with the rapid development of the image processing , reverse engineering , computer - aided design , and image guidance play an important role in dental implant surgery .
a number of dental and jaw imaging modalities , including video imaging , computed tomography ( ct ) , and magnetic radiotherapy imaging ( mri ) , are used in image - aided dental implant surgery . performing the multimodality image registration from different imaging devices has complementary significance for guiding dental implant surgery . when dentists design schemes , they want to consider the morphology of the soft tissue and the hard tissue together .
ct image and visible spectrum image fusion models   can multiply various factors and help the dentists achieve the optimal implant scheme .
traditional registrations of cone beam computed tomography ( cbct ) and other three - dimensional scanner models mainly rely on the fiducial markers method , which need to manually select the feature points . in [ 68 ] , manual feature selecting methods have been tried for the registration of the mandible ct and plaster cast of the dental models . because the images are complex and the location accuracy is limited by the experience of the operator and the operating state , the manual feature selecting method might provide misleading information and lead to instability problems .
designed an occlusal form board , with titanium spheres markers , to match the image using the titanium spheres markers as feature points . in this model ,
the position of makers is stable , but the drawback is the extra burden for patients .
the methods mentioned above can not perfectly meet the needs of developing image - aided dental surgery .
two main difficult problems are taken out in the process of the registration ; one is the feature point selection and the other is the merge of different modality images with different resolutions .
iterative closest point ( icp ) , in recent years , many researchers have extended or improved the traditional icp algorithm .
proposed the fractional icp ( ficp ) algorithm to trim abnormal points effectively , which enhanced the robustness of the icp algorithm .
choi et al .   proposed the improved k - d trees traversal method to accelerate finding process of the nearest points .
bae and lichti   further extended the improved icp method based on the boundary feature points of the point cloud , which improved the efficiency and accuracy of traditional icp algorithm greatly .
the aim of this work is to develop an improved iterative closest point ( icp ) algorithm in terms of the problem of registration with different image resolutions .
firstly , extract feature point set based on curvature characteristics , and then achieve the registration results by two procedures : the coarse registration and the precise registration . to verify the reliability of the improved icp algorithm , we test it with 3d cbct dental model and ineos blue - light scanned model .
these two models provide reconstructed ct dental data and visible light scanned dental - surface data , respectively .
experimental results show that the accuracy is increased significantly and this solution meets the requirements of the image - assisted surgery .
section 2 provides an overview of the icp algorithm and proposes an improved icp algorithm .  
section 4 reports the results of experiments conducted on the cbct model and the ineos blue scanned model and provides the discussions .
generally , different medical imaging equipment differs in imaging mechanism , which contributes to different emphases on image information and makes image resolution difference .
thus , it results in complex difficulties in the image fusion ; for example , the preprocessed 3d cbct dental model contains two parts : dental crowns and roots , while the 3d ineos blue - light dental model contains dental crowns only .
additionally , the resolution of the cbct model is 0.625  mm , while that of ineos blue - light scanner is 0.1  m . in view of data characteristics above
first of all , feature point set of the three - dimensional surface images was extracted based on curvature characteristics to realize the coarse registration and to achieve the transformation matrix .
then , the feature point set and reference point set , obtained by the initial registered transformation , are processed in the precise registration step using icp .
icp algorithm is commonly used as registration method , which enables the minimum mean square error in the distance of corresponding point or point surface between two point sets approaching the minimal by iterative calculations .
it repeats the process of calculating the optimal rigid transformation of the corresponding point set until convergence criterion is satisfied ; that is , it has met the precision of registration .
the transformation relation is shown as function ( 1 ) , and the convergence criterion is shown as function ( 2 ) : 
 ( 1)qi = rpi+t,(2)e=i=1n||qi(rpi+t)||2 , 
 where pi and qi present point sets corresponding to two images , respectively , r is a rotation matrix , t is a translation vector , and e is the error . when the error reaches the minimum , the convergence criterion meets requirement .
