research article concrete image segmentation based on multiscale mathematic morphology...

Research ArticleConcrete Image Segmentation Based on Multiscale MathematicMorphology Operators and Otsu Method

Sheng-Bo Zhou1 Ai-Qin Shen2 and Geng-Fei Li3

1Guangxi Transportation Research Institute Key Laboratory of Road and Materials of Guangxi Zhuang Autonomous RegionNanning 530007 China2Highway School Changrsquoan University Xirsquoan 710064 China3Guangxi Transportation Research Institute Nanning 530007 China

Correspondence should be addressed to Sheng-Bo Zhou zhoushengbo2005163com

Received 12 April 2015 Revised 25 August 2015 Accepted 25 August 2015

Academic Editor Antonio G B de Lima

Copyright copy 2015 Sheng-Bo Zhou et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The aim of the current study lies in the development of a reformative technique of image segmentation for Computed Tomography(CT) concrete images with the strength grades of C30 and C40 The results through the comparison of the traditional thresholdalgorithms indicate that three threshold algorithms and five edge detectors fail to meet the demand of segmentation for ComputedTomography concrete images The paper proposes a new segmentation method by combining multiscale noise suppressionmorphology edge detector with Otsu method which is more appropriate for the segmentation of Computed Tomography concreteimages with low contrastThis method cannot only locate the boundaries between objects and background with high accuracy butalso obtain a complete edge and eliminate noise

1 Introduction

The concrete can be considered as a multiphase compositematerial system which consists of mortar matrix aggregateand interfacial transition zone (ITZ) with various size poresdistributed inside the concrete Pores play a crucial role instrength and durability performance of concrete For exam-ple porosity is directly related to strength [1ndash4] Mean poresize and spacing factor have affected significantly the frostresistance of concrete [5 6] Increasing pore connectivityfactor will lead to the permeability resistance decreasing ofconcrete [7 8] In recent years tremendous interests havebeen aroused by people in pore characteristics which are cru-cial for the profound understanding of concrete deteriorationmechanism and improving concrete performance

Due to the diversity pore sizes and shapes distributedin the microstructure of concrete the analysis of poresbecomes difficult Usually the analysis of pore characteristicsis through the means of indirect methods like mercuryintrusion method (MIP) [2ndash4 7ndash9] However the hypothesisofMIPmethod that pore is cylindrical is not always the actualsituation and the predrying process of samples before testing

could result in the irreversible deformation of pore structureSome scholars [10ndash12] argue that MIP method for character-izing pore structure is not appropriate With the nondestruc-tive analysis technique developing the Computed Tomogra-phy (CT) scanner is being introduced into the characteriza-tion of microstructure in materials science fields [13ndash15]

The computer-aided image processing method may beused to extract a target object in CT images The imageprocessing method that originated in the 1920s becomes anincreasingly powerful tool to solve the hot topic in the civilengineering fields Basyigit et al [16] evaluated the relation-ship between microstructure and compressive strength ofconcrete based on the image analysis software (Image J)Marinoni et al [17] employed the threshold segmentationalgorithm and the filtering technique to investigate themortar morphology Soroushian et al [18] carried on thequantification analysis on the microcrack and void in themicrostructure of concrete using the automatic thresholdingmethod One can find that image segmentation methodscan mainly be classified into three categories thresholdsegmentation algorithm [19ndash25] edge-based algorithm [26ndash28] and interdisciplinary application of algorithms [29ndash32]

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 208473 11 pageshttpdxdoiorg1011552015208473

2 Advances in Materials Science and Engineering

Table 1 Mixing proportion and compressive strength for pavement concrete specimens

Code Cement Crushed stone Water Sand Slag Fly ash Superplasticizer Compressive strength(kgm3) () (MPa)

C30 285 1185 129 726 57 38 08 358C40 315 1170 143 717 63 42 08 479

X-ray source

Sample

Axis of rotation

Core beam

Detector

(a) (b)

Figure 1 (a) Basic principle with cone beam and muhidetector for CT scanner (b) Micro-CT scanning devices

(eg mathematic morphology) However there is no sin-gle accepted method of achieving the segmentation for allimages So finding or matching a new effective segmentationmethod is indispensable to obtain better segmentation resultsfor CT concrete image

The paper is organized as follows First the preparationof pavement concrete samples and CT testing method arepresented in Section 2 Section 3 presents the image methodsused in the segmentation and the comparative analysis ofthese methods It has been shown that the single traditionalmethod fail to perform segmentation forCT imageswith low-contrast edge effectively So a new method a combination ofmathematic morphology and Otsu method is developed inSection 4 Section 5 draws the conclusions

2 Experimental Preparation andCT Testing Method

21 Sample Preparation Pavement concrete with the worka-bility slump of 20ndash40mm and the strength grade of C30 andC40 is prepared by mixing these raw materials with differentproportionThe basicmaterials are ordinary portland cement425R river sand crushed stone (size range 5ndash265mm)and superplasticizer (06ndash1 recommended dosage and 30water reduction ratio) Six cube specimens of dimensions100 times 100 times 100mm consist of five cube specimens for testing28-day compressive strength and one for CT scanning Themixing proportions of raw materials and the compressivestrength of specimen are presented in Table 1

22 CT TestingMethod TheX-ray image analysis of concretespecimens is carried out nondestructively in the micro-CTscanner shown in Figures 1(a) and 1(b) As X-rays conductthrough the concrete specimens they are attenuated due tothe absorption of objects with different material density Thetwo-dimensional or three-dimensional image can be recon-structed based on X-ray attenuation information which ismeasured by an X-ray muhidetector Concrete specimens arescanned through micro-CT scanner with a 225 kv voltages06mA current cone beam scan mode 05 micron detectionaccuracy and 012ndash013 millimeter scanning interval

3 Traditional Methods forImage Segmentation

The aim of the segmentation for concrete specimens isto separate objects from background image However thesegmentation of CT images with low contrast is not an easytask Traditional image segmentation methods are based onthe similarities and discontinuities in the gray images [22ndash28] In this section the comparative analysis of thresholdalgorithms and edge detecting techniques is carried out

