International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
Fast Active Contours Evolution for Images with
Uniform Background/Foreground
Chetna Ahuja1, Vishal Dora2
Department Of Electronics and Communications
Samalkha Group of Institutes, Samalkha, India
Abstract – In this paper, we have worked on the curve evolution
for images with uniform background. Among model-based
techniques, deformable models offer a unique and powerful
approach to image analysis that combines geometry, physics, and
approximation theory. Chan-Vese used Mumford-Shah
functional and solved it using level set method for energy
minimisation. In our work we also have used the functional with
relaxed length and area term. Additionally we have used the
explicit level set. The main aim is to enhance the speed of contour
evolution. We have worked on remarkably reducing the
execution time of contour evolution. The results can simply be
tested on real biomedical images and some synthetic images with
uniform background. Finally the results in terms of execution
time have been compared.
Index Terms- Level-Set, biomedical images, synthetic images,
contour evolution.
I. INTRODUCTION
(i)
The external forces stretch the model towards the boundaries.
By creating the conditions for the extracted boundaries
smoothening and other related information about the shape,
colour etc. about the image the deformable models provide
ruggedness to both noise and non-linearity in the background
of the image.
Image Acoquisation
Contour Evolution
The need of consideration of this approach is to get the
description of the components involved in the image. The
contour is nothing more than an edge detection technique that
helps in getting the complete detail of the components
involved by segmentation.
Medical images can be corrupted by noise that can be the
difficult to analyse by the classical approach used for
segmentation. Therefore post processing is required for
eliminating unrequired object boundaries. To acquire this; an
intensive research is carried out to get aspiring results.
Deformable models are the solution to this problem.
These are the curves defined within an image that can be
controlled by the influence of internal contour energy as well
as the external image energy that tries to break the contour.
The internal forces keep the model smooth as
well as the external forces are defined to move the model
towards an object boundary or other desired features within an
image. By constraining extracted boundary gaps and allow
integrating boundary elements into a coherent and consistent
mathematical description such a boundary description can be
readily used by subsequent applications.
Active contour models are the curves that are based on energy
minimising functional that gets deformed to cover the images.
The internal energy of the contour produces the forces like
tension and provide rigidity that helps in keeping the model
uniform and the sharp edges are prevented. To balance this
internal energy arises that helps the contour to attain the
required spacing [1].
The total energy of the contour is:
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Etotal = Einternal + Eexternal
Segmented Image
Figure 1: Basic structure of Active Contours Evolution
II. RELATED WORKS
In last four decades, computerized image segmentation has
played an increasingly important role in medical imaging.
Segmented images are now used regularly in a multitude of
different applications, such as the quantification of tissue
volumes, diagnosis, localization of pathology, study of
anatomical structure, treatment planning, partial volume
correction of functional imaging data, and computerintegrated surgery. Image segmentation remains a difficult
task, however, due to both the tremendous variability of object
shapes and the variation in image quality. In particular,
medical images are often corrupted by noise and sampling
artifacts, which can cause considerable difficulties when
applying classical segmentation techniques such as edge
detection and thresholding. As a result, these techniques either
fail completely or require some kind of post processing step to
remove invalid object boundaries in the segmentation results
To address these difficulties, deformable models have been
extensively studied and widely used in medical image
segmentation, with promising results [4]
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
Deformable models are curves or surfaces defined
within an image domain that can move under the influence of
internal forces, which are defined within the curve or surface
itself, and external forces, which are computed from the image
data. The internal forces are designed to keep the model
smooth during deformation. The external forces are defined to
move the model toward an object boundary or other desired
features within an image [2].
A. Types of deformable models
There are basically two types of deformable models:
parametric deformable models and geometric deformable
models.
Parametric deformable models represent curves and
surfaces explicitly in their parametric forms during
deformation. This representation allows direct interaction
with the model and can lead to a compact representation for
fast real-time implementation. Adaptation of the model
topology, however, such as splitting or merging parts during
the deformation, can be difficult using parametric models.
Geometric deformable models, on the other hand,
can handle topological changes naturally. These models,
based on the theory of curve evolution and the level set
method, represent curves and surfaces implicitly as a level set
of
a
higher-dimensional
scalar
function.
Their
parameterizations are computed only after complete
deformation, thereby allowing topological adaptively to be
easily accommodated. Despite this fundamental difference,
the underlying principles of both methods are very similar.
