CN109816705B - Characteristic point registration method for missing skull - Google Patents
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Abstract
The invention discloses a skull-missing characteristic point registration method, which aims at a skull point cloud model to be registered, and comprises the steps of firstly extracting characteristic points of a skull, calculating a characteristic sequence, and carrying out coarse registration on the skull by utilizing the similarity of the characteristic sequence; then, by screening the initial point of the skull point cloud model, expressing the correlation between any points in the initial point set by using the rotation matrix and the translation vector of rigid body transformation, converting the solution of rigid body transformation into a minimization problem and solving by adopting a singular value decomposition method to obtain the rotation matrix and the translation vector of the rigid body transformation of the initial point set, thereby realizing the fine registration of the skull point cloud model. The experimental result shows that compared with some existing methods, the method provided by the invention has the advantages that the registration accuracy and speed are obviously improved, and the effective registration of different resolutions and missing skulls can be realized.
Description
Technical Field
The invention relates to the technical field of restoration of skull appearances, in particular to a method for registering characteristic points of a missing skull with different resolutions.
Background
The craniofacial reconstruction is a technology for reconstructing the facial appearance of the human craniofacial by utilizing the modern computer technical means, and the craniofacial reconstruction is realized by taking the statistical thickness of the facial soft tissues of the human as the basis and combining a certain algorithm to add the soft tissues to the craniofacial. The existing common soft tissue adding method mainly comprises a skull deformation method and a three-dimensional volume deformation method, wherein the two methods both relate to a skull registration technology, so the skull registration is an important step of craniofacial reconstruction. At present, the skull registration technology has been widely applied in the fields of cadaver identity authentication, cadaver face restoration, face plastic surgery effect prediction, medical research and the like.
The feature points are the most basic feature elements of the skull point cloud model, the feature point matching is one of basic problems to be solved in computer vision, and the final target of point cloud feature point matching is accurately presented by accurately presenting the one-to-one correspondence of the feature points between the matching point cloud and the point cloud to be matched. At present, researchers at home and abroad propose a plurality of skull point cloud model registration methods based on characteristic points. E.g. von Yun [1] Skull registration is realized by adopting fully-automatically calibrated characteristic points; cumin vancyli, summimiscidine and the like [2] The characteristic point calibration is carried out on the three-dimensional skull sample by adopting a semi-automatic characteristic point calibration method, and craniofacial restoration is realized; tonxin dragon [3] A skull characteristic point matching method based on a partition statistic variable model is provided, and accurate skull registration is realized; zhou C, etc [4] A high-precision skull registration method is provided, and effective registration of a defect-free skull can be realized; wangu, etc. of cumin [5] The three-dimensional skull automatic registration method based on edge correspondence is provided, the problem of skull automatic registration with large initial posture difference is solved, but the algorithm consumes long time; tax such as noon yang [6] The registration of the reference skull and the unknown skull is realized by adopting an iterative closest point algorithm and a thin plate spline function, but the registration effect on the defective skull with low coverage rate is not good. Although the algorithms achieve higher registration accuracy and speed in the aspect of skull registration, most of the algorithms are used for registration realized by a complete skull point cloud model, and the registration effect in the state of lacking skull is not good.
[1] Automatic calibration of three-dimensional skull feature points [ J ] optical precision engineering, 2014,22 (5): 1388-1394.
[2] Improved craniofacial reconstruction method based on soft tissue thickness at characteristic points [ J ] computer application research 2016,23 (10): 3191-3200.
[3] Study on skull feature point matching algorithm based on partition statistical variable model [ D ]. Seian, northwest university, 2013.
[4]Zhou C,Anschuetz L,Weder S,et al.Surface matching for high-accuracy registration of the lateral skull base[J].Int J CARS,2016,11:2097-2103.
[5] Cumin vancyli, summisidine, gunn, gulison narastin, et al. three-dimensional skull automatic non-rigid registration method based on edge correspondence [ J ] computer applications 2016,36 (11): 3196-3200,3206.
[6] Tax noon, weekang, wuzhongke, etc. skull face restoration method for data registration [ J ] computer aided design and graphics bulletin, 2011,23 (4): 607-614.
