METHOD SHAPE DESCRIPTOR BASED ON SHAPE MATRIX FOR ESTIMATE SHAPE OF STRUCTURING ELEMENT

METHOD SHAPE DESCRIPTOR BASED ON SHAPE MATRIX FOR ESTIMATE SHAPE OF STRUCTURING ELEMENT

Sri Huning Anwariningsih1), Agus Zainal Arifin1), Anny Yuniarti1)

1)Program Magister Information Engineering, Majors Information Engineering, Faculty of Technology Informasi, Institute of Technology Sepuluh November, Surabaya

Campus ITS, Street of Raya ITS, Sukolilo, Surabaya, 60111

Email : zahra_daffa@yahoo.com, agusza@cs.its.ac.id, anny@cs.its.ac.id

Abstract

Morphology is one of method that can be used for image processing especially for analyzing shape of object. Image Processing in morphology is conducted by passing a structuring element (strel) to an image in a way that much the same with convolution. In morphology, structuring element plays important role in image processing. Selection shape and size of structuring element can influence to result of image processing. An appropriate structuring element is used at an object, have not yet appropriate to used at other object. There is no standard guidance to determine shape of structuring element. Generally selection structuring element only relies on similarity with shape of observed object.

This research proposes method to estimate shape of structuring element based on shape matrix, that is, method of represent shape of an object in the form of matrix. This object representation will help determine shape of structuring element at observed object.

Test-drive Result in 30 sampels synthetic image data indicates that this edge detection algorithm uses method shape descriptor based on shape matrix proven can be pledged with average accuration as high as 99,6 %. Whereas at real image, this algorithm proven also can be pledged with average accuration as high as 98,4 %.

Keyword : morphology, structuring element, shape matrix, shape representationINTRODUCTION

Morphology operation many are used in processing and image analysis take example to operate for image repair (image enhancement), feature extraction, edge detection , shape analysis, and some other implementation of image processing operations.

In morphology operation, selection structuring element (strel) very influence result of image processing. Usage two different structuring elements will produce different result also even object/image that analyzed same [1].

There are some shape of structuring element that usual are used, there are rectangle, square, disk, linear, and diamond. Every shape of structuring element is referred [as] have excess and insuffiency each. Rectangle/square structuring element applicable to detect tabletop edge, under, left periphery, and right from an object. Whereas disk structuring element applicable to operates dilation/discomfortable rotation by direction because of disk structuring element is symmetrical to original object. Linear structuring element shall only detect single border [2].

Shape appropriate structuring element for one object have not yet of course according for other object. Detection tumor cell gastric more precisely uses rectangle structuring element than use diamond or line structuring [2]. Whereas detect existence of micro cracks at dolomite stone more compatible use linear structuring element because shape of micro crack like a line [3].

There is no guidance in selection shape of structuring element. Generally selection shape of structuring element is only relies on similarity by shape of observed object [2]. One of important attribute to recognize an object is shape (form). Shape is representation from an object [4]. Shape is one of important attribute to recognize an object. Selection shape of structuring element is more relied on similarity by object form. In consequence, object form can be used to determination structuring element.

Shape descriptor is technique to represent object form. A good representation will be able to depict intrinsic characteristic a shape in explicit. Representation of a shape also must invariance to rotation, scaling and transformation [4]. One of technique shape descriptor is shape matrix. Shape matrix uses global information from a shape, then form it becomes a matrix that describe a shape. Some research say that shape matrix can depict object form and invariance to scaling, rotation, and translation [5,6]. This object representation is applicable to detects shape of structuring element that come near shape of observed object.

This research proposes new method to estimate shape of structuring element that can be used detect an object. This estimation is conducted by representation analysis shape an object. Representation shape that used at this research is based on shape matrix. Shape matrix haves excellence that is has been tested invariance to translation, rotation, and scaling [7]. In other hand shape matrix can represent region that have holes. Shape matrix haves characteristic that look like characteristic structuring element. By undertaking process resizing to form from shape matrix is expected can determine shape of structuring element that look like observed object.

MORPHOLOGY

Morphology Mathematics represents object image two dimensions as a mathematics set in space Euclidean E2, where can be in the space of R2 continuous room or room discrete Z2. First an image is viewed as an intensity function to position (x,y), whereas with morphology approach, an image is viewed as set. An image object A can be represented as a set of (x,y) that value 1 or 0 where values is referred [as] show gray level scale every position.

Basic principle of morphological is usage structuring element that is basic form of object that used to analyze geometry structure from other larger and complex [8]. Its target is to getting the information hits form from an image by arrange shape and size of a structuring element.