Geometrically, a snake is a parametric
contour embedded in the image plane (x, y) ∈ _2. The contour
is represented as v(s) = (x(s), y(s))_, where x and y are the
coordinate functions and s ∈ [0, 1] is the parametric domain.
The shape of the contour subject to an image I(x, y) is dictated
by the functional
E (v) = S (v) + P (v)
The functional can be viewed as a representation of the energy
of the contour and the final shape of the contour corresponds
to the minimum of this energy.
B. Dynamic Deformable Models
C. Probabilistic Deformable Models
An alternative view of deformable models emerges from
casting the model fitting process in a probabilistic framework,
often taking a Bayesian approach. This permits the
incorporation of prior model and sensor model characteristics
in terms of probability distributions. The probabilistic
framework also provides a measure of the uncertainty of the
estimated shape parameters after the model is fitted to the
image data . It is easy to convert the internal energy measure
of the deformable model into a prior distribution over
expected shapes, with lower energy shapes being the more
likely.
D. Image Segmentation with Deformable Curves
The segmentation of anatomic structures—the partitioning of
the original set of image points into subsets corresponding to
the structures—is an essential first stage of most medical
image analysis tasks, such as registration, labelling, and
motion tracking. These tasks require anatomic structures in
the original image to be reduced to a compact, analytic
representation of their shapes. Performing this segmentation
manually is extremely laboured intensive and timeconsuming.
Most clinical segmentation is currently performed
using manual slice editing. In this scenario, a skilled operator,
using a computer mouse or trackball, manually traces the
region of interest on each slice of an image volume. Manual
slice editing suffers from several drawbacks. These include
the difficulty in achieving reproducible results, operator bias,
forcing the operator to view each 2D slice separately to
deduce and measure the shape and volume of 3D structures,
and operator fatigue. Segmentation using traditional low-level
image processing techniques, such as thresholding, region
growing, edge detection, and mathematical morphology
operations, also requires considerable amount of expert
interactive guidance. Furthermore, automating these modelfree approaches is difficult because of the shape complexity
and variability within and across individuals [8].
E. Snakes: Active Contour Model
While it is natural to view energy minimization as a static
problem, a potent approach to computing the local minima
of a functional is to construct a dynamical system that is
governed by the functional and allow the system to evolve to
equilibrium. The system may be constructed by applying the
principles of Lagrangian mechanics. This leads to dynamic
deformable models that unify the description of shape and
motion, making it possible to quantify not just static shape,
but also shape evolution through time. Dynamic models are
valuable for medical image analysis, since most anatomical
structures are deformable and continually undergo no rigid
motion in vivo. Moreover, dynamic models exhibit intuitively
ISSN: 2231-5381
meaningful physical behaviours, making their evolution
amenable to interactive guidance from a user.
Active contour models – known colloquially as snakes – are
energy-minimising curves that deform to fit image features.
Snakes lock on to local minima in the potential energy
generated by processing an image. (This energy is minimised
by iterative gradient descent, moving the model according to
equations of motion derived using the calculus of variations; a
simple Euler time-stepping scheme can be used for this
purpose, but a semi-implicit scheme is theoretically more
stable.) In addition, internal (smoothing) constraints produce
tension and stiffness that keep the model smooth and
continuous, and prevent the formation of sharp corners;
external constraints may be specified by a supervising process
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
or a human user. A pressure term can also be added to make
the models expand like balloons or bubbles. Active contour
models provide a unified solution to several image processing
problems such as the detection of light and dark lines and
edges; they are often used to segment spatial and temporal
image sequences. Unfortunately, the energy minimisation
process is prone to oscillation unless a very small time step is
used, with the side-effect that convergence is slow.
In this paper we are working on parametric
deformable models. We have combined the low- level and
mid-level image processing. The segmentation of images with
uniform background are calculated. The time of execution is
reduced without affecting the efficiency of the contour
evolution. As per increasing technology, time is the greatest
factor and to minimise it is one of the biggest achievement. So
by variations in previous work, we are trying to achieve our
goal [9].
