An approach toward fast gradient based image segmentation

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AN APPROACH TOWARD FAST GRADIENT-BASED IMAGE SEGMENTATION
By
A
PROJECT REPORT
Submitted to the Department of electronics &communication Engineering in the
FACULTY OF ENGINEERING & TECHNOLOGY
In partial fulfillment of the requirements for the award of the degree
Of
MASTER OF TECHNOLOGY
IN
ELECTRONICS &COMMUNICATION ENGINEERING
APRIL 2016

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CERTIFICATE
Certified that this project report titled “An Approach Toward Fast Gradient-Based Image
Segmentation” is the bonafide work of Mr. _____________Who carried out the research under
my supervision Certified further, that to the best of my knowledge the work reported herein does
not form part of any other project report or dissertation on the basis of which a degree or award
was conferred on an earlier occasion on this or any other candidate.
Signature of the Guide Signature of the H.O.D
Name Name

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DECLARATION
I hereby declare that the project work entitled “An Approach Toward Fast Gradient-Based
Image Segmentation” Submitted to BHARATHIDASAN UNIVERSITY in partial fulfillment of
the requirement for the award of the Degree of MASTER OF APPLIED ELECTRONICS is a
record of original work done by me the guidance of Prof.A.Vinayagam M.Sc., M.Phil., M.E.,
to the best of my knowledge, the work reported here is not a part of any other thesis or work on
the basis of which a degree or award was conferred on an earlier occasion to me or any other
candidate.
(Student Name)
(Reg.No)
Place:
Date:

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ACKNOWLEDGEMENT
I am extremely glad to present my project “An Approach Toward Fast Gradient-Based Image
Segmentation” which is a part of my curriculum of third semester Master of Science in Computer
science. I take this opportunity to express my sincere gratitude to those who helped me in bringing
out this project work.
I would like to express my Director,Dr. K. ANANDAN, M.A.(Eco.), M.Ed., M.Phil.,(Edn.),
PGDCA., CGT., M.A.(Psy.)of who had given me an opportunity to undertake this project.
I am highly indebted to Co-OrdinatorProf. Muniappan Department of Physics and thank from
my deep heart for her valuable comments I received through my project.
I wish to express my deep sense of gratitude to my guide
Prof. A.Vinayagam M.Sc., M.Phil., M.E., for her immense help and encouragement for
successful completion of this project.
I also express my sincere thanks to the all the staff members of Computer science for their kind
advice.
And last, but not the least, I express my deep gratitude to my parents and friends for their
encouragement and support throughout the project.

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ABSTRACT:
In this paper, we present and investigate an approach to fast multilabel color image
segmentation using convex optimization techniques. The presented model is in some ways related
to the well-known Mumford–Shah model, but deviates in certain important aspects. The
optimization problem has been designed with two goals in mind. The objective function should
represent fundamental concepts of image segmentation, such as incorporation of weighted curve
length and variation of intensity in the segmented regions, while allowing transformation into a
convex concave saddle point problem that is computationally inexpensive to solve. This paper
introduces such a model, the nontrivial transformation of this model into a convex–concave saddle
point problem, and the numerical treatment of the problem. We evaluate our approach by applying
our algorithm to various images and show that our results are competitive in terms of quality at
unprecedentedly low computation times. Our algorithm allows high-quality segmentation of
megapixel images in a few seconds and achieves interactive performance for low resolution images