31Threshold SegmentationMethods Thethreshold approachbased on the gray histogram is a simple practical imagesegmentation technique which only requires a gray thresholdvalue but if the threshold value is not appropriate thesegmentation performance of the method would be directlyaffected Common approaches founded on thresholdmethod

Advances in Materials Science and Engineering 3

include two-mode algorithm iterative algorithm and Otsualgorithm

311 Two-Mode Threshold Algorithm Prewitt [19] first pro-poses the two-mode method which is a typical globalthreshold approachWhen two peaks appear in the histogramof image the threshold is generally located at the valley ofthe gray histogram So the approach strongly depends on theimage operatorrsquos experience and is only applicable to suchkind of images that the obvious gray difference exists betweenbackground and objects

312 Iterative Threshold Algorithm Iterative algorithm [2023] is an adaptive threshold method The threshold isobtained by optimizing an objective functionThemain stepsare described as follows step one the initial threshold 119879

1is

determined according to formula (1) step two the image isdivided into two regions based on the threshold 119879

1 and then

the average gray for each region is calculated again step threethe threshold 119879

1is updated by a new threshold 119879

2according

to formula (2) repeat step two and step three until 119879119896+1

and119879119896are approximately equal

1198791=

(119891min + 119891max)

2

(1)

1205831=

sum119879

119894=0119894119901119894

sum119871minus1

119894=0119901119894

1205832=

sum119871minus1

119894=119879+1119894119901119894

sum119871minus1

119894=0119901119894

119879119896=

(1205831+ 1205832)

2

(2)

where 119891min is the minimum gray value of image 119891max is themaximum gray value 120583

1and 1205832are the average gray values of

1st region and 2nd region 119901119894is the frequency of occurrences

of gray 119894

313 Otsu Method Otsu method also is known as themaximal variance between-class method which was putforward in 1979 In most cases Otsu method [21 22 2425] can obtain better segmentation results Suppose that thegray is a given image range from 1 to 119871 the threshold 119879

was determined by maximizing the variance between classesaccording to formula (3) An image may be divided into twoclasses (objects and background) by the threshold 119879

1199010(119879) =

119879

sum

0

119875119894

1199011(119879) =

119871

sum

119879+1

119875119894= 1 minus 119901

0(119879)

119901119894=

119899119894

119873

1205830(119879) =

119879

sum

119894=0

119894

119901119894

1199010(119879)

1205831(119879) =

119871

sum

119894=119879+1

119894

119901119894

1199011 (

119879)

1205752

0(119879) =

119879

sum

119894=0

(119894 minus 1205830(119879))2 119875119894

1198750(119879)

1205752

1(119879) =

119871

sum

119894=119879+1

(119894 minus 1205831(119879))2 119875119894

1199011(119879)

120583 =

119871

sum

119894=0

119894119901119894

1205752

119908(119879) = 119875

0 (119879) 1205752

0(119879) + 119875

1 (119879) 1205752

1(119879)

119879lowast= arg1lt119879le119871

max 1205752

119887(119879)

(3)

where 119899119894is the number of pixels at gray level 119894 119873 is the

total number of pixels 1199010consists of pixels with gray levels

[1 119879] and 1199011consists of pixels with gray levels [119879 +

1 119871] 1199010(119879) and 119901

1(119879) are the cumulative probabilities

1205752

0(119879) and 120575

2

1(119879) are the variances of the classes 119901

0and 119901

1 120583

is the average gray level and 1205752

119908(119879) is the variance between

classes

314 Comparisons of Three Threshold Methods The abovethree threshold methods are used to implement segmenta-tion of three C30 (andashc) and three C40 (dndashf) CT concreteimages The processed images are shown in Figure 2 Someconclusions can be drawn (1) using the two-mode algorithmthe threshold value needs to be manually adjusted to obtainbetter segmentation performance so it is time-consuming(2) applying the iterative algorithm the whole gray level inthe image is classified into the background since the finaliterative threshold is 0 (3) although the ideal segmentationperformance Otsumethod can be obtained inmany applica-tions Figure 2 shows that the CT concrete images with low-contrast subject to inaccurate segmentation

32 Traditional Edge Detection Algorithms An edge is theboundary between background and objects in which thematerials density and the image intensity show abruptchanges at edgesThe popular edge detection techniques (egRoberts Prewitt Sobel Canny and LOG operators) havebeenwidely applied to detect discontinuities in gray levelThecorresponding algorithms can be expressed by the followingformulae respectively

119866 (119891 (119909 119910)) = (radic119891 (119909 119910) minus radic119891 (119909 + 1 119910 + 1))

2

+ (radic119891 (119909 + 1 119910) minus radic119891 (119909 119910 + 1))

2

12

(4)

119866 (119891 (119909 119910)) = radic1198911015840

119909(119909 119910) + 119891

1015840

119910(119909 119910) (5)

119866 (119891 (119909 119910)) =

100381610038161003816100381610038161198911015840

119909(119909 119910)

10038161003816100381610038161003816+

100381610038161003816100381610038161198911015840

119910(119909 119910)

10038161003816100381610038161003816 (6)


(a) (b)

(c) (d)

(e) (f)

Figure 2 Comparison of segmentation results for CT concrete images by three threshold methods (a)ndash(c) denote the original C30 CTimages (d)ndash(f) denote the original C40 CT images From left to right column results of original CT images two-mode algorithm iterativealgorithm and Otsu method

119866 (119891 (119909 119910))

= radic[119866119909(119909 119910) sdot 119891 (119909 119910)]

2+ [119866119910(119909 119910) sdot 119891 (119909 119910)]

2

119866 (119909 119910) =

1

21205871205902exp(

minus (1199092+ 1199102)

21205902

)

120579 (119909 119910) = arctan(

119866119909(119909 119910)

119866119910(119909 119910)