III. PURPOSED METHODOLOGY
The most basic properties of three new variational problems
which are suggested by applications to computer vision. In
computer vision, a fundamental problem is to appropriately
decompose the domain R of a function g(x, y) of two
variables. The snake is an energy-minimising parametric
contour that deforms over a series of time steps:
Esnake = ∫
element
(u(s, t)) ds
From (i) we can define Einternal as:
Einternal (u) = ( ) | |
( )|
|
And Eexternal as:
|
Eexternal (u) = k |
The active contours are called snakes are defined in (x,
y) plane through the function:
[
]
[ ]
The related discrete deformable model, the active contour,
is changed, in subsequent iterative steps, by deformations
guided and limited in order to minimize the following
functional:
Esnake = ∫
Econ (V(s)) ds
(V(s)) ds = ∫ (
(V(s)) + Eimage (V(s)) +
This is defined as a sum of energy terms. These energies can
be divided into two main groups, internal energies, function of
the same V(s) contour at a certain time step, and external,
functions that take into account characteristics of the
processed images such as edges and luminance peaks. The
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external energy drives the active contour towards the desired
points or boundaries within the image plane. The internal
energy tries to keep the snake connected and consistent,
preserving characteristics like steadiness, smoothness, tension
and stiffness [3]. The image smoothing is such that we can
apply the smoothing and the detection in any order [12].
A new model for active contours to
detect objects in a given image, based on techniques of curve
evolution, Mumford–Shah functional for segmentation and
level sets. The model can detect objects whose boundaries are
not necessarily defined by gradient. The image segmentation
aims at extracting meaningful objects lying in images either
by dividing images into contiguous semantic regions, or by
extracting one or more specific objects in images such as
medical structures.
The active contour evolution is a classical approach
of detecting the edges of the images. If the contour spread like
a 2-d curve and then emerge like an area that covers the entire
region like a removable boundary. It highlights the region
where the uniformity of the structure deforms.
The approach has great importance in biomedical images and
surveillance. The concept has been used from years but the
time in achieving the contours is too much.
We proposed an algorithm that
works in the same manner but the time for evolution is
reduced to remarkable levels. The algorithm on which we
have worked is considered from the previous work only.
The algorithm works as:
0
 STEP 1: Initialise ɸ at n=0.
 STEP 2: Compute C1 and C2 by Chan-Vese
functional.
n+1
 STEP 3: Solve PDE to obtain ɸ
 STEP 4: Evaluate C1 and C2.
 STEP 5: Stop if converge.
 STEP 6: Else go to STEP 2
The steps goes as firstly initialise the curve that covers the
whole part to be segmented like an eclipse. Then it starts
covering the segments in a way that the inner part is known as
C1 and the outer part is known as C2. These are the intensities
inside and outside the contours. Further we obtain the PDE
which comprises of internal energy and external energy terms
like µ ,ν ,λ. Solve these terms and bring them in equilibrium to
obtain ɸn+1 .With the functional we obtain the values of C1 and
C2 i.e. the mean intensities of the contours. If the contour
stops converging more than the stops the process, the
segments are attained. Else keep on working on the process
till the final segments are not attained. This algorithm is
amendment in the existing algorithm proposed by Chan-Vese.
IV. EXPERIMENTAL RESULTS
On following the algorithm, the speed of the contour
evolution can be increased remarkably. The contour evolution
is very applicable in determining the affected areas in terms
of biomedical images. Also there effect can be used in
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
surveillance techniques. The images with the uniform
background show effective results in this algorithm. Some of
the synthetic images have also been worked upon that have
shown good results. Images with noisy background are also
detectable to some extent.
Figure 3: Synthetic Image
Figure 2: Image showing original image and their segmented images.
The results can be drawn for the real images but the algorithm
works for some synthetic images and tries to evolve the
contours for some non-uniform, noisy background images.
The result for synthetic image is shown in figure.3.
The result gives the complete description of the
comparison that we have tried to explain through our research.
The results deal with the time taken in execution of the code
without affecting the efficiency of the contour evolution. This
work provides simple and fast contour evolution approach.
Figure 4: Segmented Image
The time taken in deforming the model has been reduced.
The result has been taken for both real as well as synthetic
images. The images are firstly converted to grey scale and
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
then the segmentation is done. The algorithm works for
reducing the time taken for contour evolution but the
efficiency remains the same, i.e. the area segmented remains
the same, the iterations are being reduced with the coding.
