caries is a multifactorial disease that is induced by the interaction among three factors , tooth , microflora , and diet .
radiography is a useful technique for detecting carious lesions as the caries process causes demineralization of enamel and dentin .
lesion is observed in a diagnostic image as a radiolucent ( darker ) zone since the demineralized area of the tooth does not absorb as many x - ray photons as the unaffected portion .
radiography is a valuable supplement to a thorough clinical examination of the teeth for detecting caries lesions .
various morphologic phenomena , such as pits and fissures , cervical burnout , and mach band effect , and dental anomalies , such as hypoplastic pits and concavities produced by wear , can mimic the appearance of a carious lesion [ 13 ] .
it has led to creation of digital multispectral ground surface images used in agricultural and forestry sectors . from mid-1970s to 1980s , the medicine has been evolved by invention of computerized axial tomography scanners ( cat scan ) and magnetic resonance imagery ( mri ) .
in addition , since entering to entrainment world at the end of 1980s , digital image processing has been common in this industry . by appearance of machine vision , the world of industry has been constantly evolving by robots .
purity in production of food vessels and their mass production has led to spending more time and cost on this technology
. the high detection rate of decay and restoration of tooth by dentist require the mechanized systems with high quality and detection rate . through such mechanized systems
, it is possible to control and communicate with data in optimal databank and compare them with valid values in real - time control units to provide the optimum and fastest machine vision systems .
sometimes we need to complete the detection and restoration of teeth for a moment . using the ocr frequent images of a tooth , it is possible to detect its decay and restoration in a fraction of a second .
this is related to time of a qualitative problem , and the new system stops and detection process resumes once that problem is resolved .
a dentist starts repairing the dental caries and restoration once he / she detects its location in mouth ( figure 1 ) . in the second section , we review the previous research conducted in detection of dental caries and restoration and image processing .
in addition , we introduce works related to detection with pso or other algorithms in other fields of study . in the third section , we explain briefly our proposed method for detection of dental caries and restoration . in the fourth section
then , in the discussion section , we describe results of experiment and limitation of pso with our formulation for 2d and 3d .
based on investigating previous works , no study was found on intelligent detection of dental caries and restoration using image processing and algorithms [ 5 , 7 ] . no researcher has researched in this area .
all of the detections were done by dentist , as a dentist looks at picture and detects dental caries and restoration on basis of his own experiences .  
figure 2(a ) illustrates detection of one spot of dental decay and restoration ( figure 2 ) . in another study ,
image processing was applied for detecting liquid level in bottle using some algorithms , rather than pso , which are not either popular or efficient ( figure 3 ) .
figure 3 indicates detection of liquid surface level using this algorithm [ 8 , 9 ] .
the log algorithm shows that the location of edge occurrence is neither smooth nor thin .
the steps of log algorithm can be summarized as follows [ 8 , 9 ] : ( a ) convolving of image i by two - dimensional gaussian function ; ( b ) calculation of convolved image 's laplace ; ( c ) edge pixel for passing from zero which is in l. kani was assumed to be edge conditional to white gaussian noise .
the edge detector was considered with cannulation filter f , which distributes noise and location of edge . here , the problem is to determine a filter that optimizes three criteria in recognition of a given edge .
algorithm kani   is as follows:(a)reading image i.(b)convolving on one - dimensional gaussian cover with i.(c)gaussian first derivative in the directions x and y.(d)convolved i with g along rows and bottom of columns to obtain i 
 x and i 
 y , respectively.(e)convolved i 
 x with g 
 x to reach i 
 x and i 
 y with g 
 y to have i 
 u.(f)finding results in any pixel . 
