CHAPTER 3 PROPOSED FUZZY LOGIC BASED SEGMENTATION...

45

CHAPTER 3

PROPOSED FUZZY LOGIC BASED SEGMENTATION

APPROACHES

3.1 INTRODUCTION

Fuzzy logic is a form of multi-valued logic derived from fuzzy set

theory to deal with reasoning, which is approximate rather than precise. Unlike

binary set with crisp logic, fuzzy set has its output membership values ranging

from 0 to 1. This membership value corresponds to the degree of truth. When

membership value is high it is nearer to the expected result, and when it is low

the result is negligible. Need of fuzzy system is inevitable because Fuzzy

techniques are powerful tools for knowledge representation, processing, and has

the ability to manage the vagueness and ambiguity efficiently (Zadeh 1968).

Since echocardiographic images are noisy, ambiguity in delineating

endocardium borders can be resolved effectively using fuzzy logic.

3.2 FUZZY IMAGE PROCESSING

Fuzzy image processing is the collection of all approaches that

understand, represent and process the images, its segments and features as

fuzzy sets. The representation and processing depend on the selected fuzzy

techniques and on the problem to be solved (Hamid R Tizhoosh 2009).

Fuzzy image processing has three main stages: image

fuzzification, modification of membership values, and if necessary, image

defuzzification as given in Figure 3.1.

46

Figure 3.1 Structure of fuzzy based image processing

The fuzzification and defuzzification steps are required to

stimulate fuzzy hardware. Therefore, the coding of image data (fuzzification)

and decoding of the results (defuzzification) are steps that make it possible to

process images with fuzzy techniques. The main power of fuzzy image

processing is in its middle step (modification of membership values). After

the image data are transformed from gray-level plane to the membership

plane (fuzzification), appropriate fuzzy techniques can be applied on the

membership values to obtain desirable results. This can be a fuzzy clustering,

a fuzzy rule-based approach, a fuzzy integration approach and so on (Hamid

R Tizhoosh 2009). In this thesis, fuzzy rule based approach has been

implemented.

In many image processing applications, it is required to use expert

knowledge to overcome the difficulties (e.g. object recognition, scene

analysis). Fuzzy set theory and fuzzy logic offer powerful tools to represent

and process human knowledge in the form of fuzzy if-then rules. On the other

side, many difficulties in image processing arise because the data are

uncertain. This uncertainty, however, is not always due to the randomness but

Expert

Knowledge

Membership

modification

Fuzzy logic

fuzzy set theory

Image

defuzzificationImage

fuzzification

Input

image Result

47

due to the ambiguity and vagueness. This can be resolved by applying fuzzy

rules.

3.3 SEGMENTATION OF ECHOCARDIOGRAPHIC IMAGES

USING FUZZY LOGIC

In echocardiographic images, the transition in texture properties of

blood pool and myocardium is unique to a particular echocardiographic image

due to acoustic impedance (Issac Bankman 2008). This property is utilized to

track the endocardium. However, in presence of speckle noise and poor image

acquisition ambiguity pose a great challenge in segmentation. This thesis

presents a novel technique using Texture transition guided by fuzzy logic to

resolve ambiguity and to produce accurate results. A more generalized

technique is proposed in this thesis coined as Fuzzyshed, which combines the

flexibility of fuzzy logic and edge characteristics of gradients for efficient

image segmentation. In the proposed fuzzyshed, fuzzy rules are formulated

based on edge characteristics present in the image. This approach tries to root

out the complexity of morphological operations and gives better results when

compared with the traditional watersheds.

3.4 PROPOSED TRANSTEXTURE BASED SEGMENTATION

USING FUZZY LOGIC

3.4.1 System Overview

The proposed system starts with the key frame selected from

echocardiographic video. Pre-processing of the image is done for removing

the noise and to enhance the image quality. After pre-processing,

segmentation and tracking are performed by formulating the fuzzy rules with

the help of texture properties. Figure 3.2 shows the overall system flow

diagram of proposed Transtexture based segmentation with fuzzy logic.

