# Detection of Alzheimer’s Disease Using Fractional Edge Detection

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**Corresponding Author:**Reju John, Department of Electronics and Communication Engineering, College Of Engineering, Cherthala, An Institution Of IHRD, Kerela, India, Email: [email protected]

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Received Date: Sep 10, 2018 /
Accepted Date: Sep 22, 2018 /
Published Date: Sep 29, 2018 *

### Abstract

The work consists of two phases. The rest phase of the work aims at ending out the optimized value of the fraction used in fractional filtering for image enhancement techniques in digital image processing. The work is done on MATLAB platform. The work starts with a comparative study of fractional order filter and integer order kernel filter like Sobel and Prewitt filter, used for edge detection and boundary detection of various digital images. With the view of applying fractional filtering in medical images, the work is done by utilizing Magnetic Resonance Imaging (MRI). The noise performances of these filters are analyzed upon the addition of random Gaussian noise. The Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR) of the detected images are adopted as evaluation methods for comparison. The visual comparison of the filter capability in medical image enhancement is presented in this project. It has been proved that fractional filter outperforms integer order filter. In the second phase fractional filtering with the optimized value of the fraction is utilized for the detection of Alzheimer disease (AD) from MRI scan of the brain. Based on MSE and PSNR optimized value for the fraction used in fractional filtering is found out to be 0.5. The fractional filter with fraction equal to 0.5 is used to detect Alzheimer’s disease. This could progressively help in understanding and treating Alzheimer’s disease.

**Keywords:**
Fractional filtering; Optimized image processing; Alzheimer's disease; Magnetic resonance imaging

#### Introduction

The image processing applications are invading people's lives. Being an important area of information technology, image processing problems have been a research focus for decades. Edge detection is a main part in digital image processing, as it is considered a preliminary step in image analysis and pattern recognition. Edges are the sudden changes of discontinuities in an image. They occur at the boundary between two different intensity regions in the image [1]. Edge detection methods mainly use integer-order filter, namely rest order derivative of the gradient operator or the second order derivative Laplacian operator. These operators are considered to be noise sensitive. How to detect the image edges while reducing noise is a core in the edge detection study [2]. The use of fractional order calculus in designing edge detection fractional filter greatly enhances the edge detection methodology, regarding noise sensitivity and the controllability of image features through targeting certain frequency components.

Fractional calculus, also called non integer order calculus, is a generalization of the integer order calculus. The concept of fractional calculus appeared at the same era with the integer- order calculus early in the nineteenth century. Due to the efforts of many scientists, in the past two hundred years, fractional calculus has developed to be a standalone pure mathematical branch [3]. Integr- order Kernel filter is mainly used for edge detection purpose in image processing. The Problems associated with the above filter are:

• Noise sensitive

• Possibilities of the loss of image details while using especially rest order filters

In image processing, it was found that the fractional differential operators have many advantages over the integer order ones. The fractional derivative involves infinite number of terms, unlike the integer derivative which involves just infinite terms. Thus, the fractional derivative is considered to be a global operator. The fractional operator can consider more neighboring pixels information, extracting more image texture details. There exist different definitions of fractional differentiation. They are Grunwald-Letnikovs (G-L) definition, Riemann-Liouvilles definition and Caputos definition [4]. In this Project G-L definition is used for developing the mask required for fractional filtering which is a solution to the problem defined.

The aim of the project is to optimize fractional filtering and thereby applying the same for the early detection of Alzheimer’s disease. Following are the aim and objectives of the work:

• To perform a comparative study of fractional filter and integer order filter in edge detection of a given MRI image

• The performance of the filters is to be evaluated based on MSE and PSNR values of the filtered image after adding a random Gaussian noise on the original image

• To and the optimum value of the fraction

• To apply fractional filtering with the optimized fraction for detecting Alzheimer’s disease from MRI scans