)

(7)

119866 (119891 (119909 119910)) = nabla2(119866 (119909 119910) lowast 119891 (119909 119910))

119866 (119909 119910) =

1

21205871205902exp(minus

1199092+ 1199102

21205902

)

(8)

Figure 3 shows the results of edge detection using thedifferent edge detectors It can be detected that the traditionaledge operators have good performance in edge detectionand localization but the question reported in the literatures[26ndash28] remains (1) these detectors may lead to the lossof boundary information so the severed edges need to beconnected by applying other theories (2) removing noiseability of the operators like Roberts Prewitt and Sobeloperators is poor (3) although the Canny and LOGoperatorshave stronger ability to eliminate noise part of boundaries arestill incomplete and (4) the threshold of segmentation alsoneeds to be adjusted manually

4 Image Segmentation Based on MathematicalMorphology Method and Otsu Method

Mathematical morphology is an interdisciplinary theory forthe analysis and processing of digital images based on settheory It was first introduced into image processing fields byMatheron and Serra in 1964 As a powerful image processingtool now it has been widely used in many domains likemedical image processing [32] remote sensing image analysis[33] industrial inspection [34] materials science [35] andso forth Morphological image processing consists of a setof operators (eg erosion dilation opening and closing)that transform images according to the different geometricalstructures characterizations

41 Mathematical Morphology Method In morphologymethod erosion and dilation operators are the basicstructuring element sets Many improved image processingoperators are formed by combining the basic operators forobtaining many image processing tasks For a gray image let119860(119909 119910) and 119861(119909 119910) be the original image (the domain 119885

119860)

and the structuring element (the domain 119885119860) respectively

and (119904 119905) denotes the translation parameters The generalframework of erosion and dilation is given by

(119860Θ119861) (119904 119905) = min 119860 (119904 + 119909 119905 + 119910)

minus 119861 (119909 119910) | (119904 + 119909) (119905 + 119910) isin 119885119860 (119909 119910) isin 119885

119861

(119860 oplus 119861) (119904 119905) = max 119860 (119904 minus 119909 119905 minus 119910)

+ 119861 (119909 119910) | (119904 minus 119905) (119905 minus 119910) isin 119885119860 (119909 119910) isin 119885

119861

(9)


(a) Original CT image (b) Sobel operator (c) Roberts operator (d) Prewitt operator

(e) Canny operator (f) LOG operator (g) Original CT image (h) Sobel operator

(i) Roberts operator (j) Prewitt operator (k) Canny operator (l) LOG operator

Figure 3 Comparisons of edge detection performance using different edge operators for (a)ndash(f) original CT image of C30 concrete and theedge image of different operators and (g)ndash(l) original CT image of C40 concrete and the edge image of different operators respectively

The erosion and dilation of the gray image 119860 by thestructuring element 119861 mean subtracting and adding 119861 fromand to center 119860(119909 119910) respectively Let us choose 3 times 3window as the structuring element119861 the erosion and dilationprocesses of 119860 by 119861 are described individually in Figures 4and 5 Suppose that ldquo4rdquo is the center the erosion of 119860 by 119861

can be understood as the center of119861 ismoved to the point ldquo4rdquoand then let us subtract every element in window 119861 from 4 tofind theminimum in the newwindow119861 Finally the point ldquo4rdquois replaced by the minimum within the new window 119861 whilethe dilation of 119860 by 119861 means that the point ldquo4rdquo is replacedby returning the maximum value within the new window 119861The final processed images are obtained by implementing thesame process for every point in the gray 119860

42 Morphological Filters Themorphological filter is a non-linear filter approach based on a series of morphological

operators Compared with the smoothing filter or thesharpening filter the morphological filter can better filternoise and protect the image details [36ndash38] The openingoperator and the closing operator are the basic ones in themorphological filter method A random filter approach isalso generated by combinations of the basic operators Theopening operator and the closing operator may be expressedby the formula (10) The opening operator can often filter thepeak noise while the closing operator can filter the valleynoise So one can obtain a new algorithm by combining thesebasic operators for removing various noise in an image

119860 ∘ 119861 = (119860Θ119861) oplus 119861

119860 ∙ 119861 = (119860 oplus 119861)Θ119861

(10)

To verify the performance of the morphological filter inthis paper we considered the following morphological filter


1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 2 4 1

1 2 1 3 1

1 4 2 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 1 3

1 3 1 0 5

1 4 3 1 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 1 3 1

1 4 3 2 1

1 1 1 1 1

0 1

0 1 0

1 1

0 2 0

2 3 2

0 2 0

A B Erosion of center 4 Subtracting B from A

Erosion of right neighborhood Subtracting B to A Minimum of center 4 erosion Final erosion of A

minus1

minus1

minus2minus2minus2minus2minus2

minus2

minus2

minus2

minus2

minus2

minus2

minus2

minus2minus2minus2minus2

center 3

Figure 4 Example of an erosion (the red box represents the erosion of center 119860)

1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 6 4 1

1 6 7 6 1

1 4 6 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 5 3

1 3 5 6 5

1 4 3 5 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 7 3 1

1 4 3 2 1

1 1 1 1 1

4 4 4 4 4

4 5 6 7 4

4 6 7 6 4

4 7 6 5 4

4 4 4 4 4

0 2 0

2 3 2

0 2 0

A B Dilation of center 4 Adding B to A

Adding B to ADilation of right neighborhood Maximum of center 4 dilation Final dilation of Acenter 3

Figure 5 Example of a dilation (the red box represents the dilation of center 119860)

operators including the single opening filtering the singleclosing filtering and the mixed filtering Experiment resultsare shown in Figures 6(a)ndash6(f) inwhich (a) denotes the origi-nal image (b) is an artificial image added the salt-and-peppernoise and (c)ndash(f) are the filtered images Some conclusionscan be drawn the opening operator can only filter the white

point and the closing operator can only filter the black pointin the image while the combinations of opening and closingcan remove both the white noise and the black noise