48

Figure 3.2 System Flow Diagram of Proposed Transtexture

3.4.2 Forming Fuzzy Sets (Fuzzification)

In this proposed work, fuzzification of image is done using texture

properties of the image. Texture properties are calculated using Gray Level

Co-occurrence Matrix (GLCM) at desired direction. The gray-level co-

occurrence matrix P[i, j] is defined by first specifying a displacement vector

d = (dx, dy) and counting all pairs of pixels separated by ‘d’ having gray

levels ‘i’ and ‘j’ in the direction ‘s’. Any texture properties like energy,

homogeneity, Entropy and Contrast (Haralick et al 1973) can be used for

segmentation. Each texture property constitutes an input membership function

for the Fuzzy Inference System (FIS). However, running time of fuzzy based

Calculating texture

properties

Gaussian Smoothening Adaptive Thresholding

Forming the Contour

Pre-processing

Key Frame Selection

Formulating

Fuzzy Membership

Functions

Framing Fuzzy RulesFuzzy System

Evaluation

Identifying Edge Points

Segmented Output

Building Fuzzy

Inference

System

Boundary

Tracking

Input Video

49

algorithm increases with number of inputs. Hence, it is important to choose

appropriate inputs for fuzzy system.

Segmentation methods like active contours (Jierong Cheng et al

2004) and watershed (Ivana Mikic et al 1988) have proven that energy

component of an image contribute more towards edge detection.

Homogeneity is the measure of closeness in distribution of elements in Gray

Level Co-occurrence Matrix (GLCM), which assists in determining the

transitions in image at ambiguous regions. Hence energy and homogeneity

were used in this technique.

Energy = デデ P態托棚 [i , j]択辿 (3.1)

Homogeneity =デデ沢渡宕 [辿 ,棚]登套怠袋|辿貸棚| (3.2)

where P - Gray Level Co-occurrence Matrix for current pixel under

consideration

The proposed fuzzy system is shown in Figure.3.3,

Figure 3.3 Fuzzy system overview

50

3.4.3 Fuzzy Rule Formation

In this proposed work, input membership functions are chosen to

be Gaussian as these curves have the advantage of being symmetric and

nonzero at all points. Output membership functions are opted to be triangular

because these straight line membership functions have the advantage of

simplicity and produces crisp output. The Gaussian membership function is

given by the equation

Gaussian(x: ヅ,ぴ ) = e貼 (灯貼ヅ )鉄鉄涜鉄 (3.3)

Mean of the image is the average of all pixels as given in equation

(3.4). Standard deviation of the image is average deviation of one pixel from

another, as given in equation (3.5).

µ =怠朝デ捲沈朝沈退怠 (3.4)

j = 謬怠択デ (x辿伐 µ)態択辿退怠 (3.5)

where 捲沈 – Current pixel texture value.

µ – Mean of input membership function.

j – Standard deviation of input membership function.

In equation 3.3 determining µ is important in defining membership properties

which can be done using texture transition.

Any echocardiographic image can be segmented in three regions

namely endocardium, myocardium and epicardium. Texture properties of

myocardium and blood pool are constant throughout the region, therefore

µmyocardium, µBlood-pool can be assigned directly to the Gaussian input

membership function. By heart’s anatomy, endocardium is the tissue

separating myocardium and blood pool. Hence endocardium shows a

transition in texture characteristics which is illustrated in Figure 3.4. However,

51

the transition is not clear due to ambiguity caused by acoustic impedance

mismatch during acquisition. Hence, µendocardium is computed as an average of

transition values.

Figure 3.4 Transition Characteristics of LV

Figure 3.5 a, b shows the plots for input membership functions energy and

homogeneity

(a) (b)

Figure 3.5 (a) Gaussian membership functions for Energy

(b) Gaussian membership functions for Homogeneity

Figure 3.6 shows the plot for triangular membership function.