the traditional icp algorithm used in registration requires one of the two point sets to be the subset of the other one .
the relatively initial positions of two point sets are limited strictly in icp , which ensure no big gap between the two point sets .
when the constraints are unsatisfied or the huge deviation exists , it will affect the processing results and make the registration unreliable .
the data of the cbct dental model and the ineos blue scanned model are both stored in stl file form and 3d models .
the image surface discrete curvatures are sampled as the feature set . because the stl model is comprised of many triangular meshes , an improved voronoi method is implemented to calculate vertex curvature . as shown in figure 1 , v0 is a vertex of the network model
. the curvature of v0 can be calculated by 
 ( 3)k=2jja  ( j=1,2,  ,n ) , 
 where j is the angle between the side v0vj and the side v0vj+1 , and a is the area of all triangle meshes which are connected with v0 . set  as the threshold . when the curvature of one point is greater than  , it will be marked as feature point and put it into alternative feature list .
the feature point set is defined as p = { pi | pi  r ; i = 1,2 , 3 ,  , np}. the improved three point 's translational transformation method is used in this paper based on curvature characteristics to calculate rotation matrix r and translation vector t , so as to realize the semiautomatic extraction of corresponding points for two dental image models . at the same time , this method can reduce the interference of human factors in the matching process and enhance the accuracy of coarse registration . for the two image models ,
select three points , whose curvatures in the top 10 percent and distributions are homogeneous , as the reference points from the reference model and the corresponding points are in target model . after achieving reference points
, we calculate the curvature of each vertex in target model and compare it with their value of the reference points . when the error is smaller than the setting threshold , mark this point as the centralized point of corresponding points and put it into corresponding points list .
due to the fact that there are some feature points with the same or similar curvature , it is common to lead to one reference point corresponding to some points .
so we construct more powerful constraint condition , the distance of three points , and the area of triangle of three points , further to select the corresponding point set .
this constraint condition is independent of rigid transformation and will improve the reliability and efficiency of determining corresponding points , and its specific steps are as follows .
assume there are three known reference points m1(x1 , y1 , z1 ) , m2(x2 , y2 , z2 ) , and m3(x3 , y3 , z3 ) and three corresponding points n1 , n2 , and n3 that need to be determined . let a , b , and c represent the distance between m1 , m2 or m1 , m3 and m2 , and m3 , respectively .
the computing function of the distance and the area are shown as follows : 
 ( 4)a=(x1x2)2+(y1y2)2+(z1z2)2,b=(x1x3)2+(y1y3)2+(z1z3)2,c=(x2x3)2+(y2y3)2+(z2z3)2,s=+b+c2(+b+c2b)(+b+c2c ) . 

the distance constraint condition is : 
 ( 5)|dmimjdninj|< ,  ( i , j=1,2,3 ) , 
 where dmimj and dninj are the distances between any two points of the reference points m1 , m2 , and m3 , and the corresponding points n1 , n2 , n3 , respectively .
the area constraint condition is shown by : 
 ( 6)|s(m)s(n)|< , 
 where s(m ) is the area of triangle composed of m1 , m2 , and m3 ; s(n ) is the area of triangle composed of the three corresponding points n1 , n2 , and n3 ; and  is the set error . through the above stated constraint conditions , we can select the corresponding points n1 , n2 , and n3 of the reference points m1 , m2 , and m3 . local coordinate system of one of the two image models is built by reference points in the reference model .
assume that m1 is the origin of coordinate and the direction from m2 to m3 is x axis direction .
local coordinates can be expressed by tm = ( t1(m ) , t2(m ) , t3(m ) ) , where 
 ( 7)t1(m)=m3m1|m3m1|,t2(m)=(m3m1)(m2m1)|(m3m1)(m2m1)|,t3(m)=t1(m)t2(m ) .