TABLE I
TIME REDUCTION IN EXECUTION OF ACTIVE CONTOUR MODEL
Titles/Figure
values
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Old Method
New Method
8 min 30 sec
(510 sec)
12 min
(720 sec)
8 min 23 sec
(503 sec)
10 min
(600 sec)
14 min
(840 sec)
3 sec
Segmented
Ratio
0.115861
11 sec
0.017590
8 sec
0.088375
8 sec
0.084337
9 sec
We can see that the efficiency remains the same as the
segmented ratio comes equal in both the algorithms but the
time leap is tremendously reduced.
Figure.7 plots the comparison between the two algorithms and
we can see the difference in execution time of both the
algorithms.
Comparison
1000
840
800
720
600
600
510
0.104173
503
400
200
Old Method
0
1000
840
800
510
600
503
200
0
0.01759
0.088375
0.084337
0.104173
Figure 5: Graph showing time taken by old method v/s segmented ratio
New Method
12
8
8
8
9
6
2
[1]
[2]
3
[3]
[4]
0
0.115861
0.01759
0.088375
0.084337
0.104173
Figure 6: Graph showing time taken by new method v/s segmented ratio
Now as individually we have plotted the graph between the
segmented ratio and the time taken by both the algorithms as
shown in figure.5 and figure.6. corresponding to the Table I.
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8
9
0.084337
0.104173
The deformable model is the efficient tool used for analysis of
the segments of an image, as the uniformity is the key
factor .if the uniformity of the image is maintained the
segments emergence is least. With all the non-uniformities,
the contour break in segments and that is the main concept of
our research[1]. We have successfully shown the results for
fast contour evolution. The graph explicitly explains the
difference in time by the base approach In our base paper the
idea of using the explicit equation for the contour evolution.
In original paper,‘ µ‘ is set to be zero which is the area term.
In our work we have set both ‗ν‘ (length) and ‗µ‘ (area) as
zero. There is tremendous leap in execution time by using the
new functional.
11
10
8
0.088375
V. CONCLUSION
400
0.115861
11
0.01759
Figure 7: Comparison between time of execution the two methods of contour
evolution
720
600
4
3
0.115861
[5]
[6]
[7]
REFERENCES
Vese, L.A., Chan, T.F.: A multiphase level set framework for image
segmentation using the Mumford and Shah model. Int‘l Journal of
Computer Vision 50(3) (2002) 271–2
D. Mumford and J. Shah, ―Optimal approximation by piecewise
smooth functions and associated variational problems,‖ Commun. Pure
Appl.Math, vol. 42, pp. 577–685, 1989.
M. Kass, A. Witkin, and D. Terzopoulos, ―Snakes: Active contour
models,‖ Int. J. Comput. Vis., vol. 1, pp. 321–331, 1988.
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. In:
IEEE Int‘l Conf. on Computer Vision. (1995) 694–699.
Gonzalez, C. R. ve Woods, E. R.: Digital image processing, USA:
Addison –Wesley Publishing, p. 976, 1993.
S. Osher and J. A. Sethian, ―Fronts propagating with curvaturedependent speed: algorithms based on Hamilton-Jacobi formulations,‖
J. Computational Physics, vol. 79,pp. 12–49, 1988.
J.A. Sethian. Level Sets Methods and Fast Marching Methods:
Evolving Interfaces in Computational Geometry, Fluid Mechanics,
http://www.ijettjournal.org
Page 2633
International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6- June 2013
[8]
[9]
[10]
[11]
[12]
[13]
Computer Vision, and Material Science. Cambridge University Press,
1999.
T. Cohignac, C. Lopez, and J.M. Morel. Integral and local affine
invariant parameters and application to shape recognition. In D. Dori
and A. Bruckstein, editors, Shape Structureand Pattern Recognition.
World Scientific Publishing, 1995.
Invins et.al.Snakes-Active Contour Model
C. Xu, J.L. Prince, Snakes, shapes, and gradient vector flow, IEEE
Trans. Image Process. 7 (3) (1998).
G. Sapiro, Geometric Partial Differential Equations and Image
Analysis, Cambridge University Press, New York, 2001.
N. Paragios, R. Deriche, Geodesic active contours and level sets for the
detection and tracking of moving objects, IEEE Trans. Pattern Anal.
Machine Intell. 22 (3) (2000) 266–280.
D.Jayadevappa, S.Srinivas Kumar, and D.S.Murty, A New Deformable
Model Based on Level Sets for Medical Image Segmentation, IAENG
International Journal of Computer Science, 36:3, IJCS_36_3_01.
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