1 2 2 1

Blood-Pool

MyocardiumMyocardium

Endocardium Endocardium

52

Figure 3.6 Triangular membership functions for pixel classification

Fuzzy rules were formulated based on the knowledge of heart’s

anatomy. The rules were to exhibit the transition phenomenon explained

above. Based on input membership values the fuzzy rules guide the fuzzy

system to produce the output as edge or non edge pixel.

1. If the energy value belongs to blood pool and the

Homogeneity value belongs to blood pool then current pixel is

not an edge pixel.


Homogeneity value belongs to endocardium then current pixel

is not an edge pixel.


Homogeneity value belongs to myocardium then current pixel


4. If the energy value belongs to endocardium and the


not an edge pixel.



is an edge pixel.

- - -Non-edge

___Edge

53




7. If the energy value belongs to myocardium and the


not an edge pixel.







Figure 3.7 Fuzzy rules for Defuzzification

The fuzzy rules formation is described in Figure 3.7 and 3D-

simulation of membership rules is shown in Figure 3.8

54

Figure 3.8 3D- Simulation of membership rules

3.4.4 Results of Transtexture

Analysis of heart function was done with various views of

echocardiographic images; experiments were conducted over different views.

Several meaningful quantifications could be derived from the segmented

results; the process of quantification was given in chapter 6. Table 3.1 gives

error with respect to manual segmentation.

Table 3.1 Absolute Error Calculation for Transtexture

Axis View Number of

expert

selected

points

Number of

matching points in

Texture

based fuzzy

Absolute

error

(in

pixels)

Percentage

Error

Apical four

chamber150 133 18 12%

Apical two

chamber150 136 14 9%

Parasternal

short axis150 134 16 11%

Parasternal

long axis150 132 18 12%

55

The segmentation results of Transtexture for various views of

echocardiography are shown in Figure 3.9. For clarity, the segmented

results are overlapped over the input image.

Figure 3.9 (a) Short axis view end diastole

Figure 3.9 (b) Parasternal long axis view end diastole

56

Figure 3.9 (c) Parasternal Long axis view end systole

Figure 3.9 (d) Apical two chamber view end diastole

Figure 3.9 Segmentation results of Transtexture

57

3.4.5 Noise Resistance

Once the boundary has been tracked it is necessary to check the

robustness of the method. Speckle noise is the common noise present in the

ultrasound images (Gary Jacob et al 2002), the proposed method’s robustness

towards speckle noise needs to be analysed. Hence, to check the noise

resistance of the proposed Transtexture method, speckle noise has been added

at random (ranging from 1% to 30%) to the images and segmentation has

been performed with different edge detection methods.

Figure 3.10 a) Segmentation results of various methods on a sample

image without noise b) c) d) Segmentation results of various

methods over a sample image with noise at 10% 20% and

30% respectively.

58

The segmented curve is compared with that of experts curve and

error in segmentation due to noise is computed using the Euclidean distance

measure (Borgefors 1986). Figure 3.11, plots the error rate of various edge

detection methods against noise levels. Result shows that integration of

texture properties and fuzzy logic makes the delineation reliable up to 20% of

speckle noise. The Error Rate (ER) is calculated as,

継迎 =

軽憲兼決結堅"剣血"結捲喧結堅建"嫌結健結潔建結穴"喧剣件券建嫌伐軽剣┻ 剣血"兼欠建潔月件券訣"喧剣件券建嫌"決検"建月結喧堅剣喧剣嫌結穴兼結建月剣穴軽憲兼決結堅"剣血"結捲喧結堅建"嫌結健結潔建結穴"喧剣件券建嫌 "捲 100

Figure 3.11 Error rates of various segmentation methods against noise

levels

From Figure 3.11 it can be observed that the proposed Transtexture

based segmentation is resistive to noise level up to 15% and produces

acceptable results. Hence, the proposed system is adaptable to noisy images

which are common in ultrasound imaging.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

5 10 15 20 25 30

Erro

r Rat

e

Noise added (%)

Proposed Transtexture

Canny

Sobel

Prewitt

59

3.5 PROPOSED FUZZYSHEDS - A NOVEL WATERSHED

SEGMENTATION

3.5.1 Watershed Definition and Principles

The basic idea of watershed segmentation has been to consider the

object as catchment basins in topography. Image data can be interpreted as a

topographic surface where the gradient image gray-level represent altitudes.

