB is a 4 or 8 connected structural element which depends upon the seed filling algorithm. The
cardinality
on being greater than one, any one of them is arbitrarily selected as the
seed point, . The final representative set, RP for the proposed algorithm is a combination of
and . i.e.,
(22)
The seed point
ranges between zero to seven and further the region filling in the reconstruction phase of the
algorithm uses these seed point indices to reconstruct the original shape.
3.4. The Reconstruction Algorithm
The representative point set, RP of the boundary extracted binary shape generated by the
representation algorithm is used by the proposed lossless reconstruction algorithm. Similar to the
MST and MSD, the boundary image K can be reconstructed using N dilations of RCij with Bj
is stored to refer it as one of the constraints in the representative table which
 (23)
for all j=1…4
N 4 dilations are needed to reconstruct the contour/ boundary of the given shape. This
reconstruction algorithm is much faster than most other algorithms in the literature since the
overlapping level is reduced to some points of the lines. Looking into the
point set, RP the initial seed point for region filling is identified and is fed to the appropriate seed-filling
field of the representative