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INTRODUCTION:
The importance of grouping performed by the human visual system has been evident at
least since the Gestalt movement in psychology. Not surprisingly, grouping is also considered
essential for a wide range of computational vision problems. For instance, intermediate-level
vision problems such as stereo or motion estimation benefit from appropriate region support for
correspondence estimation. Higher-level problems, such as image indexing, foreground-
background separation, or recognition by parts, can also benefit from a useful segmentation of the
image. The problem of image segmentation and grouping is, therefore, a long-standing challenge
in computer vision. In 1989, Mumford and Shah introduced their famous image model, and showed
how it can be applied to many segmentation problems. Unfortunately, it is highly non-linear and
cannot be easily optimized. Existing convex approaches typically suffer from high computational
costs, especially when separating into many distinct regions.
In this paper, we propose a model incorporating all the basic aspects of the gradient-based
Mumford-Shah approach while maintaining an easy and efficiently-to-handle convex saddle point
structure to enable fast computation. Our work is inspired by the seminal previous work on the
Mumford-Shah functional by Alberti et al. And the works of Pock et al. And Strekalovskiy et al.
which build upon Alberti’s investigations. In Section II we introduce our model by considering
the binary segmentation case. We derive its unique saddle point representation and present non-
trivial extensions that allow for multi-region segmentation and proper color information treatment.
In Section III, we show how a primal-dual convex optimization algorithm can be applied to solve
the saddle point problem. To efficiently treat multi-region segmentation, we introduce a very fast,
approximative projection scheme in Section III-C. We conclude with an evaluation of our
approach and compare our results to other state-of-the-art techniques.

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CONCLUSION:
In this paper we have introduced a very fast method for unsupervised, gradient based image
segmentation. We have evaluated our approach on different test cases, and achieve high-quality
results at a fraction of the usually required computation time. This work is intended as a proof of
concept of the ideas behind the modeling and transformation process presented in Section II. We
feel that these ideas can be applied to a more general class of optimization problems that tries to
minimize gradient norms specifically excluding boundaries. While the presented approach works
autonomously, additional user input can be incorporated to increase the visual quality of the
segmentation. For example, it would be an interesting and useful extension to let the user influence
the weights for each energy term in the objective function locally at each pixel.
Because of the short computation times it would also be interesting to see real time
interaction of the user with the algorithm via some sort of GUI. The presented approach is
independent of the domain dimension, so for future work we plan to consider 3D image
segmentation and video segmentation. From a mathematical standpoint we would like to
investigate the justification of the convex relaxation process used to obtain a convex-concave
saddle point formulation in Section II and the detailed influence of the approximative projection
scheme presented in Section III-C on convergence of the algorithm. In addition, the full-color
model presented in Section II-D could be extended to have connected restriction sets (similar to
the work of Strekalovskiy et al. on the Mumford-Shah functional), which would further improve
quality.

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REFERENCES:
[1] A. Levin, D. Lischinski, and Y. Weiss, “A closed-form solution to natural image matting,”
IEEE Trans. Pattern Anal. Mach. Intell., vol. 30, no. 2, pp. 228–242, Feb. 2008.
[2] I. Kokkinos and P. Maragos, “Synergy between object recognition and image segmentation
using the expectation-maximization algorithm,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 31,
no. 8, pp. 1486–1501, Aug. 2009.
[3] T. Pock, D. Cremers, H. Bischof, and A. Chambolle, “An algorithm for minimizing the
Mumford–Shah functional,” in Proc. IEEE 12th Int. Conf. Comput. Vis., Sep. 2009, pp. 1133–
1140.
[4] E. Strekalovskiy, A. Chambolle, and D. Cremers, “A convex representation for the vectorial
Mumford–Shah functional,” in Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR),
Providence, RI, USA, Jun. 2012, pp. 1712–1719.
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J. Imag. Sci., vol. 5, no. 4, pp. 1113–1158, 2012.
[6] J. Lellmann, J. Kappes, J. Yuan, F. Becker, and C.Schnörr, “Convex multi-class image labeling
by simplex-constrained total variation,” in Proc. 2nd Int. Conf. Scale Space Variat. Methods
Comput. Vis. (SSVM), 2009, pp. 150–162.
[7] E. Strekalovskiy and D. Cremers, “Generalized ordering constraints for multilabel
optimization,” in Proc. IEEE Int. Conf. Comput. Vis. (ICCV), Washington, DC, USA, Nov. 2011,
pp. 2619–2626.
[8] T. Pock, A. Chambolle, H. Bischof, and D. Cremers, “A convex relaxation approach for
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Miami, FL, USA, Jun. 2009, pp. 810–817.
[9] D. Cremers, T. Pock, K. Kolev, and A. Chambolle, “Convex relaxation techniques for
segmentation, stereo and multiview reconstruction,” in Markov Random Fields for Vision and
Image Processing. Cambridge, MA, USA: MIT Press, 2011.

An approach toward fast gradient based image segmentation

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