#### Fractional Calculus Based on G-L Definition

Fractional calculus is also called as non-integer order calculus, is considered as a platitude of integer order calculus. The concept of fractional calculus appeared at the same era as that of integer order calculus early in nineteenth century. Due to the e orts of many scientists, in the past two hundred years, fractional calculus has developed to be a standalone pure mathematical branch [3,4]. In image processing, it was found that the fractional differential operators have many advantages over the integer order ones. The fractional derivative involves infinite number of terms, unlike the integer derivative which involves just infinite terms. Thus, it is considered to be a global operator. There exist different definitions of fractional differentiation. They are Grunwald-Letnikovs (G-L) definition, Riemann-Liouvilles definition and Caputos definition. In this project Grunwald-Letnikovs (G-L) definition is used to develop a fractional order filter. It is defined as follows:

1

By Taylors theorem,

2

3

4

5

From equation (5) it is clear that the fractional derivative has boundless number of terms, unlike the integer derivative which involves just infinite terms. The fractional operator can consider more neighboring pixels information, extracting more image texture details.

By the use of the G-L definition, the classical rest-order Sobel operator is generalized to constitute a fractional-order [5] operator for edge detection The fractional order filter mask (from G-L definition) used in this project is shown in **Table 1**.

G-L definition | ||
---|---|---|

(( 2 - )/4 | ( 2 - )/2 | ( 2 - )/4 |

-( )/2 | - | -( )/2 |

01-Feb | 1 | 01-Feb |

**Table 1:** Fractional Order Filter Mask.

#### Results and Discussions

The simulation is done in MATLAB software. The study was conducted on MRI images. As the rest step a random Gaussian noise with mean equal to 0 and variance equal 0.003 variance is added to the gray scale image of the MRI scan and the masks (both First order and fractional Order Sobel Mask) were used for detecting the edges of the noisy image. The images obtained in the case of fractional filtering extract more image texture details. It is because of the fact that it can consider more neighboring pixels information.∞

**Optimization of fractional filter**

The detection was performed with various values of the fraction on a number of MRI images and each is quantitatively compared with First order filter. Two quantitative parameters were used to compare the performance of integer order filter and fractional order filter:

MSE- The rest parameter is the mean square error.

PSNR- The Peak signal to noise ratio of the edge detected noisy images is found out by the expression PSNR = 10 log(256^{2}=MSE).

The MSE and PSNR values were obtained for Sobel, Prewitt rest order filters and fractional order with various fractions. The average of those values for different MRI scans is tabulated in the table shown in **Table 2**.

S.no. | Filter Type | MSE | PSNR |
---|---|---|---|

1 | Sobel First Order | 7380 | 9.48 |

2 | fractional order with =0.1 | 13383 | 6.9 |

3 | fractional order with =0.28 | 8136 | 9.06 |

4 | fractional order with =0.5 | 2934 | 13.5 |

5 | fractional order with =0.7 | 4546 | 11.6 |

**Table 2:** Comparative study of filters in terms of MSE and PSNR.

From this analysis it was concluded that for a fractional filter, at 0.5 the MSE is at its minimum value and PSNR at its maximum value. Hence the fraction 0.5 is found to be the optimized value.

#### Methodology Used in Detection of Alzheimer's Disease

The MRI scan datasets are obtained from www.oasis-brains.org. The data format is analyzed format. The T2 axial MRI scan is extracted from the dataset. A series of image processing techniques are applied to the MRI before the volumetric measurement of gray matter and white matter. A sample MRI image of a 16 year old male is taken into consideration as shown in **Figure 1**.

**Boundary detection**

One of the initial steps to analyze the MRI is to isolate gray matter and white matter. To do this the cranium or the skull has to be removed. This is done by boundary detection algorithm till the region of interest was visible. The skull removed image of the above sample MRI image is shown in **Figure 2**.

**Segmentation**

Edge detection method was adopted using the optimized fractional filter to separate the gray matter from the boundary detected image. We have proved that at fraction 0.5 the fractional filter performs at its best [6]. The mask used for fractional filter by setting the fraction to 0.5 is shown in **Table 3**.

