This document provides an overview of different techniques for segmenting brain tumours from MRI images using MATLAB. It includes flowcharts and descriptions of watershed transform, split and merge segmentation, localised region active contours, fuzzy c-means clustering with level sets, bounding box segmentation based on symmetry, and a spatial fuzzy clustering level set method. The document analyzes sample results and concludes the fuzzy level set method overcomes issues with other techniques like needing reinitialization or not handling multiple regions well. Future work could make the methods fully automated and extend them to 3D segmentation.

1. BRAIN TUMOUR SEGMENTATION OF
MRI IMAGE USING MATLAB

2. Contents
1. Preview
2. Flowchart
3. Background theory and/or literature reviewwork
4. Methodology
5. Result analysis
6. Conclusion and future work
7. References
Department of Electronics and Communication Engineering, MIT, Manipal

3. Preview
Department of Electronics and Communication Engineering, MIT, Manipal
1) Convert it to gray scale image.
2) Apply high pass filter.
3) Apply median filter to enhance the quality of the image.
4)Apply watershed transform; you will find that it results in
Over segmentation due to a lot of minimas.
c
start

4. 1) Apply morphological operations to the image such as
Opening and closing.
2) Calculate regional maxima to obtain the foreground
Markers and superimpose them over the original image.
3)Calculate background markers using thresholding and
Then applying the watershed transform of the distance
Function to get the water-rigde lines.
4)Superimpose the foreground ,background markers and
The segmented region in order to visualize the result. Label
Matrix can also be displayed as color matrix
stop
C
5)Superimpose this color matrix over the original image.

5. • The resulting boundaries form closed and connected regions.
• The boundaries of the resulting regions always correspond to contours which
appear in the image as obvious contours of objects.
• The union of all the regions forms the entire image region.
Advantages & Disadvantages
Advantages:
Disadvantage:
• It produces excessive over-segmentation

7. SPLIT AND MERGE SEGMENTATION

9. Advantages:
• The image could be split progressively according to our demanded
resolution because the number of splitting level is determined by
us.
• We could split the image using the criteria we decide, such as
mean or variance of segment pixel value.
• In addition, the merging criteria could be different to the splitting
criteria.
Disadvantage:
• It may produce the blocky segments.

10. localised region based active contour
1) The construction of a family of local energies at each
point along the curve.
2) Each point moves to minimize the energy computed
in its own local region.
3) local neighborhoods are split into local interior and local
exterior by the evolving curve.
4) energy optimization is then done by fitting a model to
each local region.
stop
start

13. Advantages:
• lower sensitivity to contour initialisation and noise.
• feasibility of segmentation of color images even in the absence of
gradient-defined boundaries.
• better ability to capture concavities of objects
Disadvantages:
• computational time, sensitive initial boundary, kernel size

14. 1) Set the m value, the number of clusters c and the size
Of the spatial constraint window used to average the
Membership matrix.
2) Estimate an initial bias field signal B0 from the corrupted
MRI images.
3) Calculate the membership matrix U_ik.
4) For each pixel take the average of the membership
Matrix x around a window of specified value. Normalize
the membership matrix so for each image pixel the
summation of the membership values corresponding
to different clusters equals to one.
C
start
Multi-Phase level set evolution and Bias field correction

15. 5) Calculate the prototype centres vi and estimate the bias
Field Bk.
C
6) Test if the difference between the norm of the previous
calculated membership matrix and the norm of the current
membership matrix ||Ul||− ||Ul+1|| is less than a pre-specified
error or if the algorithm exceeds certain number of iterations
than exit.
stop

17. • They are versatile, robust, accurate, and efficient techniques.
• This techniques is able to handle sharp corners and cusps in the propagating
solution, as well as topological changes, and three-dimensional effects.
• By employing fast narrow band adaptive techniques, the computational labor is
the same as other methods, with the advantages of increased accuracy and
robust modeling .
Disadvantages:
• The drawback to level set techniques is that they require considerable thought in
order to construct appropriate velocities for advancing the level set function.
Advantages:

18. Multiplicative intrinsic component optimization

20. • It is robust, accurate and efficient than the current method.
• It can be applied to higher field (e.g. 7 T) MRI scanners, the intensity
inhomogeneities have more complicated profiles than 1.5 T and 3 T
MR images.
• It is numerical stable in computation of the bias field.
• This method doesn’t require separate methods for estimating energy
and bias field, and also for segmentation of MR images.
• It is independent of initialisation
Disadvantages:
• It does not make use of contours ,rather it separates the image into
different regions.
Advantages:

21. 1) First the intracranial regions are marked.
2) On each input MR slice (axial view), FBB first locates the
left-right axis of symmetry of the brain.
3) The algorithm searches for an axis-parallel rectangle on
the left side that is very dissimilar from its reflection about
the axis of symmetry on the right side.
4) FBB algorithm finds the rectangle D, i.e., the four
unknown parameters lx, ux, ly and uy in two linear
passes of the image. It first finds ly and uy in a vertical
sweep and then finds lx and ux in a horizontal sweep
of the pair of images.
C
start
Bounding Box method based on symmetry

22. 5) Based on these values the bounding box is located.
C
stop

23. Elapsed time is 1.485019 seconds.
E(l) E(l)
w
ww
h
hh
h
h
h
w w
w
E(l) E(l)
h-height
w-width
E(l)-Energy function

24. Advantages:
• It makes use of the bounding boxes that are used to segment large
number of slices in very short period of time.
• It is fully automated and does not need any initialization.
• The importance of indexing a large number of tumour regions is that the
images of similar cases can be used for treatment of a new case.
Disadvantages:
• It only approximately segments the tumour region in the form of
rectangular boxes and does not segment the every tiny cusp or edges of
the tumour region.

25. Spatial fuzzy clustering with the level set method
1)Define membership function 𝛍 𝑚𝑛 for nth object of 𝑚 𝑡ℎ
cluster and the cost function for spatial clustering over the
MR image.
2)Apply Fuzzy clustering method to divide the image into
different clusters.
3) Choose your region of interest and apply level set
method.
4) A level set contour(purple) will segment the tumour region .
stop
start
4) After T iterations , a dialog box will appear asking whether
to continue another set of iterations. if “yes” , go back
To step 4,otherwise a green contour (final) will appear in place
of the purple contour.
Flowchart

26. • In Fuzzy clustering , the centroid and scope of each class are estimated
adaptively in order to minimize a pre-defined cost function.
• FCM uses a membership function 𝛍 𝑚𝑛 to indicate the degree of
membership of the 𝑚 𝑡ℎ
cluster to the nth object.
• The standard FCM cost function is optimized when the pixels close
to the centroid are maximized and those farther away are
minimized.
Fuzzy level set method Background theory

27.  Ј = 𝑛=1
𝑁
𝑚=1
𝐶
𝛍 𝑚𝑛
𝑙
||𝑖 𝑛 − 𝛎 𝑚||
2
: cost function
𝑚=1
𝐶
𝛍 𝑚𝑛 = 1 0 ≤ 𝛍 𝑚𝑛 = 1 𝑛=1
𝑁
𝛍 𝑚𝑛 > 0
 𝛍 𝑚𝑛=
||𝑖 𝑛 − 𝛎 𝑚||−2/(𝑙−1)
𝑘=1
𝐶 ||𝑖 𝑛 − 𝛎 𝑘||−2/(𝑙−1)
 𝛎𝑖= 𝑛=1
𝑁 𝛍 𝑚𝑛
𝑙
𝑖 𝑛
𝑛=1
𝑁 𝛍 𝑚𝑛
𝑙
 𝛍 𝑚𝑛
′
=
𝛍 𝑚𝑛
𝑃
ℎ 𝑚𝑛
𝑞
𝑘=1
𝐶 𝛍 𝑘𝑛
𝑃
ℎ 𝑘𝑛
𝑞
 ℎ 𝑚𝑛 = 𝑘∈𝑁 𝑛
𝛍 𝑘𝑛
Membership function
& it’s properties
:Centroid of the 𝑖 𝑡ℎ 𝑐𝑙𝑢𝑠𝑡𝑒𝑟
:Variable containing the spatial information
:new fuzzy variable where p and q control their
respective contribution