Region edges correspond to high watersheds and low-gradient region interiors

correspond to catchment basins. Figure 3.12, illustrates the one dimensional

view of watersheds formation (Han Sun et al 2005).

Figure 3.12 Illustration of One dimensional watershed

3.5.2 Watershed Lines

Watershed lines are those regions which do not correspond to any

catchment basins in an image. Each region formed within a watershed line

must contain only one catchment basin. Figure 3.13 is the illustration of

watershed lines.

Inte

nsit

y

Image size

Catchment

Basin た2

Catchment

Basin た1

た1 た2

Watersheds

Minima

60

(a) (b)

Figure 3.13 a) Sample image b) Watershed lines superimposed on

original image

3.5.3 Proposed System Overview

The process had started with pre-processing step to remove

acquisition noise which is done by Gaussian filtering technique. Gradient

image was generated using Sobel mask, followed by the fuzzy flooding stage

for creating watersheds; final output will be the image with segmented

objects. Figure 3.14, shows the overall system diagram of the proposed fuzzy

shed.

Figure 3.14 System Flow Diagram of Proposed Fuzzyshed

Watershed Lines

Image

Pre-processing

Gradient image

Object detection

phase

Fuzzy flooding

Segmented

Image

Fuzzy

System

61

3.5.4 Forming Fuzzy Sets

The Gaussian membership function is given by the equation,

Gaussian(捲┺ 航┸ 購 ) 噺結貼 (猫貼杯 )鉄鉄配鉄 (3.6)

where x – Current pixel’s intensity value.

µ – Gradient value of the object under flooding.

j – Local standard deviation of the image.

Standard deviation of the image is average deviation of one pixel

from another. Figure 3.15 shows the fuzzy system structure of proposed

Fuzzyshed.

Figure 3.15 Fuzzy system structure of the proposed Fuzzyshed method

62

3.5.5 Fuzzy Flooding Phase

If g(x) is gradient over the image function f(x), then first change in

gradient magnitude represents the first object boundary. Fuzzy system

processes all neighbouring pixels and evaluates whether they belong to same

object or not. This allows object boundary detection in all possible directions.

Evaluation process is again performed on those neighbours who passed

previous evaluation and for a neighbour identified as a boundary pixel,

evaluation is not performed. This enables to end the process when entire

boundary of current object is detected. In a digital space with eight connected

neighbours there is a strong chance for a pixel to be evaluated more than

once, hence possesses a complexity of O(n2), where n is the number of pixels

in the image. So to reduce the computational complexity, evaluation is done

only to those pixels which were not processed earlier.

This evaluation process is called as fuzzy flooding, as this process

explores the entire object and stops when detecting object boundary and

avoids retracing of objects. Thus only unexplored neighbours are evaluated

there by restricting the time complexity to O(n). Figure 3.16, illustrates the

fuzzy flooding process for a sample object.

3.5.6 Iterative Phase

Fuzzy system evaluates neighbours of the first boundary pixel

identified during the previous flooding phase. Flooding phase is resumed on a

pixel which passes the evaluation. Therefore if no pixel passes the evaluation

then one of the failed neighbours is chosen as current pixel with a condition

that preferred neighbour must not belong to a set, processed in earlier

flooding phases. Before resuming the flooding process the mean value of

input membership function is set as gradient value of current pixels

neighbourhood that passed evaluation.

63

(a) (b) (c)

(d) (e) (f)

Figure 3.16 Result of fuzzy flooding on a sample image. a) Original

image (b – f) Objects identified at each flooding phase.