Fractional Order Filter Mask | ||
---|---|---|

0.0625 | 0.125 | 0.0625 |

-0.25 | -0.5 | -0.25 |

0.5 | 1 | 0.5 |

**Table 3:** Fractional Order Filter Mask with = 0:5.

By proper thresholding gray matter is obtained as shown in **Figure 3**.

**Volume calculation**

Using MATLAB commands the volume of gray matter and white matter were evaluated. Based on the volumetric difference (D) between gray matter and white matter brain condition were classified [7] as follows: D< 60mm3 - Healthy Brain; 60< D <100mm3 - Chance of normal Atrophy; D>100mm3 - Chance of AD.

The above steps were carried out for different MRI scan of different cases. The result and inference obtained are tabulated in **Table 4**.

S.no. | Age | Gray matter Volume | White matter volume | Volume difference | Comment |
---|---|---|---|---|---|

1 | 16 | 382 | 438 | 50 | Healthy |

2 | 62 | 344 | 415 | 71 | Chance of Atrophy |

3 | 65 | 261 | 561 | 300 | Chance of AD |

4 | 63 | 495 | 536 | 41 | Healthy |

**Table 4:** Numerical Results.

#### Conclusions

Medical Imaging has played a very important role in the study and diagnosis of a lot of diseases over the past four decades. One of which is Alzheimer disease (AD), specially the use of the Magnetic Resonance Imaging (MRI) in detecting its progress. The AD is a progressive degenerative disease of the brain that leads to dementia. It leads to nerve cell death and tissue loss throughout the brain. Over time, the brain shrinks dramatically, especially in the hippocampus, affecting nearly all the brain functions. Also, the ventricles (uidlled spaces within the brain) grow larger. These changes can be visually noticed by the MRI. The fractional filter can be used for edge detection in analyzing such progressions thereby it can be an aid for the early detection of AD.

#### Limitation

One cannot arrive at a clear demarcation to distinguish AD and normal atrophy when the difference in gray matter and white matter volume lies on the borderline. As detailed in [6] the decrease rate in the case of AD is 1% per year as compared to the sluggish rate in the case of a normal atrophy. The limitation can be done away with a repeated check up with in a gap of 6 months.

#### Future Scope

One of the major externally unnoticeable symptoms in an AD patient is the brain shrinkage especially grey matter volume. The fractional filter can be used for edge detection in analyzing such progressions thereby it can be an aid for the early detection of AD. This can serve as a teaching aid for the medical students to validate their understandings. The use of image processing for medical diagnosis is increasing extensively during these days. The work moves in a direction beneficial to the medical community.

#### References

- Gonzalez RC and Woods RE (2002) Digital Image Processing- 2nd edition. Prentice Hall.
- Torre V and Poggio TA (1986) On edge detection, IEEE Trans. Pattern Analysis and Machine Intelligence 8: 187-163.
- Oldham KB and Spanier J (1974) The Fractional Calculus, Academic Press.
- Whalley LJ (2012) Spatial distribution and secular trends in the epidemiology of Alzheimer's disease, Neuroimaging Clin N Am 22: 1-10.
- .Ismail SM, Radwan AG, Madian AH and Mohamed F (2016) Comparative Study of Fractional Filters for Alzheimer Disease detection on MRI Images, IEEE, 39th International Conference on Telecommunication and Signal Processing 720-723.
- John Rand Kunju N (2018) Optimization of Grunwald-Letnikov's (G-L) based Frac-tional Filter Used for Image Enhancement. IEEE International conference on inventive communication and computational technologies.
- https://www.alzforum.org

Citation: John R, Kunju N (2018) Detection of Alzheimer’s Disease Using Fractional Edge Detection. Global J Technol Optim 9: 230 DOI: 10.4172/2229-8711.1000230

Copyright: © 2018 John R, et al. This is an open-access article distributed under the terms of the creative commons attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.