28. • Level set Method utilizes dynamic variational boundaries for an image
segmentation.
• It is possible to approximate the evolution of the level set contour by
tracking the zero level set 𝝘(𝑡).
• The implicit contour may be compromised of series of single or more zero
iso-contours.
• The advancing force F has to be regularised by an edge indication function
g in order to stop level set evolution near the optimal solution.
• But this method is not so stable as it has to comply with the CFL condition
and the SDF needs to be reinitialised periodically.

29. 𝝓 𝑡, 𝑥, 𝑦 < 0 𝑥, 𝑦 𝑖𝑠 𝑖𝑛𝑠𝑖𝑑𝑒 𝝘(𝑡)
𝝓 𝑡, 𝑥, 𝑦 = 0 𝑥, 𝑦 𝑖𝑠 𝑎𝑡 𝝘(𝑡)
𝝓 𝑡, 𝑥, 𝑦 > 0 𝑖𝑠 𝑜𝑢𝑡𝑠𝑖𝑑𝑒 𝝘(𝑡)
𝜕𝝓
𝜕𝑡
+ 𝐹 𝛻𝝓 = 0
𝝓 0, 𝑥, 𝑦 = 𝝓0(𝑥, 𝑦)
𝑔 =
1
1 + |𝛻( 𝐺 𝝈 ∗ 𝐼)|
𝜕𝝓
𝜕𝑡
= 𝛍𝛇 𝝓 + 𝛏(𝗴, 𝝓)
𝛇 𝝓 = ∆𝝓 − div (
𝛻𝝓
𝛻𝝓
)
𝛏(𝗴, 𝝓)=λ𝛅(𝝓)div ਣ
𝛻𝝓
|𝛻𝝓 |
+ 𝛎ਣ𝛅(𝝓)
𝝓0(𝑥, 𝑦) =
−𝐶, 𝝓0 𝑥, 𝑦 < 0
𝐶, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝝓 𝑘+1
𝑥, 𝑦 = 𝝓 𝑘
𝑥, 𝑦 +𝞽[𝛍𝛇(𝝓 𝑘
)+𝛏(ਣ, 𝝓 𝑘
)]
The new level set method:The traditional level set formulation:

30. • We go for a fast level set method which is more stable and does not
require re-initialisation of the SDF.
• 𝛇 𝝓 is the penalty momentum of 𝝓 deviating away from the signed
distance function.
• The term 𝛏 𝗴, 𝝓 𝑖𝑛𝑐𝑜𝑟𝑝𝑜𝑟𝑎𝑡𝑒𝑠 𝑖𝑚𝑎𝑔𝑒 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑖𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 attracts 𝝓
towards the variational boundary.
• The penalty term 𝛇 𝝓 forces 𝝓 to approach the genuine SDF
automatically.

31. • It begins with spatial fuzzy clustering ,whose results are utilized to initiate
the level set segmentation , estimate controlling parameters and regularize
level set evolution.
• It automates the initialization and parameter configuration using the level set
evolution , using spatial fuzzy clustering.
• The enhanced FCM can accommodate the results of FCM directly for
evolution.
The new fuzzy level set Method

32. 𝑅 𝑘: 𝑟𝑘 = 𝛍 𝑛𝑘 , 𝑛 = 𝑥 × 𝑁 𝑦 + 𝑦 : 𝑡ℎ𝑒 𝑟𝑒𝑔𝑖𝑜𝑛 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝝓0(𝑥, 𝑦)= −4𝜀(0.5 − 𝑩 𝑘): the signed distance function
𝛅 𝜀(𝝌)=
0, 𝑥 > 𝜀
1
2𝜀
1 + 𝑐𝑜𝑠 πϰ/𝜀 , 𝑥 < 𝜀
∶
𝑩 𝑘 = 𝑅 𝑘 ≥ 𝑏0: here 𝑩 𝑘 is the binary image
𝑏0(∈ (0,1)):adjustable threshold
𝛏 𝗴, 𝝓 = λ𝛅 𝝓 𝑑𝑖𝑣 𝑔
𝛻𝝓
𝛻𝝓
+ 𝗴𝙂(𝑅 𝑘)𝛅(𝛟)
The new fuzzy level set method