Structuring Element

Structuring element can be supposed with mask at usual image processing. Structuring element haves origin point. Hereunder is example structuring element with origin point in (0,0) shown with letter O (Figure 1).

Structuring element at Figure 1(a) can be represented in binary matrix like at Figure 1(b) where number 1 and number 0 show gray level value.

In morphology, the important key is selection structuring element. Structuring element haves two important components that is shape and size where both of them can influence testing result. Selection shape of structuring element also influences result image.

Operations in MorphologyIn morphology, there are some operation, that is :

1.Translation.

Translation that means an image moved at direction (x,y) where (x,y) is matrix co-ordinate. Translation operation is expressed as

(1)

2. Dilation

Dilation operation are conducted to enlarge size of object segment by add layer around object [9]. Dilation operation will conduct admission filling process at image come [from] that have smaller size is compared to structuring element (strel).

Dilation A by B expressed as:

(2)

3. Erosion

Erosion operation is the opposite of the of dilation operation. At this operation, object size is minimized by erode around object until result image tend to minimized become thin [9]. Erosion operation will conduct reduction at image come from smaller just than structuring element.Erosion A by B dinotasikan is defined as :

(3)

(4)

4. Opening

Opening at an image A by strel B defined as erosion process that continued by dilation process where both process referred conducted in repetitive for all dot (x,y).

(5)

Equation (5) can be written down into form

(6)

Opening operation are used to break parts of from object that only linked with only 1 or 2 pixel, and eliminate very small object. Opening can joint feature that broken(break narrow joins), and eliminate enlargement effect at object (remove protrusions).

5. Closing

at an image A by strel B defined as erosion process that continued by dilation process where both process referred conducted in repetitive for all dot (x,y).

(7)

There are some operation usefulness closing that is : (1) close or eliminate small holes existing in object segment, (2) join 2 object segments that each other bunch up (close pause between 2 very nearby objects), (3)also conducted in a few erosion-dilation network (for example 3 times dilations, last 3 times erosions) if hole gauge or distance between big enough object.

Operation closing also tends to will refine object at image, nevertheless by joint fractions (fuses narrow breaks and thin gulf) and eliminate small holes at object.

6. Morphological Gradient

Dilation operation and erosion often be combined to maximize morphology operation at image processing. According to Soille [10] there are three types morphological gradient, that is :

a.Basic morphological gradient where dilated_image eroded_image

b.Internal gradient where original_image eroded_image

c.External gradient where dilated_image original_image.

Where dilated_image is image of dilation result, whereas eroded_image is image of erosion result.

Equation for Morphological gradient is:

(8)

Equation for Internal gradient is:

(9)

Equation for External gradient is:

(10)

Internal gradient will sharpen internal boundary from object until object will be bolder compared to its background. Whereas at external gradient, boundary object will be darker than its background (Figure 2). At binary image, internal gradient will become mask from internal boundary from object [10].

OBJECT REPRESENTATION

Shape is one of important attribute to recognize an object. Shape recognition becomes important factor in object recognition.

Shape Representation

A good representation will be able to depict intrinsic characteristic from a shape in explicit. Basically form of an object can be represented in the form of internal and external characteristic.

Approach shape in structural is wrong representation way used occasionally shape at representation method shape at morphology [5, 11]. Shape is defined as a group of connective dots [6]. Thus an object is told have formed if all dots at object referred [as] linked.

In taxonomy, there are some technique in representation shape that is in the form of contours, region, and transforms. Contour-based equal to boundary-based that is represent shape based on its boundary. Region-based based on area from an object, whereas technique transform represents shape in the form of coefficient transform, usual use Fourier transform and also wavelet (Figure 3).

Technique region-based is divided into some methods (Figure 4).

Shape Matrix Representation

Shape Matrix applicable to represents a shape. Shape matrix is polar quantization from a form (Figure 5a). Middle Dot co-ordinate (0,0) is middle dot from shape object and tinder axis x is tinder that withdrawn from middle dot [go] toes furthermost dot from shape. If shape are altered into polar co-ordinate form (r, ) then shape will not be influenced by its position and rotation angle; corner [7]. Shape matrix also not influenced by scale from shape object is referred [as]. Shape matrix invariant to translation, rotation, and scaling from shape referred [as] [7].