similarly , the local coordinate built by corresponding points n1 , n2 , and n3 is tn = ( t1(n ) , t2(n ) , t3(n ) ) . by formula deducing
, we could obtain rotation matrix r and translation vector t corresponding to the transformation of coordinate tm to tn : 
 ( 8)r = tn(tmt),(9)t = n1+n2+n33r(m1+m2+m3)3 .
then , the matrices  r and t are applied to the two target point sets and we could realize the course registration
. the accuracy of coarse registration can not satisfy the ultimate requirements [ 16 , 17 ] , so icp algorithm is adopted for getting higher registration accuracy .
assume that the feature point sets of blue - light scanner dental model and cbct dental model are p = { pi | pi  r ; i = 1,2 , 3 , 
, np } and q = { qj | qj  r ; j = 1,2 , 3 , 
, nq } , respectively , where np and nq stand for the number of the elements ( np  nq ) .
r , t are the rotation matrix and translation vector , which are obtained through the coarse registration .
then carry out the icp algorithm to make precise registration that consists of the following stages . 

step 1given that k = 0 , p = p , p = { pi | pi  r ; i = 1,2 , 3 ,  , np } ,
r = r , and t = t , use k - d tree method to calculate the corresponding point set d = { qj | j = i = 1,2 , 3 ,  , np } , which belongs to q , and each point qj is with the least euclidean distance to the point pi  ( i = 1,2 , 3 ,  , np ) .
define the initial residual error ; that is , r = ( 1/np)i=1||pi  d(i)|| . 
  given that k = 0 , p = p , p = { pi | pi  r ; i = 1,2 , 3 ,  , np } , r = r , and t = t , use k - d tree method to calculate the corresponding point set d = { qj | j = i = 1,2 , 3 ,  , np } , which belongs to q , and each point qj is with the least euclidean distance to the point pi  ( i = 1,2 , 3 , 
define the initial residual error ; that is , r = ( 1/np)i=1||pi  d(i)|| . 

step 2use r and t transform point set p to obtain the point set p , where p = rp + t. then calculate the corresponding point set d = { qj | j = i = 1,2 , 3 , 
, np } , which also belongs to q , and each point qj is with the least euclidean distance to the point pi . then compute the residual error r = ( 1/np)i=1||pi  d(i)|| . 
 
use r and t transform point set p to obtain the point set p , where p = rp + t. then calculate the corresponding point set d = { qj | j = i = 1,2 , 3 , 
, np } , which also belongs to q , and each point qj is with the least euclidean distance to the point pi . then compute the residual error r = ( 1/np)i=1||pi  d(i)|| . 
 step 3judge whether the precision meets the requirements after iterating k(k  0 ) times .
 r |  , is satisfied stop iterating . otherwise , continue to step 4 . 

step 4calculate the rotation matrix r and translation vector t of transform relation between p and d through the singular value decomposition ( svd ) method .
then renew k = k + 1 , and transfer to step 2 . 
  calculate the rotation matrix r and translation vector t of transform relation between p and d through the singular value decomposition ( svd ) method . then renew k = k + 1 , and transfer to step 2 .
the singular value decomposition ( svd ) method , used to calculate the rotation matrix and translation vector , is demonstrated in the appendix . 

the experimental procedures include acquiring data , preprocessing , extracting feature points , and registration .
firstly , using 3d sirona ineos blue blu - ray scanner ( resolution is 0.02  mm ) patient 's plaster dental model is scanned .
next , the own software of scanner is applied to obtain stl format dental file .
geomagic software is used to preprocess the exported file , and then , export the preprocessed file , which is stl that format includes dental crown only .
sirona galileos system ( resolution is 0.1  mm ) is adopted to scan the same patient 's mandible to obtain the ct scanning data .
the data is dicom format and then it is imported into commercial processing software called mimics , which is used to reconstruct 3d ct model .
the ineos blue dental model , showed in figure 4 as the sample , set the threshold  = 0.01 .