 
convolving on one - dimensional gaussian cover with i. gaussian first derivative in the directions x and y. convolved i with g along rows and bottom of columns to obtain i 
 x and i 
 y , respectively .
convolved i 
 x with g 
 x to reach i 
 x and i 
 y with g 
 y to have i 
 u. finding results in any pixel .
standard pso algorithm has a population with m members , where each member is one potential solution in d - dimensional space of the problem [ 11 , 12 ] . in the standard pso algorithm , in the t iteration , the d - dimension of rate and situation of i member vary according to ( 1 ) and ( 2 ) , respectively ; w , c 
 1 , and c 
 2 are nonnegative real constant parameters ; and r 
 1 and r 
 2 are independent random numbers with uniform distribution in the range of 0 to 1 .
consider ( 1)vidt+1=vidt+c1r1,idtpidtxidt+c2r2idtpgdtxidt , 
 ( 2)xidt+1=xidt+vidt+1 . 
  in fitness function , to obtain the threshold value for detecting the lesions in specific point ( the center of lesions ) based on the experience , we calculate an average of the selected color of the whole pixels of the image of human teeth .
hence , we do not take into account the points around the image of teeth which are not considered as the part of the human tooth .
we multiply this average by 20% to obtain the threshold value for detecting the point where the lesions are formed around it .
because the quality of pictures may change by receivers , we alter this 20% to 1 to 3% , indeed 17% to 23% using  variable ( ( 3 ) formula ) . by multiplying the specified value by  instead of  ,
the threshold value for the points surrounding pixels can be found ( formula ( 4 ) ) . consider(3)threshold  x=20100i=1i = row  j=1j = columnpi , j ;  pi=1,  ,row , j=1, 
,columnai=1i = row  j=1j = columncount = count+1 ;  pi=1,  ,row , j=1,  ,columna , 
 ( 4)threshold  x  around=20100i=1i = row  j=1j = columnpi , j ;  pi=1,  ,row , j=1, 
,columnai=1i = row  j=1j = columncount = count+1 ;  pi=1,  ,row , j=1,  ,columna . 
 
the threshold value ( threshold x ) for the central point is always less than the threshold value ( thresholdaround ) for surrounding areas .
since this is the start point and end point of lesion , the threshold value will be always higher than that in other points , unless the lesion is improved . for detecting the edges in four directions , we move pixel by pixel and review the threshold value of surrounding points , until a pixel is found with a threshold value higher than the threshold value of surrounding points .
we save the spacing of these points to the central point ( formula ( 5 ) ) .
then , we calculate the average of all points within a certain range around the central point ( formula ( 6 ) ) .
consider(5 ) 
 ( 6 ) 
  by investigating some conditions one can recognize that the central point can be the central point of lesion ( formula ( 7 ) ) .
the conditions are as follows : ( 1 ) the color of considered point should be lower than the threshold value . ( 2 ) the average of whole points within a certain range around the central point should be lower than the threshold value .
( 3 ) the difference between horizontal and vertical edges should be less than the threshold value separately , since this causes not going further away from the main edge of the teeth .
last part of fitness function is related to existence or nonexistence of preapical lesion in x point and around x point ( 7 ) .
consider ( 7)exist_carious_lesion=1;cxxi , jthreshold  x  around , cxavg  pointthreshold  x  around , ab||cdthreshold  x  around0;other . 
 
p , row , column , a and count are pixel ( point ) of picture , maximum row of picture , maximum column of picture , point of carious lesions and restoration teeth in picture , and number of selecting points for calculation .
p 
 i , j is color value of image(i , j , 1 ) or image(i , j , 2 ) or image(i , j , 3 ) .
x 
 i , j is one point in place of image(x 
 i , x 
 j , 1 ,  , 3 ) and x 
 i is value of 1 ,  , row , x 
 j is value of 1 ,  ,
column , and c 
 x is constant value to avoid detection out of tooth .
in this section , study results are presented .   figure 4(b ) shows a tooth with no decay and restoration , while the one in figure 4(a ) shows distribution of particles for detection of dental caries and restoration .
figures 5 , 6 , and 7 show presence of decay and restoration in one tooth . through the experiments conducted in this research ,
distribution of particles can be observed in ( a ) of figures 4 , 5 , 6 , and 7 .
secondly , particles start to move in any picture . during running , pso algorithm calculates value of transferring for any particle . after running the algorithm ,
if the carious lesions or restoration is in teeth , pso algorithm can recognize it and identify its location .  
figure 4 indicates a picture where there are no dental caries and restoration , while figures 5 , 6 , and 7 illustrate that three other pictures have one case of dental caries and restoration .