43 Proposed Segmentation Method by Combining Multi-scale Noise Suppression Morphology Edge Detector with Otsu


(a) Original CT image (b) Image with adding noise (c) Single opening filter

(d) Single closing filter (e) Opening followed by closing (f) Closing followed by opening

Figure 6 Comparisons of filtering performance using the above morphological operators with a 3 times 3 cross structuring element

Method (MNSMO) Many morphology edge detection algo-rithms [39ndash41] have been developed for performing a specialimage processing task The new operators are generated bythe combinations of the basic morphologic operators Forexample you can get the internal boundaries of objects inan image by subtracting the image by erosion from theoriginal image while the external boundaries of objects canbe obtained by subtracting the original image from the imageby dilation Besides the structuring element dimensions maybe adjusted to obtain more subtle results In the paperthe designed multiscale noise suppression morphology edgedetection operator can not only be used for detecting theboundaries between the background and variable size objectsin a concrete image but also can be used for removing noise

431 Designing Idea of MNSMO Algorithm Combinationsof the opening operator and the closing operator are usedto detect the edge and remove noise in the original 119860(119909 119910)The structuring elements 119861 with variable dimensions areused to detect the subtle boundaries information Throughcomparing the testing results the structuring element withthe ldquodiskrdquo shape (shown in Figure 7) is more suitable forthe pore edge detection Finally Otsu algorithm is appliedto carry out the binary processing The designed multiscalenoise suppression morphology edge detection operator isshown in the formula below

1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3

Figure 7 The structuring element with 119877 = 3 and 119873 = 4 ldquodiskrdquoshapes

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE119899)]Θ119861 (SE (119899 minus 1))

119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)

432 Description of MNSMO Algorithm The flowchart forthe MNSMO algorithm is shown in Figure 8


Original imageA(x y)

Opening operation to A(I1)

Closing operation to I1(I2)

Choosing SE and shape

1 3 5 and 7 ldquodisk-rsquorsquoshaped(SE dimension is equal to

(Ij0)

(Ij1)

Otsu binary segmentation of Iimage

Processed imageG(x y)

Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7

Eroding IJ operation (SE = J minus 2)

J = SE + 2

Dilating operation to I2 (SE = J)

Eroding operation to Ij0 (SE = J)

IJ = Ij0 minus Ij1

elements)

Figure 8 Flowchart applying ldquoMNSMOrdquo method to implement CT concrete image segmentation

The main image processing steps are summarized asfollows

Step 1 The original image is filtered by using the morpholog-ical operator of the opening followed by the closing

Step 2 The disk-shaped multiscale structuring elements aredesignated as 1 3 5 and 7

Step 3 It is the multiscale edge detection through using theerosion and dilation operators

Step 4 The Otsu method is used to implement the binariza-tion for the above processed image

44 Application of MNSMO Method in the Image Segmen-tation The segmentation of six concrete images includingthree C30 (A1ndashA3) specimens and three C40 (A1ndashA3) spec-imens is implemented by using the MNSMO method inthe matlab70 platform Figure 9 illustrates the segmentationresults For each C30 (G1ndashG3) or C40 (G1ndashG3) image thepore edge and the pore shape can be automatically andaccurately located Comparedwith other image segmentationmethods it can be seen that theMNSMOmethod has severaldistinct advantages (1) noise in the image can be effectivelyeliminated (2) both the internal boundaries and the externalboundaries of the pores have been detected accurately andno discontinuity of the edge appears in the six images and(3) by comparison it is more simple for implementing thesegmentation for an image using the MNSMO method thatonly the structuring element shape and dimensions needbe adjusted manually besides it is not sensitive to the lowcontrast of the image

5 Conclusions

Three thresholdmethods (eg two-mode algorithm iterativealgorithm and Otsu algorithm) are inaccurate and time-consuming for the segmentation of a CT concrete imageAlthough traditional edge detection algorithms can betterlocate the boundaries between objects and background theedge discontinuity needs to be further solved And it is poorto restrain noise for some algorithms such as Sobel Robertsand Prewitt

In this paper a new segmentation method is pro-posed based on mathematical morphology theory namedldquoMNSMOrdquoTheMNSMOmethod is a combination operatorof noise suppression operator edge detection operator andautomatic threshold segmentation algorithm First the oper-ator of opening followed by closing is used to filter noise in animage then the edge is located by designing the eroding anddilating operators by using the multiscale dimensions andthe ldquodiskrdquo shape structuring element Finally Otsu methodis applied to implement the binarization of image

Compared with the segmentation methods reported inthe literatures ldquoMNSMOrdquo not only can accurately locatethe boundaries between objects and background but is anautomatic image processing method so it avoids subjectingto human error

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study was financially supported by the Fundamen-tal Research Funds for the Central Universities (nos


C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)

Figure 9 The segmentation performance of pore from background by applying the MNSMOmethod

2013G5210010 and 2013G2313001) and the National NaturalScience Foundation of China (no 51278059)

References

[1] A Lubeck A L G Gastaldini D S Barin and H C SiqueiraldquoCompressive strength and electrical properties of concretewithwhite Portland cement and blast-furnace slagrdquoCement andConcrete Composites vol 34 no 3 pp 392ndash399 2012

[2] P Duan Z Shui W Chen and C Shen ldquoEfficiency of mineraladmixtures in concrete microstructure compressive strengthand stability of hydrate phasesrdquoApplied Clay Science vol 83-84pp 115ndash121 2013

[3] R Kumar and B Bhattacharjee ldquoPorosity pore size distributionand in situ strength of concreterdquoCement and Concrete Researchvol 33 no 1 pp 155ndash164 2003

[4] B B Das and B Kondraivendhan ldquoImplication of pore sizedistribution parameters on compressive strength permeability

and hydraulic diffusivity of concreterdquoConstruction and BuildingMaterials vol 28 no 1 pp 382ndash386 2012