[7]Liu X,Zhu L,Liu X,et al.Hierarchical skull registration method with a bounded rotation angle[C].ICIC,2017.7,pp 563-573.
[8] Optimized registration of a Zhaofu, zhou Ming quan, skull point cloud model [ J ] optical precision engineering, 2017,25 (7): 1927-1933.
Disclosure of Invention
The invention aims to provide a skull-missing feature point registration method, which solves the problems of poor registration effect under the conditions of large difference of skull point cloud resolution, missing and the like in the prior art.
In order to realize the task, the invention adopts the following technical scheme:
a method for registering characteristic points of a missing skull comprises the following steps:
step 1, respectively extracting characteristic points of skull point cloud models U and S to be registered to correspondingly obtain a characteristic point set S 1 And S 2 ；
Step 2, coarse skull registration
Computing a feature point set S 1 And S 2 Sequence of attributes at each feature point, for S 1 Each feature point s in 1i Corresponding attribute sequence F s1i Calculating S 2 Of each feature point s 2j Property sequence F of s2j And F s1i Of (2) Tonimoto coefficient T 1i Determining S by means of threshold screening 1 And S 2 To obtain S 1 And S 2 The rigid body transforms a rotation matrix and a translation vector to realize coarse registration of the skull point cloud model U and the skull point cloud model S;
step 3, skull fine registration
The skull point cloud model U and the skull point cloud model S have the same point number through initial point screening, the corresponding 3D point sets are respectively A and B, the correlation between any points in the A and the B is represented by using a rotation matrix and a translation vector of rigid body transformation, the solution of the rigid body transformation is converted into a minimization problem, a singular value decomposition method is adopted for solution, the rotation matrix and the translation vector of the rigid body transformation of the A and the B are obtained, and therefore the fine registration of the skull point cloud model U and the skull point cloud model S is achieved.
Further, the feature point extraction in step 1 specifically includes:
for any point p on a skull point cloud model i Let its k near neighborhood be Nbhd (p) i ) Nbhd (p) can be calculated from any point p in the neighborhood i ) The covariance matrix of (a) is:
in the formula (I), the compound is shown in the specification,
is Nbhd (p) i ) Average value of (d);
and (3) carrying out direction adjustment on normal vectors of all points on the skull point cloud model to ensure that the normal vectors meet the following requirements:
n i ·n j <0(i≠j) (2)
in the formula, n i 、n j Respectively representing arbitrary points p on the skull point cloud model i 、p j The normal vector of (a);
point p i Main curvature k of 1 ,k 2 The mean curvature H and the gaussian curvature K are respectively expressed as:
wherein L = f xx n，N＝f yy n，M＝f xy n，E＝f x f x ，F＝f x f y ，G＝f y f y N is a point p i Normal vector n of i ，f x 、f y Respectively representing partial differential of the curved surface z to x and y; f. of xx 、f yy 、f xy Respectively representing the second partial differential of the curved surface z to x, the second partial differential of y, and partial differential of y after partial differential of x is solved;
and calculating S (p) to extract the characteristic points of the skull, wherein the calculation formula of S (p) is as follows:
in the formula, k 1 (p) and k 2 (p) is the principal curvature of point p;
at any point p in the skull point cloud model i The criterion for judging whether the feature points are the feature points is as follows:
if S (p) i )>max(S(p i1 ),S(p i2 ),...,S(p ik ) P) then point p i Is a salient point;
if S (p) i )<min(S(p i1 ),S(p i2 ),...,S(p ik ) P) then point p i Are pits.
Wherein, S (p) i )、S(p i1 ),S(p i2 ),...,S(p ik ) Is a point p i Point p i Is a neighborhood point p i1 ,p i2 ,...,p ik Values of S (p) calculated by the formulas (6), respectively;
and taking the convex points and the concave points as characteristic points of the skull point cloud model.
Further, the attribute sequence at each feature point described in step 2 is composed of gaussian curvature and average curvature of the feature point.