calculate the vertex curvature of the dental crown using the improved voronoi method mentioned before .
when the curvature value of any point is more than  , mark it as a feature point and put it into point set list , which is denoted by p. the red dots showed in figure 6 represent the feature points .
the resolution of 3d ineos blue dental data is higher than cbct data , while cbct model includes the integral dental data .
the improved three point 's translational transformation method is used to realize coarse registration , and the results are shown in figure 7 . select three corresponding points m1 , m2 , and m3 as reference points from cbct dental model and set the threshold 0.00015 . then extract the corresponding points n1
, n2 , and n3 and calculate rotation matrix r and translation vector t. the results are listed in table 1 . formula ( 8) is used to realize coarse registration , and figure 8 is the result of coarse registration .
based on the results of coarse registration , the precise registration is carried out for improving the accuracy of registration further .  
figure 9 is the result , which reveals that the two models can be fused more accurately .
supported by the vc6.0 platform , we used vc++ and opengl to conduct simulation and experiments .
we show dental models registration results to evaluate the accuracy of our algorithm , and the average distance of corresponding points is calculated . for the first experiment the average distance of the coarse registration , shown in table 2 , is 0.7291  mm while it is reduced to 0.3835  mm after precise registration .
other four groups of patient 's dental image data are carried out by the same procedure , which also conclude ineos blue scanner and cbct 3d dental models and yield the same conclusion .
the total average distance of the precise registration is 0.8266  mm , compared with 1.4486  mm of the coarse registration . comparing with the coarse registration accuracy ,
the precise one is improved significantly , which basically meets the requirements of helping dentist for designing remedies .
considering the characteristic of the stl model data itself , we take the cbct 3d dental model as the reference model and adopt the constraint - based curvature method .
as mentioned earlier , extract the corresponding feature points automatically in the ineos blue scanner dental model .
experimental results show that the method could extract the corresponding feature points correctly and be operated simply and reliably .
moreover , it efficiently overcomes the shortages of both the traditional surface - based marking method and the corresponding manually selected feature points method .
multimodality image registration and fusion technology can make full use of the complementary characteristics which are provided by different imaging models .
the technology could perfectly integrate the image data to provide abundant information for clinical diagnosis . the improved icp method proposed in this paper realized
the feature points extraction and image registration successfully between the ineos blue scanner dental model and the cbct 3d dental model .
besides , it provides reliable registration method in the computer - aided dental implant design system
. the research and the method in this paper will be the reference and application for similar studies and other multimodality image registrations .
imperfectly , in the process of extracting feature points with curvature characteristics , the threshold has to be appropriately adjusted according to the model complexity and the accuracy requirements , which make the registration accuracy to a larger degree depend on the reasonable choice .
as the traditional icp algorithm can not realize the image registration with different resolution , we propose an improved icp algorithm in this paper .
the procedure of this algorithm used in the registration of 3d cbct dental model and 3d ineos blue scanning dental model is discussed in detail .
 multimodality image registration and fusion has complementary significance for guiding dental implant surgery . as the needs of the different resolution image registration , we develop an improved iterative closest point ( icp ) algorithm that focuses on the registration of cone beam computed tomography ( ct ) image and high - resolution blue - light scanner image . 
 the proposed algorithm includes two major phases , coarse and precise registration . 
 firstly , for reducing the matching interference of human subjective factors , we extract feature points based on curvature characteristics and use the improved three point 's translational transformation method to realize coarse registration . 
 then , the feature point set and reference point set , obtained by the initial registered transformation , are processed in the precise registration step . 
 even with the unsatisfactory initial values , this two steps registration method can guarantee the global convergence and the convergence precision . 
 experimental results demonstrate that the method has successfully realized the registration of the cone beam ct dental model and the blue - ray scanner model with higher accuracy . 
 so the method could provide researching foundation for the relevant software development in terms of the registration of multi - modality medical data . 