[5] Z Giergiczny M A Glinicki M Sokołowski and M ZielinskildquoAir void system and frost-salt scaling of concrete containingslag-blended cementrdquo Construction and Building Materials vol23 no 6 pp 2451ndash2456 2009

[6] SMarusin ldquoThe effect of variation in pore structure on the frostresistance of porous materialsrdquo Cement and Concrete Researchvol 11 no 1 pp 115ndash124 1981

[7] N Neithalath M S Sumanasooriya and O Deo ldquoCharacteriz-ing pore volume sizes and connectivity in pervious concretesfor permeability predictionrdquoMaterials Characterization vol 61no 8 pp 802ndash813 2010

[8] S-S Park S-J Kwon S H Jung and S-W Lee ldquoModeling ofwater permeability in early aged concrete with cracks based onmicro pore structurerdquo Construction and Building Materials vol27 no 1 pp 597ndash604 2012


[9] M Moukwa and P-C Aıtcin ldquoThe effect of drying on cementpastes pore structure as determined by mercury porosimetryrdquoCement and Concrete Research vol 18 no 5 pp 745ndash752 1988

[10] S Diamond ldquoMercury porosimetry an inappropriate methodfor the measurement of pore size distributions in cement-basedmaterialsrdquo Cement and Concrete Research vol 30 no 10 pp1517ndash1525 2000

[11] S Diamond ldquoReply to the discussion by S Wild of the paperlsquomercury porosimetrymdashan inappropriate method for the mea-surement of pore size distributions in cement-basedmaterialsrsquordquoCement and Concrete Research vol 31 no 11 pp 1655ndash16562001

[12] S Chatterji ldquoA discussion of the paper lsquoMercury porosimetrymdashan inappropriate method for the measurement of pore size dis-tributions in cement-based materialsrsquo by S Diamondrdquo Cementand Concrete Research vol 31 no 11 pp 1657ndash1658 2001

[13] Y-F Fan andH-Y Luan ldquoPore structure in concrete exposed toacid depositrdquo Construction and Building Materials vol 49 pp407ndash416 2013

[14] A P Jivkov D L Engelberg R Stein and M Petkovski ldquoPorespace and brittle damage evolution in concreterdquo EngineeringFracture Mechanics vol 110 pp 378ndash395 2013

[15] T Tomoto A Moriyoshi H Takahashi H Kitagawa and MTsunekawa ldquoDamage to cement concrete pavements due toexposure to organic compounds in a cold regionrdquo Constructionand Building Materials vol 25 no 1 pp 267ndash281 2011

[16] C Basyigit B Comak S Kilincarslan and I S Uncu ldquoAssess-ment of concrete compressive strength by image processingtechniquerdquo Construction and Building Materials vol 37 pp526ndash532 2012

[17] N Marinoni A Pavese M Foi and L Trombino ldquoCharacteri-sation of mortar morphology in thin sections by digital imageprocessingrdquo Cement and Concrete Research vol 35 no 8 pp1613ndash1619 2005

[18] P Soroushian M Elzafraney and A Nossoni ldquoSpecimenpreparation and image processing and analysis techniques forautomated quantification of concrete microcracks and voidsrdquoCement and Concrete Research vol 33 no 12 pp 1949ndash19622003

[19] J M S Prewitt ldquoParametric and nonparametric recognitionby computer an application to leukocyte image processingrdquoAdvances in Computers vol 12 pp 285ndash414 1972

[20] B Lehallier P Andrey Y Maurin and J-M Bonny ldquoIterativealgorithm for spatial and intensity normalization of MEMRIimages Application to tract-tracing of rat olfactory pathwaysrdquoMagnetic Resonance Imaging vol 29 no 9 pp 1304ndash1316 2011

[21] N R Pal and S K Pal ldquoA review on image segmentationtechniquesrdquo Pattern Recognition vol 26 no 9 pp 1277ndash12941993

[22] P K Sahoo S Soltani and A K C Wong ldquoA survey ofthresholding techniquesrdquoComputer Vision Graphics and ImageProcessing vol 41 no 2 pp 233ndash260 1988

[23] C K Leung and F K Lam ldquoPerformance analysis for a classof iterative image thresholding algorithmsrdquoPattern Recognitionvol 29 no 9 pp 1523ndash1530 1996

[24] M A Snyder D G Vlachos and V Nikolakis ldquoQuantita-tive analysis of membrane morphology microstructure and

polycrystallinity via laser scanning confocal microscopy appli-cation toNaX zeolitemembranesrdquo Journal ofMembrane Sciencevol 290 no 1-2 pp 1ndash18 2007

[25] Y M George B M Bagoury H H Zayed and M I RoushdyldquoAutomated cell nuclei segmentation for breast fine needleaspiration cytologyrdquo Signal Processing vol 93 no 10 pp 2804ndash2816 2013

[26] C Lopez-Molina B De Baets H Bustince J Sanz and EBarrenechea ldquoMultiscale edge detection based on Gaussiansmoothing and edge trackingrdquo Knowledge-Based Systems vol44 pp 101ndash111 2013

[27] B Wei and Z Liu ldquoThe effective particles edge detectionmethod based on laplacerdquo Procedia Engineering vol 29 pp3096ndash3099 2012

[28] D Dıaz-Pernil A Berciano F Pena-Cantillana and M AGutierrez-Naranjo ldquoSegmenting images with gradient-basededge detection using Membrane Computingrdquo Pattern Recogni-tion Letters vol 34 no 8 pp 846ndash855 2013

[29] T M Nguyen Q M Jonathan Wu D Mukherjee and HZhang ldquoA finite mixture model for detail-preserving imagesegmentationrdquo Signal Processing vol 93 no 11 pp 3171ndash31812013

[30] S K Mylonas D G Stavrakoudis and J B TheocharisldquoGeneSIS aGA-based fuzzy segmentation algorithm for remotesensing imagesrdquo Knowledge-Based Systems vol 54 pp 86ndash1022013