our algorithm in figure 4(b ) does not show any dental caries and restoration . in comparison ,
the algorithm shows the place of dental caries and restoration for figures 5(b ) , 6(b ) , and 7(b ) through a green line crossing a yellow line .
the algorithm converges very fast between 1 and 50 iterations . in other words , convergence occurs very fast .
it has been shown that when six people without having any consultation with each other observe and interpret an x - ray radiographic stereotype , only 50% of them will have the same opinions ; moreover , when radiographs are shown to a person at two different times , different interpretations are presented .
hence , it is recommended that , in order to interpret the radiographs , two independent people are used , and if there is disagreement between them , they should consult with each other to find an agreement , and if not so , one can ask a third person to offer his / her opinion ; in this case , differences will be reduced from 50% to 25%
. of mass particle swarm optimization ( pso ) features , one can refer to the system memory in this system , in which the knowledge of proper solutions can be maintained by all the particles ; in other words , in the algorithm of mass particle , every particle can benefit from its past information , while there are no such behaviors and features in other evolutionary algorithms .
also , in this algorithm , the populations are connected with each other and they solve their problem through the exchange of the information in a high speed convergence way . using pso algorithm with the help of image interpretation , the x - ray radiography processing error can be minimized .
the differences in the interpretations of x - ray radiographies can be reduced from 25% to less than 8% , as well .
our results show that this method can detect dental caries and restoration in digital radiography pictures .
the error rate of this method was 8% , so that it can be implemented for detection of dental caries and restoration by dentist , since the error rate can be even reduced below 0.5% .
therefore , we will do detection and repair of tooth diagnosis intelligently in the future . this method will come to help some special robots for our area with ability of dental lesions restoration without human intervention in the future . according to the authors of this paper , introducing this intelligent
detecting lesions system in the future , as a result of designing the robots , will create a more prominent role , and developing of this intelligent system will support the clinicians in dental offices .
we also can apply color 2d image , because we just need to change detection value .
if it has any problem , we will change some parameters to solve this problem .
also we need to test more different images that some different systems can take images of teeth . our method is not a new algorithm .
in fact , we use pso algorithm and we have implemented the part of fitness by our formula .
therefore , we used both of image processing methods and particle swarm optimization ( pso ) algorithm for detecting teeth decay and restoration .
our results show that this method can detect dental caries and restoration in digital radiography pictures .
the error rate was 8% , so that it is possible to use for detection of dental caries and restoration by dentist . using the addition of some parameters , it is possible that the error rate can be even reduced below 0.5% .
this method can be potentially used for detection of dental caries and restoration in the future . as the guideline for future works
, the authors of this work recommend working on detection of dental caries and restoration using image processing and other popular algorithms .
 
 background / purpose . in terms of the detection of tooth diagnosis , 
 no intelligent detection has been done up till now . 
 dentists just look at images and then they can detect the diagnosis position in tooth based on their experiences . using new technologies , scientists will implement detection and repair of tooth diagnosis intelligently . in this paper , we have introduced one intelligent method for detection using particle swarm optimization ( pso ) and our mathematical formulation . 
 this method was applied to 2d special images . using developing of our method 
 , we can detect tooth diagnosis for all of 2d and 3d images . 
 materials and methods . in recent years , it is possible to implement intelligent processing of images by high efficiency optimization algorithms in many applications especially for detection of dental caries and restoration without human intervention . in the present work , 
 we explain pso algorithm with our detection formula for detection of dental caries and restoration . 
 also image processing helped us to implement our method . and to do so , pictures taken by digital radiography systems of tooth are used . 
 results and conclusion . 
 we implement some mathematics formula for fitness of pso . 
 our results show that this method can detect dental caries and restoration in digital radiography pictures with the good convergence . 
 in fact , the error rate of this method was 8% , so that it can be implemented for detection of dental caries and restoration . 
 using some parameters , it is possible that the error rate can be even reduced below 0.5% . 
1. Introduction
2. Materials and Methods
3. Particle Swarm Optimization (PSO)
4. Results
5. Discussion
6. Conclusion