3.5.7 Fuzzyshed – Pseudocode.

Input : Gradient of input image, f

Output : Labeled image, L

MF: mirror of f // used to avoid repeated processing.

p: current pixel; N(p): Neighbour pixel of p;

1. f(p) 柑 Gradient of p;

2. ヅ = f(p);

3. ぴ = standard deviation of image

4. Q丹,Q脱,Q嘆柑 FIFO QUEUE;

5. p = f(1,1);

6. MF = 0; // initialize all pixels to 0;

7. while ( All pixels in f are not processed)

8. {

9. While (Q丹塙 empty) // object detection phase

64

10. {

11. p = dequeue 盤Q丹匪;12. if (MF(p) = = 0 )

13. {

14. if(Fuzzy evaluation of p is true)

15. {

16. enqueue岾Q丹,N(p)峇 ;

17. enqueue(Q嘆,p);

18. MF(p) = 1;

19. } // end of inner if

20. else

21. {

22. enqueue(p,Q脱) ;

23. } // end of else

24. }// end of outer if

25. } // end of while

26. while(Q嘆塙 empty) // Fuzzy flooding

27. {

28. p = dequeue(Q嘆) ;

29. L(p) = label;

30. }

31. label = label + 1;

32. p = dequeue(Q脱) ;

33. enqueue (Q丹,p) ;

34. µ = p; // reinitialize input membership function to current

object’s mean value.

35. }

65

Segmentation results of Fuzzyshed for echocardiographic images

for different axes views are shown in Figure 3.17. Table 3.2 gives error with

respect to manual segmentation and Table 3.3 gives Comparison of Proposed

fuzzy methods with existing methods.

3.5.8 Results of Proposed Fuzzyshed

(a) (b)

Figure 3.17 a) Sample image b) Results of proposed Fuzzyshed

Table 3.2 Absolute Error Calculation for Fuzzyshed

Axis ViewNumber of

expert

selected points

Number of

matching points

in Fuzzyshed

Absolute

error

(in pixels)

Percentage

Error

Apical four

chamber150 136 14 9%

Apical two

chamber150 142 8 6%

Parasternal

short axis150 136 14 9%

Parasternal

long axis150 138 12 8%

66

Table 3.3 Comparison of proposed fuzzy based methods with existing

methods

MethodACC if

APD<2

CA if

APD<2-2.5ACC+CA

Rejected

if APD>2.5

Canny 82.80% 2.80% 85.60% 14.40%

Prewitt 80.20% 1.60% 81.80% 18.20%

Sobel 79.00% 0.70% 79.70% 20.30%

Traditional Watershed 80.60% 1.20% 81.80% 18.20%

Texture Based Fuzzy 83.00% 2.80% 85.80% 14.20%

Transtexture 84.92% 4.40% 89.32% 10.68%

Fuzzyshed 87.24% 5.40% 92.64% 7.36%

ACC-Acceptable, CA-Conditionally Accepted, APD- Average Pixel Difference

3.6 CONCLUSION

In this chapter two novel fuzzy logic based segmentation techniques

have been proposed and discussed. The first proposed Transtexutre based

segmentation method uses endocardial border model to segment the

endocardium of Left Ventricle. Fuzzy rules were framed based on endocardial

border model and combination of texture properties such as energy and

homogeneity. This proposed fuzzy system effectively segmented

endocardium at ambiguous regions which can be observed from segmentation

results. It can be inferred from the results that Texture properties coupled with

fuzzy logic produced good segmentation results with error percentage as low

as 10.68%. Experimental results show that the novel Transtexture based fuzzy

system is highly robust to noise and produces acceptable results up to 15% of

noise. The second proposed Fuzzyshed has the unique way of stimulating

flooding process of watersheds using dynamic fuzzy rules. The novel

Fuzzyshed method overcomes the problem of over-segmentation existing in

morphological watershed, by avoiding creation of watershed lines.

Experimental results proved that proposed Fuzzyshed based segmentation is

adaptable to echocardiographic images and produces good segmentation

results with an accuracy of 92%.

CHAPTER 3 PROPOSED FUZZY LOGIC BASED SEGMENTATION...

Documents

Transcript of CHAPTER 3 PROPOSED FUZZY LOGIC BASED SEGMENTATION...