# Image Fusion based Edge Detection Using Mathematical Morphology

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#### Image Fusion based Edge Detection Using Mathematical Morphology

M.Prema Kumar1, Dr. P. Rajesh Kumar2

1Associate Professor, Department of ECE, Shri Vishnu Engineering College for Women, Bhimavaram.

2Associate Professor, Department of ECE, AU College of Engineering, Andhra University, Visakhapatnam.

Abstract: Edge detection is one of the most commonly used operations in image analysis, and there are probably more algorithms in the literature for enhancing and detecting edges. Edges form the outline of an object. An edge is the boundary between an object and the background, and indicates the boundary between overlapping objects. If the edges in an image can be identified accurately, all of the objects can be located and basic properties such as area, perimeter, and shape can be measured. In this paper, we extract the detailed edge information by the fusion of proposed two edge detection algorithms, Adaptive Multi-Structure Morphological Edge detection algorithm and Adaptive Multi-Scale Morphological Edge detection Algorithm. Finally, the experiment results indicate that the novel algorithm ensures the continuity, integrity, and accurate location of image edge than other edge detection operators using mathematical morphology.

Keywords: Mathematical Morphology, Edge Detection, Image Processing.

1. INTRODUCTION

Edge detection is a very important area in the field of Computer Vision. Edges define the boundaries between regions in an image, which helps with segmentation and object recognition. They can show where shadows fall in an image or any other distinct change in the intensity of an image. Edge detection is a fundamental of low-level image processing and good edges are necessary for higher level processing [1]. Mathematical morphology

[2] is a nonlinear filtering method. In the traditional edge detection algorithm based on morphology, the structure element (SE) is fixed, symmetric, and single, so the extracted edge has the deficiency of discontinuity and blurring.

However, for a real time image processing, the single edge detection method [7] can only reflect the edge information from certain aspect, and it is not effective to extract the edge with only one structure or only one scale [3]. This paper proposes adaptive multi-structure and adaptive multi-scale morphological edge detection algorithm based on image fusion. It fuses the edge extracted by multi-structure elements with the one detected by multi-scale elements to get the final binary edge image with optimal threshold segmentation. The experimental results indicate that the new edge detection algorithm can reasonably consider accurate edge location. The steps of new algorithm are shown in figure 5.

This paper is organized as follows: Section 2 presents Mathematical Morphological operations, Section 3 presents, Adaptive Multi-structure Morphological Edge detection algorithm, Section 4 presents Adaptive Multi- scale Morphological edge detection algorithm, Section 5 presents image fusion using PCA, Section 6 presents

Experimental results, and finally Section 7 reports conclusion.

2. MATHEMATICAL MORPHOLOGY

In morphology, basic operations include erosion, dilation, opening and closing [4]. The erosion of an image I by a flat structuring element b at any location (x,y) is defined as the minimum value of the image in the region coincident with b when the origin of b is at (x,y). In equation form, the erosion at (x,y) of an image I by a structuring element b is given by

[ I b] (x,y) = min {I(x + s, y + t)} (1)

(s,t)

The dilation of an image I by a flat structuring element b

at any location (x,y) is defined as the maximum value of

the image in the window outlined by when the origin of is at (x,y). In equation form, the erosion at (x,y) of an image I by a structuring element b is given by

[I b] (x,y) = max {I(x – s, y – t)} (2)

(s,t)

The opening of image I by structuring element b, denoted

I b is

I b = (I b) b (3)

Similarly, the closing of I by b, denoted I b, is

I b = (I b) b (4)

3. EDGE DETECTION USING ADAPTIVE MULTISTRUCTURE MORPHOLOGICAL

ALGORITHM

Because of the unicity and fixity of SE in traditional edge detection using mathematical morphology, there are two main deficiencies [5]: on the one hand a single SE can only detect the edge of the same direction with the SE, but is not sensitive to different directions; on the other hand large-scale SE has strong ability to restrain noise, but the detected edge image is rough, small-scale SE is good at checking the details of the edge, but weak at noise suppression. In order to effectively restrain noise and preserve image edge information, we use multi- structure morphological adaptive algorithm to get the edge images. We calculate the gray scale distance of original image to adaptively define the weights of SEs.

The eight structuring elements of different directions with the size of 5X5 are shown in figure 1.