Further, the S is determined by the threshold screening mode 1 And S 2 To obtain S 1 And S 2 The rigid body transformation rotation matrix and translation vector of (1), comprising:
calculating the Tonimoto coefficient T 1i If the minimum value is smaller than the set threshold epsilon, extracting a corresponding characteristic point pair as a matching point pair; if no point pair smaller than the threshold value epsilon exists, continuing S 1 Searching for matching point of next characteristic point until S 1 All feature points of (2) are in S 2 Until the search is finished;
get S 1 And S 2 Taking the matched characteristic point pair as a final registration point pair, and calculating a point set S by adopting a quaternion method 1 And S 2 The rotational matrix and the translation vector of the rigid body transformation.
Further, the method for representing the correlation between any points in a and B by using the rotation matrix and the translation vector of the rigid body transformation converts the solution of the rigid body transformation into a minimization problem and solves the minimization problem by using a singular value decomposition method to obtain the rotation matrix and the translation vector of the rigid body transformation of a and B, and comprises the following steps:
any point a in the point set A i And any point B in the point set B j The correlation of (d) is expressed as:
b j ＝Ra i +t (8)
in the formula, R represents a rotation matrix of rigid body transformation, and t represents a translation vector of the rigid body transformation;
the solution of the rigid body transformation (R, t) can be converted to the minimization problem as follows:
in the formula, the set SE (3) is a euclidean training set of 3D space, 1= [1, 1., 1=] T ，||·|| F Is an F norm;
equation (9) can be written in a form that depends only on the rotation matrix R:
wherein R.epsilon.SO (3) is a three-dimensional rotating group, and A 'and B' are defined as:
A'＝[a′ 1 ,...,a' N ]＝A{I N -(1/N)11 T } (11)
B'＝[b′ 1 ,...,b' N ]＝B{I N -(1/N)11 T } (12)
in the formula I N Is a cell matrix, a' i And b' i Is respectively from a when the point set is translated in rigid body transformation i And b j N, N represents the number of points in point set a or B;
in equation (10), the solution is obtained by Singular Value Decomposition (SVD), and thus:
in the formula (I), the compound is shown in the specification,
is a left-singular vector matrix of the left,
is a diagonal matrix containing singular values,
is a matrix of right singular vectors,
referring to three-dimensional space, then:
wherein, S is a matrix for avoiding matching of tiny point clouds when the point set contains noise, and diag () represents a diagonal matrix;
by using the formula (13), the rotation matrix R can be obtained from the formula (10) as
R＝VSU T (15)
Thereby obtaining the rigid body transformation rotation matrix R and the translation vector t of A and B.
Compared with the prior art, the invention has the following technical characteristics:
in the experiment of the method, an unknown skull is registered with 260 known skull, and a most similar reference skull is found, and the result shows that the characteristic point-based skull registration method is remarkably improved in registration accuracy and speed compared with the existing methods; the invention is a rapid and accurate skull registration method, which can realize effective registration of different resolutions and missing skull.
Drawings
FIG. 1 is an unknown skull U;
fig. 2 (a), (b), (c) and (d) are reference skulls S1, S2, S3 and S4, respectively;
FIG. 3 (a), (b), (c) and (d) are initial relative positions of U and S1, U and S2, U and S3, and U and S4, respectively;
fig. 4 (a), (b), (c) and (d) are respectively the front and side of the U and S1 registration result, the front and side of the U and S2 registration result, the front and side of the U and S3 registration result and the front and side of the U and S4 registration result;
FIG. 5 is an overall flow chart of the method of the present invention.
Detailed Description
The invention provides a method for registering characteristic points of a missing skull, which comprises the steps of extracting a skull point cloud or concave or convex characteristic points, and calculating a characteristic sequence of the characteristic points to realize coarse registration of the skull; and then, a point cloud registration algorithm based on Singular Value Decomposition (SVD) is adopted to realize fine registration of the skull, so that final accurate matching of the unknown skull and the reference skull is realized. The SVD-based point cloud registration algorithm can realize fine registration of the skull without iteration, so that the registration speed of the algorithm is greatly improved compared with that of the iterative closest point algorithm under the condition of ensuring the registration accuracy. The specific method of the invention is as follows:
step 1, respectively extracting characteristic points of skull point cloud models U and S to be registered, wherein the specific method comprises the following steps:
for the skull point cloud model, the points on the skull point cloud model have the characteristic of being convex or concave or flat in a local area, and the convex points and the concave points are the characteristic points of the skull point cloud model to be extracted. The specific extraction process of the feature points is as follows:
for any point p on a skull point cloud model i Let k be Nbhd (p) i ) Then p i The normal vector of (2) is the normal vector of the tangent plane fitted to all the neighboring points at the point. Here, p i Normal vector n of i The solution is obtained by Principal Component Analysis (PCA).
