various methods for image segmentation

BRAIN TUMOUR SEGMENTATION OF MRI IMAGE USING MATLAB

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

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 inOver segmentation due to a lot of minimas.

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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 andThe segmented region in order to visualize the result. LabelMatrix can also be displayed as color matrix

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5)Superimpose this color matrix over the original image.

• 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

SPLIT AND MERGE SEGMENTATION

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.

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.

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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

1) Set the m value, the number of clusters c and the size Of the spatial constraint window used to average theMembership matrix.

2) Estimate an initial bias field signal B0 from the corruptedMRI images.

3) Calculate the membership matrix U_ik.

4) For each pixel take the average of the membershipMatrix x around a window of specified value. Normalize the membership matrix so for each image pixel the summation of the membership values correspondingto different clusters equals to one.

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Multi-Phase level set evolution and Bias field correction

5) Calculate the prototype centres vi and estimate the biasField Bk.

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6) Test if the difference between the norm of the previouscalculated membership matrix and the norm of the currentmembership matrix ||Ul||− ||Ul+1|| is less than a pre-specified error or if the algorithm exceeds certain number of iterations than exit.

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• 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:

Multiplicative intrinsic component optimization

• 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:

1) First the intracranial regions are marked.

2) On each input MR slice (axial view), FBB first locates theleft-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 verticalsweep and then finds lx and ux in a horizontal sweep of the pair of images.

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Bounding Box method based on symmetry

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

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Elapsed time is 1.485019 seconds.

E(l) E(l)

w

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h

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h

h

w w

w

E(l) E(l)

h-heightw-widthE(l)-Energy function

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.

Spatial fuzzy clustering with the level set method

1)Define membership function for nth object of 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 .

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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

• 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 to indicate the degree of membership of the 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

||||: cost function

=

=

𝛍𝑚𝑛❑ ′=

𝛍𝑚𝑛❑ 𝑃 h𝑚𝑛

❑ 𝑞

∑𝑘=1

𝐶

𝛍𝑘𝑛❑ 𝑃 h𝑘𝑛

❑ 𝑞

h𝑚𝑛= ∑𝑘∈𝑁𝑛

𝛍𝑘𝑛❑

Membership function & it’s properties

:Centroid of the

:Variable containing the spatial information

:new fuzzy variable where p and q control their respective contribution

• 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 ).

• 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.

{𝝓 (𝑡 ,𝑥 , 𝑦 )<0 (𝑥 , 𝑦 )𝑖𝑠 𝑖𝑛𝑠𝑖𝑑𝑒𝝘(𝑡)𝝓 (𝑡 , 𝑥 , 𝑦 )=0 (𝑥 , 𝑦 )𝑖𝑠 𝑎𝑡𝝘(𝑡)𝝓 (𝑡 ,𝑥 , 𝑦 )>0 𝑖𝑠 𝑜𝑢𝑡𝑠𝑖𝑑𝑒𝝘(𝑡)

{ 𝜕𝝓𝜕𝑡

+𝐹 |𝛻𝝓|=0

𝝓 (0 ,𝑥 , 𝑦 )=𝝓0(𝑥 , 𝑦)

𝑔=1

1+¿𝛻(�́�𝝈∗𝐼 )∨¿¿

(, )

=λ(𝝓)div + 𝛎𝗴𝛅(𝝓) =

+𝞽[𝛍𝛇()+𝛏(𝗴, )]

The new level set method:The traditional level set formulation:

• We go for a fast level set method which is more stable and does not require re-initialisation of the SDF.

• is the penalty momentum of deviating away from the signed distance function.

• The term attracts towards the variational boundary.

• The penalty term forces to approach the genuine SDF automatically.

• 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

𝑅𝑘: {𝑟 𝑘=𝛍𝑛𝑘 ,𝑛=𝑥×𝑁 𝑦+𝑦 }: h𝑡 𝑒𝑟𝑒𝑔𝑖𝑜𝑛𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡

): the signed distance function

(𝝌)

: here is the binary image

():adjustable threshold

()𝛅(𝛟)

The new fuzzy level set method

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

(a)

(b)

• 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:

CODE

Result analysis

Figure1: Fuzzy C-means clustering (FCM) applied to the MRI

Figure 2: A level set segmentation

Figure 3:The final result

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:

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.

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.

[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.

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