 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SE with 00 SE with 22.50
 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 SE with 450 SE with 67.50 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 SE with 900 SE with 112.50 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 SE with 1350 SE with 157.50

G4(x,y) = d2 + d3 +d4 + d5 + d7 + d8 + d9 + d10 + d11 +d12

+ d13 + d14 +d15 + d16 + d17 + d18 + d19 + d21 + d22 +d23

+d24+ d25 ; —for direction 67.50

G5(x,y) = d2 + d3 +d4 + d5 + d6 + d8 + d9 + d10 + d11+d12

+d13 + d14 + d16 + d17 + d18 + d19 + d20 + d21 + d23+ d25 ;

—-for direction 900

G (x,y) = d

+ d +d

+ d + d

+ d + d + d + d +d

6 2 3 4 5

6 7 9 10

11 12

+ d13 + d14 + d15 + d17 + d18 + d19 + d20+d21 + d22 +d23

+d24+ d25 ;

—for direction 112.50

G7(x,y) = d2 + d3 +d4 + d5 + d6 + d8 + d9 + d10 + d11+d12

+d13 + d14 + d16 + d17 + d18 + d19 + d20 + d21 + d23+ d25 ;

—-for direction 1350

G8(x,y) = d2 + d3 +d4 + d5 + d6 + d7 + d8 + d10 + d11

+d12 + d13 + d14 + d15 + d16 +d18 + d19 + d20+d21 +d24+ d25 ;

—for direction 157.50

As for the whole image, the gray-scale distances of each edge and adaptive weights of SEs can be calculated as below:

M 1

EDk =

x2

N 1

y2

Gk (x,y), k=1,2,.,8 (6)

Figure 1. SEs with different directions.

8

wk = EDk / (

k 1

EDk ) , k=1,2,.,8 (7)

 a9 a8 a7 a6 a5 a10 a23 a24 a25 a4 a11 a22 a1 a2 a3 a12 a21 a20 a19 a18 a13 a14 a15 a16 a17

The edge E extracted adaptively by multi-structure morphology is given by

8

Figure 2. Image Sub-block

E1=

k 1

wk [(I bk ) bk -( I bk ) bk) ] (8)

Figure 2 shows the sub-block with the size 5X5, in which a1 is the gray-scale value of the center pixel, and a2,a3,a4..,a25 stand for its neighborhood gray scale value, then the gray-scale distance of a1 and its neighborhood can be performed as:

dk= |a1-ak|, k= 2,3,4,.,25. (5)

The larger the gray-scale distance, the higher extent of salutation, and the bigger possibility that the pixel is an edge point in the image. The Edge Gray-Scale distances of a1 can be defined as follows.

G1(x,y) = d4 + d5 + d6 + d7 + d8 + d9 + d10 + d12

+d13 + d14 + d15 + d16 + d17 + d18 + d19 + d20 + d21 + d23+

d24 + d25 ; –for direction 00

G2(x,y) = d4 + d5 + d6 + d7 + d8 + d9 + d10 + d12

+d13 + d14 + d15 + d16 + d17 + d18 + d19 + d20 + d21 + d22

+ d23+ d24 + d25; –for direction 22.50

G3(x,y) = d2 + d3+ d4 + d6 + d7 + d8 + d9 + d10 + d11 + d12 + d14 + d15 + d16 + d17 + d18 + d19 + d20 + d22 + d23+

d24 ; —-for direction 450

4. EDGE DETECTION USING ADAPTIVE MULTISCALE MORPHOLOGICAL

ALGORITHM

Multi-scale morphology overcomes the contradictions of large-scale SEs, and small-scale SEs are good at keeping edge This operator takes advantages of large-scale SE to identify edge reliably, as well as location property of small-scale SE to track edge from coarse to fine, then uses the approach of adaptively determining weight based on image variance to synthesize the edge image.

Multi-scale SE is defined as: bb.b. (9)

Where b and k are scale parameter and limited SE, respectively. The equation expresses that large-scale element is derived from a series of dilation operations of small-scale SEs. In this paper b is a 5×5 crisscross structuring element.