At concept of shape matrix, a shape is transformed into a matrix by polar quantization of the shape. Assuming O is the center of gravity of the shape and OA with length L is the maximum radius of the shape, to obtain an mxn matrix representation of the shape, OA divided into (n-1) equal distance and draw circle centering at O and radii L/(n-1), 2L/(n-1), , (n-1)L/(n-1). If the circles intersect the maximum radius of the shape line (line OA) at i1, i2, , in-1, then starting from i1, i2, , in-1 and counter clockwise, divided each circle into m equal arcs, each arc being degrees. Then an mxn matrix is constructed according to the following algorithm.Whereas to determine element values at shape matrix explained at algorithm hereunder:

1.Create an mxn matrix and Call it M2.For i = 0 to (n 1)

3. For j = 0 to (m 1)

4. If the point with polar coordinates (

lies in the shape then M(i,j) = 1 Otherwise M(i,j) = 1Besides load information about region, shape matrix also loads information about boundary until shape matrix also can represent a region object that have hole (Figure 6).

At shape matrix, an object will be represented in a form matrix size m x n. Characteristic shape matrix look likes characteristic structuring element. Similarity both of them is form of matrix m x n by element value 1 or 0 where values is referred [as] show position pixel in an object. Form shape matrix will be fickle accommodate shape of observed object. This condition indicates that there is similarity between object representation and observed object.

This fact in accordance with reason of selection structuring element. Selection structuring element based on similarity with observed object. Object Representation based on shape matrix with various of level bests applicable to determine shape of structuring element.

TESTING DESIGN

Testing Design in general estimation shape of structuring element based on shape matrix from research can be seen at Figure 7. Steps taken is (1) Determination of test image and image ground truth, (2) Determine shape matrix from test image and conduct process resizing at shape matrix to be able to determine form structuring element, (3) Operate gradient morphology at test image with structuring element step result (2), and (4) Calculate accuration of operation result image gradient morphology based on shape matrix with image ground.

Test Image There are two type of test images that is images synthetic (Figure 8(a)) and also real image (Figure 8(b)). Test Image that used [by] 40 units. Size of synthetic image is made same that is 140 x 140 pixels. Whereas size of real image is not defined. Test Image consist of a variety of forms either form that or irregular form. This condition bent on to test whether shape of structuring element that proposed in this research applicable to detect edge any forms wake up.

In other hand to test accuracy of research result, will be conducted experiment also to image that in rotation and also that altered its size (either enlarged or minimized) (Figure 8(c)). In other hand, testing will be conducted to object that have hole (Figure 8(d)) and also objects that disjointed (Figure 8(e)).

Image Ground Truth

Whereas image making ground truth is conducted manually. Size of Image ground truth is adapted with test image. Image ground truth is binary image. At image ground truth, edge of an object will be given white color, where white color is given value 1 (Figure 9).

Test-drive Scenario

Test-drive at form determination structuring element based on algorithm shape matrix that developed at this research conducted at all of group data sample of test image. At each test image, marginally will be conducted three testing phases. The first step is searching size of shape matrix from object at test image. Determination size of shape matrix as used in testing based shape matrix minimum size that already can detect object. Second Step is conducts process testing detects edge to look for boundary from object of test image. Last Step is conducts evaluation of algorithm success rate by count/calculate system accuration in conducting detect edge. This Accuration will be compared to algorithm that use structuring element that in form of disk, diamond, and square.

RESULT AND DISCUSSION

After conducted testing to 40 test images of the size structuring element 3 x 3, got result that level of average accuration detect edge uses form structuring element based on shape matrix reaches 99,6 % (Tables 1). Whereas average accuration at real image is 98,4% (Tables 2). This Result indicates that method of form determination structuring element based on shape representation can be pledged.

In visual, result image detects edge uses form structuring element bases on object representation also succeeds detect object edge at test image (Picture 10).

At this research, one of factor that influence result accuration is form from object and image ground truth. From research got the fact that method shape descriptor bases on shape matrix can be pledged to estimate form structuring element. Excess from method this is the form structuring element correspond to observed object, until form structuring element that got really is representation of form observed object. However selection of size shape matrix m x n very influence result of object form representation. Must furthermore research to discuss about method of size election correct shape matrix.

Tables 1. Calculation Akurasi Citra Sintetis

NoName ObjekAccuration (%)