[31] X D Bai Z G Cao Y Wang Z H Yu X F Zhang and C NLi ldquoCrop segmentation from images by morphology modelingin the CIE Llowastalowastblowast color spacerdquo Computers and Electronics inAgriculture vol 99 pp 21ndash34 2013

[32] L Gui R Lisowski T Faundez P S Huppi F Lazeyras andMKocher ldquoMorphology-driven automatic segmentation of MRimages of the neonatal brainrdquo Medical Image Analysis vol 16no 8 pp 1565ndash1579 2012

[33] C Kurtz N Passat P Gancarski andA Puissant ldquoExtraction ofcomplex patterns from multiresolution remote sensing imagesa hierarchical top-downmethodologyrdquoPattern Recognition vol45 no 2 pp 685ndash706 2012

[34] B Naegel ldquoUsingmathematical morphology for the anatomicallabeling of vertebrae from 3D CT-scan imagesrdquo ComputerizedMedical Imaging and Graphics vol 31 no 3 pp 141ndash156 2007

[35] S K Sinha and PW Fieguth ldquoSegmentation of buried concretepipe imagesrdquo Automation in Construction vol 15 no 1 pp 47ndash57 2006

[36] F F Costa A J Sguarezi Filho C E Capovilla and I R SCasella ldquoMorphological filter applied in a wireless deadbeatcontrol schemewithin the context of smart gridsrdquoElectric PowerSystems Research vol 107 pp 175ndash182 2014

[37] K Lingadurai and M S Shunmugam ldquoUse of morphologicalclosing filters for three-dimensional filtering of engineeringsurfacesrdquo Journal of Manufacturing Systems vol 24 no 4 pp366ndash376 2005

[38] K L Mak P Peng and K F C Yiu ldquoFabric defect detectionusing morphological filtersrdquo Image and Vision Computing vol27 no 10 pp 1585ndash1592 2009

[39] M Fathy and M Y Siyal ldquoAn image detection technique basedon morphological edge detection and background differencingfor real-time traffic analysisrdquo Pattern Recognition Letters vol 16no 12 pp 1321ndash1330 1995


[40] Alaknanda R S Anand and P Kumar ldquoFlaw detection inradiographic weld images usingmorphological approachrdquoNDTand E International vol 39 no 1 pp 29ndash33 2006

[41] T-G Li S-PWang andN Zhao ldquoGray-scale edge detection forgastric tumor pathologic cell images bymorphological analysisrdquoComputers in Biology and Medicine vol 39 no 11 pp 947ndash9522009

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Table 1 Mixing proportion and compressive strength for pavement concrete specimens

Code Cement Crushed stone Water Sand Slag Fly ash Superplasticizer Compressive strength(kgm3) () (MPa)

C30 285 1185 129 726 57 38 08 358C40 315 1170 143 717 63 42 08 479

X-ray source

Sample

Axis of rotation

Core beam

Detector

(a) (b)

Figure 1 (a) Basic principle with cone beam and muhidetector for CT scanner (b) Micro-CT scanning devices

(eg mathematic morphology) However there is no sin-gle accepted method of achieving the segmentation for allimages So finding or matching a new effective segmentationmethod is indispensable to obtain better segmentation resultsfor CT concrete image

The paper is organized as follows First the preparationof pavement concrete samples and CT testing method arepresented in Section 2 Section 3 presents the image methodsused in the segmentation and the comparative analysis ofthese methods It has been shown that the single traditionalmethod fail to perform segmentation forCT imageswith low-contrast edge effectively So a new method a combination ofmathematic morphology and Otsu method is developed inSection 4 Section 5 draws the conclusions

2 Experimental Preparation andCT Testing Method

21 Sample Preparation Pavement concrete with the worka-bility slump of 20ndash40mm and the strength grade of C30 andC40 is prepared by mixing these raw materials with differentproportionThe basicmaterials are ordinary portland cement425R river sand crushed stone (size range 5ndash265mm)and superplasticizer (06ndash1 recommended dosage and 30water reduction ratio) Six cube specimens of dimensions100 times 100 times 100mm consist of five cube specimens for testing28-day compressive strength and one for CT scanning Themixing proportions of raw materials and the compressivestrength of specimen are presented in Table 1

22 CT TestingMethod TheX-ray image analysis of concretespecimens is carried out nondestructively in the micro-CTscanner shown in Figures 1(a) and 1(b) As X-rays conductthrough the concrete specimens they are attenuated due tothe absorption of objects with different material density Thetwo-dimensional or three-dimensional image can be recon-structed based on X-ray attenuation information which ismeasured by an X-ray muhidetector Concrete specimens arescanned through micro-CT scanner with a 225 kv voltages06mA current cone beam scan mode 05 micron detectionaccuracy and 012ndash013 millimeter scanning interval

3 Traditional Methods forImage Segmentation

The aim of the segmentation for concrete specimens isto separate objects from background image However thesegmentation of CT images with low contrast is not an easytask Traditional image segmentation methods are based onthe similarities and discontinuities in the gray images [22ndash28] In this section the comparative analysis of thresholdalgorithms and edge detecting techniques is carried out

31Threshold SegmentationMethods Thethreshold approachbased on the gray histogram is a simple practical imagesegmentation technique which only requires a gray thresholdvalue but if the threshold value is not appropriate thesegmentation performance of the method would be directlyaffected Common approaches founded on thresholdmethod





1is


1 and then



2according



1198791=

(119891min + 119891max)

2

(1)

1205831=

sum119879

119894=0119894119901119894

sum119871minus1

119894=0119901119894

1205832=

sum119871minus1

119894=119879+1119894119901119894

sum119871minus1

119894=0119901119894

119879119896=

(1205831+ 1205832)

2

(2)




of gray 119894



1199010(119879) =

119879

sum

0

119875119894

1199011(119879) =

119871

sum

119879+1

119875119894= 1 minus 119901

0(119879)

119901119894=

119899119894

119873

1205830(119879) =

119879

sum

119894=0

119894

119901119894

1199010(119879)