The algorithm is for edge detection using multi-scale is as follows:

Step 1: Obtain the mean value images using open-close morphological filters in different scales:

Ik(x,y)= ( Ibkbk + I bkbk )/2 (10)

Step 2: Use the mean value images got in step 1 to calculate the image variances in different scales:

2 =|I – I |2 (11)

k k

Step 3: According to image variances above, the weighting coefficient:

k

n

wk= 2/

k

2 (12)

Step 4: Tkhe1n the edge extracted by multi-scale adaptive morphology is given by following equation:

n

E2= [ wk [(I bk ) bk – ( I bk ) bk) ] (13)

k 1

5. EDGE IMAGE FUSION USING PCA

From the two sections above, we get two images of edge detection, in which E1 is the edge image extracted adaptive multi-structure morphology, and E2 is detected by adaptive multi-scale morphology. These two edge images are fused into a single image using PCA and calculate final detected binary edge image with optimal threshold segmentation.

The PCA based image fusion is summarized as follows:

The PCA fusion method calculates the output image as a weighted sum of input images, where the weights are the elements of the dominant eigenvector [6]. The set of N input images is organized into a matrix X, where each row is a lexicographically ordered input image. Let vector be the average of all the rows in X, and let e be a column vector with all elements equal to 1.

The covariance matrix is given by

(12)

Where M is the total number of pixels in an image.

The fused image is given by

(13)

where vj is the jth component of the dominant eigenvector, corresponding to the largest eigenvalue of C.

6. EXPERIMENTAL RESULTS

Proposed Edge detection mechanism is performed on a Lena 256*256 pixel image that consists of a total of 65536 pixels. The RGB colored image have been converted to grayscale image to specify a single intensity value that varies from the darkest (0) to the brightest

1. for each pixel shown in figure 3.

Figure 3 a) RGB Color image b) Grayscale Image

The edge detection result of Lena image of our method is presented in figure 4. The proposed algorithm is compared with existing morphological edge detection operators. Performance can be compared by considering the number of edge pixels detected by various methods using mathematical morphology as shown in table 1. It is evident that proposed edge detection algorithm perform well than other methods.

Table 1: No. of edge pixels

 Operator Count Dilation Type 3066 Erosion Type 3706 Dilation-Erosion Type 3989 Proposed Method 4768
7. CONCLUSION

SEs of different shapes have different effects on preserving image details, and SEs of different scales make different impact on de-noising. According to the fact that single edge detection method can only reflect the edge information from certain aspect, this paper proposes a adaptive multi-structure and adaptive multi- scale morphological edge detection algorithm based on image fusion. It fuses the edge extracted by multi- structure elements with the one detected by multi-scale elements to get the final binary edge image with the optimal threshold segmentation. The experimental results show that the novel algorithm is not only more efficient than the morphological edge detection operators but also ensures the continuity, integrity, and accurate location of image edge.

References

1. Ehsan Nadernejad, Edge Detection Techniques: Evaluations and Comparisions, Applied Mathematical Sciences, Vol 2, 2008, no 31, 1507-1520.

2. Chao Li, Lindu Zhao, Shengnan sun, An Adaptive Morphological Edge Detection Algorithm based on Image

Fusion, 010 3rd International Congress on Image and Signal Processing.

3. Isabelle Bloch, Henri Maitre, Fuzzy mathematical morphologies: a comparative study, Pattern Recognition, vol. 28, no. 9, September 1995, pp. 1341-1387.

4. Jian Liu, Research on morphological filter algorithms based on mathematical morphology Harbin Institute of Technology, Harbin. 2006.

5. Allan G.Hanbury, jean Serra, Morphological operators on a unit circle, IEEE transactions on image processing, J. Vol.10, no.12,2001.

6. Cher Hau Seng, Abdesselam bouzerdoum, Two stage Fuzzy Fusion With Applications to Through the wall Radar Imaging, IEEE Geoscience and Remote Sensing Letters , Vol 10, No 4 , July 2013.

7. Hankyu Moon, Rama Chellappa, Azriel Rosenfeld, Optimal Edge-Based Shape Detection, IEEE Transactions on Image Processing, Vol 11, No 11, November 2002.

 Dilating Type 🙁 I b) – I Eroding Type: I- (I b) Dilating-ErodingType:(I b)- (I b) Edge detection Using fusion of Adaptive Multi- structure Morphological Algorithm and AdaptiveMulti-scale Morphological Algorithm

Figure 4: Experimental Result

Figure 5: Block diagram of proposed algorithm