SMSqHeDisk

1Form 1

99,9999,9998,3398,33

2Form 2

97,9897,9798,0098,00

3Form 3

98,2898,2898,2098,20

4Form 4

99,6199,6198,5198,51

5Form 5

99,9799,9899,3199,31

6Form 6

99,7699,7699,3499,34

7Form 7

99,9899,9899,1599,15

8Form 8

99,9799,9798,8898,88

9Form 9

99,9799,9798,5798,57

10Form 1099,9999,9999,4199,41

11Star

99,9999,9898,5198,51

12Box

100,00100,0099,9899,98

13Flag

99,9299,9299,6299,62

14Flower

98,2998,2698,2898,28

15Boxblunt100,00100,0099,8299,82

16Float

99,2799,2797,7697,76

17Circle 199,9999,9999,0099,00

18Circle 299,9799,9798,8398,83

19Oval

99,9999,9999,3799,37

20Square

100,00100,0099,9899,98

21PMI

100,00100,0099,9499,94

22Segienam99,9999,9999,2899,28

23Trilateral 1100,00100,0099,0599,05

24Trilateral 299,9199,9198,7398,73

25Head

95,4095,3995,4095,40

26Trapezium100,00100,0099,4299,42

27Zoom

99,6999,6999,3999,39

28Pentagon100,00100,0099,2299,22

29Trapezium 2100,00100,0099,3099,30

30Leaf

99,9999,9999,2799,27

Average99,699,598,998,9

Tables 2. Calculation Akurasi Citra Riil

NoName ObjekAccuration (%)

SMSqHeDisk

1Breast

97,0296,4196,8196,81

2Tooth

98,5398,5396,8997,80

3Blood Cell99,5299,5198,0698,06

Average98,498,197,297,2

CONCLUSIONAlgorithm based on shape matrix applicable to determines shape of structuring element from an object either at synthetic image or real image. Shape of structuring element based on shape matrix also can handle object form that experience of scaling change and rotation, object form with hole, and image with object disjointed.

Factor that influence accuration level is object form and threshold value. Highest Accuration result detects edge for entire synthetic image data uses structuring element based on shape matrix is 100 % and the lowest accuration is 95,4 %. Whereas average accuration for synthetic image is 99,6 %. Whereas accuration flattens flatten real image data as high as 98,4%.

BIBLIOGRAPHY

[1] Cun Jin, Xue , Fen-Zhen, Su, and Jun-qi, Zhou., An Adaptive Algorithm to Define Optimal Size of Structuring Element, Journal of Image and Graphics, 11:317 324, 2006

[2] Gangway Li, Tan, Su-pinWang, NanZhao, Gray-scale Edge Detection for Gastric Tumor Pathologic Cell Images by Morphological Analysis, Biology and Medicine Journal, 39: 947 952, 2009.

[3] Obara, Boguslaw, Identification of Transcrystalline Microcracks Observed in Microscope Images of a Dolomite Structure using Image Analysis Methods Based di atas Linear Structuring Element Processing, Journal Computers & Geosciences, 33:151158, 2007.

[4] Loncaric, Sven, A Survey of Shape Analysis Techniques, Thesis Ph.D., University of Zagreb, Croasia, 1999.

[5] Goshtasby, Ardeshir, Description and Discrimination of Planar Shapes Using Shape Matrices, IEEE Transaction On Pattern Analysis and Machine Intelligence, 7:738 743, 1985.

[6] Costa, Luciano da Fontoura and Cesar, Roberto Marconed, Jr, Shape Representation and Analysis: Theory and Practice , 2nd Edition, CRC Press, London, 2009.

[7] Goshtasby, Ardeshir, Intersience 2-d and 2-d and 3-d Image Registration for Medical, Remote Sensing, and Industrial Applications, John Wiley & Sons, Inc., New York, 2005.

[8] Serra, J, Image Analysis and Mathematical Morphology, Academic Press, Inc., London, 1982.

[9] Murni, Aniati., Diktat Kuliah : Processing Citra Digital, Indonesia University, Jakarta, 2004.

[10] Soille P., Morphological Image Analysis: : Principles and Applications, Springer Verlag, Germany, 1999.

[11] Haralick. S, S. Sternberg, and X. Zhuang., Image Analysis Using Mathematical Morphology, IEEE Transactions di atas PAMI, 9: 532-550, 1987.

(b)

(a)

B

Fig 1. Structuring Element

Point O is origin point,

binary representation of strel

Figure 2. Image Result of Morphological Gradient

Figure 3. Taxonomi of Shape Representation

(Costa dan Cesar,2009)

Figure 4. Taxonomi Region-Based Shape Representation

(Costa dan Cesar, 2009)

Figure 5. (a) Shape , (b) Shape Matrix

(Goshtasby, 2005)

A

Figure 6. (a) Shape with Hole ,

(b) Shape Matrix (Goshtasby, 1985)

Figure 7. Design Systems

Finish

Calculate Accuration

Edge detection using morphological gradient operation

Determine shape matrix from test image

Determine test image and ground truth

Start

Figure 8. Test Image (a) Normal Test Image, (b) Test Image with rotation Variation, (c) Test Image With Hole, (d) Test Image with Separate Object, (e) Image Riil

(e)

(d)

(c)

(b)

(a)

EMBED PBrush

Figure 9. Ground Truth

(e)

(d)

(c)

(b)

(a)

(b)

(a)

Figure 10. Edge Detection

(a) Ground Truth, (b) Shape Matrix

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