1205831(119879) =

119871

sum

119894=119879+1

119894

119901119894

1199011 (

119879)

1205752

0(119879) =

119879

sum

119894=0

(119894 minus 1205830(119879))2 119875119894

1198750(119879)

1205752

1(119879) =

119871

sum

119894=119879+1

(119894 minus 1205831(119879))2 119875119894

1199011(119879)

120583 =

119871

sum

119894=0

119894119901119894

1205752

119908(119879) = 119875

0 (119879) 1205752

0(119879) + 119875

1 (119879) 1205752

1(119879)

119879lowast= arg1lt119879le119871

max 1205752

119887(119879)

(3)




1 119871] 1199010(119879) and 119901


1205752

0(119879) and 120575

2


0and 119901

1 120583



classes




2


2

12

(4)

119866 (119891 (119909 119910)) = radic1198911015840

119909(119909 119910) + 119891

1015840

119910(119909 119910) (5)

119866 (119891 (119909 119910)) =

100381610038161003816100381610038161198911015840

119909(119909 119910)

10038161003816100381610038161003816+

100381610038161003816100381610038161198911015840

119910(119909 119910)

10038161003816100381610038161003816 (6)


(a) (b)

(c) (d)

(e) (f)


119866 (119891 (119909 119910))

= radic[119866119909(119909 119910) sdot 119891 (119909 119910)]

2+ [119866119910(119909 119910) sdot 119891 (119909 119910)]

2

119866 (119909 119910) =

1

21205871205902exp(

minus (1199092+ 1199102)

21205902

)

120579 (119909 119910) = arctan(

119866119909(119909 119910)

119866119910(119909 119910)

)

(7)

119866 (119891 (119909 119910)) = nabla2(119866 (119909 119910) lowast 119891 (119909 119910))

119866 (119909 119910) =

1

21205871205902exp(minus

1199092+ 1199102

21205902

)

(8)





119860)



(119860Θ119861) (119904 119905) = min 119860 (119904 + 119909 119905 + 119910)

minus 119861 (119909 119910) | (119904 + 119909) (119905 + 119910) isin 119885119860 (119909 119910) isin 119885

119861



119861

(9)










119860 ∘ 119861 = (119860Θ119861) oplus 119861

119860 ∙ 119861 = (119860 oplus 119861)Θ119861

(10)



1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 2 4 1

1 2 1 3 1

1 4 2 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 1 3

1 3 1 0 5

1 4 3 1 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 1 3 1

1 4 3 2 1

1 1 1 1 1

0 1

0 1 0

1 1

0 2 0

2 3 2

0 2 0



minus1

minus1


minus2

minus2

minus2

minus2

minus2

minus2

minus2


center 3


1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 6 4 1

1 6 7 6 1

1 4 6 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 5 3

1 3 5 6 5

1 4 3 5 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 7 3 1

1 4 3 2 1

1 1 1 1 1

4 4 4 4 4

4 5 6 7 4

4 6 7 6 4

4 7 6 5 4

4 4 4 4 4

0 2 0

2 3 2

0 2 0













1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3


minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)


119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)








(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







1is


1 and then



2according



1198791=

(119891min + 119891max)

2

(1)

1205831=

sum119879

119894=0119894119901119894

sum119871minus1

119894=0119901119894

1205832=

sum119871minus1

119894=119879+1119894119901119894

sum119871minus1

119894=0119901119894

119879119896=

(1205831+ 1205832)

2

(2)




of gray 119894



1199010(119879) =

119879

sum

0

119875119894

1199011(119879) =

119871

sum

119879+1

119875119894= 1 minus 119901

0(119879)

119901119894=

119899119894

119873

1205830(119879) =

119879

sum

119894=0

119894

119901119894

1199010(119879)

1205831(119879) =

119871

sum

119894=119879+1

119894

119901119894

1199011 (

119879)

1205752

0(119879) =

119879

sum

119894=0

(119894 minus 1205830(119879))2 119875119894

1198750(119879)

1205752

1(119879) =

119871

sum

119894=119879+1

(119894 minus 1205831(119879))2 119875119894

1199011(119879)

120583 =

119871

sum

119894=0

119894119901119894

1205752

119908(119879) = 119875

0 (119879) 1205752

0(119879) + 119875

1 (119879) 1205752

1(119879)

119879lowast= arg1lt119879le119871

max 1205752

119887(119879)

(3)




1 119871] 1199010(119879) and 119901


1205752

0(119879) and 120575

2


0and 119901

1 120583



classes




2


2

12

(4)

119866 (119891 (119909 119910)) = radic1198911015840

119909(119909 119910) + 119891

1015840

119910(119909 119910) (5)

119866 (119891 (119909 119910)) =

100381610038161003816100381610038161198911015840

119909(119909 119910)

10038161003816100381610038161003816+

100381610038161003816100381610038161198911015840

119910(119909 119910)

10038161003816100381610038161003816 (6)


(a) (b)

(c) (d)

(e) (f)


119866 (119891 (119909 119910))

= radic[119866119909(119909 119910) sdot 119891 (119909 119910)]

2+ [119866119910(119909 119910) sdot 119891 (119909 119910)]

2

119866 (119909 119910) =

1

21205871205902exp(

minus (1199092+ 1199102)

21205902

)

120579 (119909 119910) = arctan(

119866119909(119909 119910)

119866119910(119909 119910)

)

(7)

119866 (119891 (119909 119910)) = nabla2(119866 (119909 119910) lowast 119891 (119909 119910))

119866 (119909 119910) =

1

21205871205902exp(minus

1199092+ 1199102

21205902

)

(8)





119860)



(119860Θ119861) (119904 119905) = min 119860 (119904 + 119909 119905 + 119910)

minus 119861 (119909 119910) | (119904 + 119909) (119905 + 119910) isin 119885119860 (119909 119910) isin 119885

119861



119861

(9)










119860 ∘ 119861 = (119860Θ119861) oplus 119861

119860 ∙ 119861 = (119860 oplus 119861)Θ119861

(10)