33. A comparison of initialisation of level set method with negative v
in (a) and a positive v in (b).
(a)
(b)

34. • The balloon force can now be derived from spatial fuzzy
clustering.
• Once approaching the object, the level set function will
automatically slow down as it comes closer to the object to be
segmented and become totally dependent on the smoothing
term.
Disadvantages:
• Without the proper use of controlling parameter, segmentation
could be excessive or insufficient.
Advantages:

35. CODE

45. Result analysis
Figure1: Fuzzy C-means clustering (FCM) applied to the MRI

46. Figure 2: A level set segmentation

47. Figure 3:The final result

48. Conclusion and Future work
• Each of the techniques segments the image appropriately. But these
methods cannot be compare on the basis of time and iterations.
• Watershed transform requires a lot of morphological operations for the
image to be properly segmented.
• In our method split-merge gives appropriate results ,but the results
should be post processed.
• Parametric active contours are not able to divide the contours if there
are multiple regions.
• In level set methods , SDF has to be reinitialized again and again.
• Bounding box only approximately segments the regions.
• Fuzzy level set method encounters all these problems. There is no
problem of re-initialization in this method and we can set the time step
large and get faster as well as stable evolution.
Conclusion:

49. Future work:
• Although these methods are able to give robust and accurate results for
much complex regions in 2-D images ,but there is always a scope of
improvement.
• These methods can be developed to be totally automated without affecting
the stability of the segmentation by reducing the number of parameters.
• But these methods can be extended to segment 3-D tissues.

50. References
[1] Ammara Masood, Adel Ali Al-Jumaily, Fuzzy C Mean Thresholding based
Level Set for Automated Segmentation of Skin Lesions, Journal of Signal
and Information Processing, 4, 66-71,2013.
[2] A.B.M. Faruquzzaman1, Nafize Rabbani Paiker1, Jahidul Arafat1, Ziaul
Karim1 , and M. Ameer Ali2, Object Segmentation Based on Split and
Merge Algorithm, 978-1-4244-2409-2, 19-21 Nov. 2008.
[3]D. Chaudhuri, B.B. Chaudhuri and C.A. Murthy, A New Split–and-Merge
Clustering Technique, Pattern Recognition Letters 13, pp. 399-409, 1998.
[4]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.
[5] Li F, Ng M, Li C. Variational fuzzy Mumford-Shah model for image
segmentation. SIAM J Appl Math 2010;70(7):2750–70,2010.

51. [6] Lions P, Mercier B. Splitting algorithms for the sum of two nonlinear operators.
SIAM J Numer Anal 1979;16(6):964–79,1979.
[7] M. E. Brummer, R. M. Mersereau, R. L. Eisner, R. J. Lewine, “Automatic
detection of brain contours in MRI data sets”, IEEE Trans. Medical Imaging, vol. 12,
no. 2, pp. 153 -166,1993.
[8] Rachana Rana1, H.S. Bhadauria2, Annapurna Singh, Study of Various Methods
for brain Tumour Segmentation from MRI Images, International Journal of Emerging
Technology and Advanced Engineering, (pp. 2250-2459), Volume 3, Issue 6, June
2013.
[9] Rajesh C. Patil, Dr. A. S. Bhalchandra, Brain Tumour Extraction from MRI Images
Using MATLAB, International Journal of Electronics, Communication & Soft
Computing Science and Engineering, 2277-9477, Volume 2, Issue 1,2011.
[10] Shawn Lankton, Student Member, IEEE, and Allen Tannenbaum, Member,
IEEE, Localizing Region-Based Active Contours,Year of Publication 2008 IEEE
transactions on image processing, vol. 17, no. 11, Nov. 2008.

52. THANK YOU!!!