1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 2 4 1

1 2 1 3 1

1 4 2 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 1 3

1 3 1 0 5

1 4 3 1 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 1 3 1

1 4 3 2 1

1 1 1 1 1

0 1

0 1 0

1 1

0 2 0

2 3 2

0 2 0



minus1

minus1


minus2

minus2

minus2

minus2

minus2

minus2

minus2


center 3


1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 6 4 1

1 6 7 6 1

1 4 6 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 5 3

1 3 5 6 5

1 4 3 5 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 7 3 1

1 4 3 2 1

1 1 1 1 1

4 4 4 4 4

4 5 6 7 4

4 6 7 6 4

4 7 6 5 4

4 4 4 4 4

0 2 0

2 3 2

0 2 0













1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3


minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)


119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)








(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b)

(c) (d)

(e) (f)


119866 (119891 (119909 119910))

= radic[119866119909(119909 119910) sdot 119891 (119909 119910)]

2+ [119866119910(119909 119910) sdot 119891 (119909 119910)]

2

119866 (119909 119910) =

1

21205871205902exp(

minus (1199092+ 1199102)

21205902

)

120579 (119909 119910) = arctan(

119866119909(119909 119910)

119866119910(119909 119910)

)

(7)

119866 (119891 (119909 119910)) = nabla2(119866 (119909 119910) lowast 119891 (119909 119910))

119866 (119909 119910) =

1

21205871205902exp(minus

1199092+ 1199102

21205902

)

(8)





119860)



(119860Θ119861) (119904 119905) = min 119860 (119904 + 119909 119905 + 119910)

minus 119861 (119909 119910) | (119904 + 119909) (119905 + 119910) isin 119885119860 (119909 119910) isin 119885

119861



119861

(9)










119860 ∘ 119861 = (119860Θ119861) oplus 119861

119860 ∙ 119861 = (119860 oplus 119861)Θ119861

(10)



1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 2 4 1

1 2 1 3 1

1 4 2 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 1 3

1 3 1 0 5

1 4 3 1 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 1 3 1

1 4 3 2 1

1 1 1 1 1

0 1

0 1 0

1 1

0 2 0

2 3 2

0 2 0



minus1

minus1


minus2

minus2

minus2

minus2

minus2

minus2

minus2


center 3


1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 6 4 1

1 6 7 6 1

1 4 6 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 5 3

1 3 5 6 5

1 4 3 5 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 7 3 1

1 4 3 2 1

1 1 1 1 1

4 4 4 4 4

4 5 6 7 4

4 6 7 6 4

4 7 6 5 4

4 4 4 4 4

0 2 0

2 3 2

0 2 0













1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3


minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)


119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)








(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials












119860 ∘ 119861 = (119860Θ119861) oplus 119861

119860 ∙ 119861 = (119860 oplus 119861)Θ119861

(10)



1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 2 4 1

1 2 1 3 1

1 4 2 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 1 3

1 3 1 0 5

1 4 3 1 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 1 3 1

1 4 3 2 1

1 1 1 1 1

0 1

0 1 0

1 1

0 2 0

2 3 2

0 2 0



minus1

minus1


minus2

minus2

minus2

minus2

minus2

minus2

minus2


center 3


1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 6 4 1

1 6 7 6 1

1 4 6 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 5 3

1 3 5 6 5

1 4 3 5 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 7 3 1

1 4 3 2 1

1 1 1 1 1

4 4 4 4 4

4 5 6 7 4

4 6 7 6 4

4 7 6 5 4

4 4 4 4 4

0 2 0

2 3 2

0 2 0













1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3


minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)


119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)








(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 2 4 1

1 2 1 3 1

1 4 2 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 1 3

1 3 1 0 5

1 4 3 1 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 1 3 1

1 4 3 2 1

1 1 1 1 1

0 1

0 1 0

1 1

0 2 0

2 3 2

0 2 0



minus1

minus1


minus2

minus2

minus2

minus2

minus2

minus2

minus2


center 3


1 1 1 1 1

1 2 3 4 1

1 3 4 3 1

1 4 3 2 1

1 1 1 1 1

1 1 1 1 1

1 1

1 4 1

1 1

1 1 1 1 1

1 1 1 1 1

1 4 6 4 1

1 6 7 6 1

1 4 6 4 1

1 1 1 1 1

1 1 1 1 1

1 2

1 3 3

1 4

1 1 1 1 1

1 1 1 1 1

1 2 3 5 3

1 3 5 6 5

1 4 3 5 3

1 1 1 1 1

1 1 1 1 1

1 2 3 4 1

1 3 7 3 1

1 4 3 2 1

1 1 1 1 1

4 4 4 4 4

4 5 6 7 4

4 6 7 6 4

4 7 6 5 4

4 4 4 4 4

0 2 0

2 3 2

0 2 0













1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3


minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)


119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)








(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









1198661(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE2)

minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE2)]Θ119861 (SE1)

1198662(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE3)

0 0 0 0 0 0

00

00

00000

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

1

1

1 11

1

1

OriginSE =

R = 3


minus ((119860 ∘ 119861) ∙ 119861)Θ119861 (SE3)]Θ119861 (SE2)

119866119899(119909 119910) = [((119860 ∘ 119861) ∙ 119861) oplus 119861 (SE119899)


119866 (119909 119910) =

1

119899

119899

sum

119894=1

119866119894(119909 119910)

(11)








(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









(Ij0)

(Ij1)



Yes

SE = 1

No

I = (I3 + I5 + I7)3

If SE le 7


J = SE + 2



IJ = Ij0 minus Ij1

elements)








5 Conclusions






Acknowledgments



C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




C30(A1) C30(A3)C30(A2)

C30(G1) C30(G3)C30(G2)

C40(A1) C40(A3)C40(A2)

C40(G1) C40(G2) C40(G3)



References





















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials














































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article concrete image segmentation based on multiscale mathematic morphology...

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