Nbhd (p) can be calculated from any point p in the neighborhood i ) The covariance matrix of (a) is:
in the formula (I), the compound is shown in the specification,
is Nbhd (p) i ) Average value of (a).
Then, p i Normal vector n of i That is, the eigenvector corresponding to the minimum eigenvalue of the covariance matrix X. In order to ensure the consistency of the normal vector directions of the points, the normal vectors of all the points on the skull point cloud model are subjected to direction adjustment so as to meet the following conditions:
n i ·n j <0(i≠j) (2)
in the formula, n j Representing arbitrary points p on a skull point cloud model j The normal vector of (2).
For point p i Since there is a curved surface z = f (x, y) approximating p i So that point p can be used i And the curvature of the local curved surface fitted with the neighborhood points of the local curved surface to characterize the curvature. Then, point p i Main curvature k of 1 ,k 2 The mean curvature H and the gaussian curvature K are respectively expressed as:
wherein L = f xx n，N＝f yy n，M＝f xy n，E＝f x f x ，F＝f x f y ，G＝f y f y N is a point p i Normal vector n of i ，f x 、f y Respectively representing partial differential of the curved surface z to x and y; f. of xx 、f yy 、f xy The method respectively represents the second partial differential of the curved surface z to x, the second partial differential of y, partial differential of x and partial differential of y after partial differential of x.
Next, the characteristic points of the skull are extracted by calculating S (p) by the formula
In the formula, k 1 (p) and k 2 The sum is the principal curvature of the point p, and is calculated by equation (3).
For any point p in the skull point cloud i The criterion for judging whether the feature points are the feature points is as follows:
if S (p) i )>max(S(p i1 ),S(p i2 ),...,S(p ik ) P) then point p i Is a salient point;
if S (p) i )<min(S(p i1 ),S(p i2 ),...,S(p ik ) P) then point p i Are pits.
Wherein, S (p) i1 ),S(p i2 ),...,S(p ik ) Is a point p i Neighborhood point p i1 ,p i2 ,...,p ik The S (p) values calculated by the equations (6), respectively.
By adopting the method, the concave or convex characteristic points of the skull point cloud model are extracted, and based on the characteristic points, the coarse registration of the skull can be realized.
Step 2, coarse skull matching
For two skull point cloud models U (unknown skull) and S (reference skull) to be registered, the feature point sets of the two skull point cloud models are assumed to be S respectively 1 And S 2 . Then to S 1 At any point s 1i First, its Gaussian curvature K is calculated 1i And average curvature H 1i Obtaining a sequence of attributes
Then find the point s 1i At S 2 The matching point in (1).
Searching feature point set S 1 And S 2 The specific steps of the matching points are as follows:
step 2.1, firstly, calculating a characteristic point set S 1 And S 2 Sequence of attributes at each feature point
Wherein i =1,2,. N 1 ，j＝1,2,..,n 2 ，n 1 And n 2 Respectively represent S 1 And S 2 The number of characteristic points in; the attribute sequence of each feature point is composed of the gaussian curvature and the mean curvature of the feature point.
Step 2.2, for S 1 Each feature point s in 1i Corresponding attribute sequence
Calculating S 2 Of each feature point s 2j Property sequence of
And
of (2) Tonimoto coefficient T 1i ：
In the above formula, C and D respectively represent a characteristic point s 1i And a characteristic point s 2j T denotes the Tonimoto coefficient.
Step 2.3, calculating the Tonimoto coefficient T 1i If the minimum value is smaller than the set threshold epsilon, extracting a corresponding characteristic point pair as a matching point pair; if no point pairs smaller than the threshold value epsilon exist, continuing S 1 Of the next characteristic pointSearch for matching points up to S 1 All feature points of (2) are in S 2 Until the search is finished; the threshold value epsilon is an integer, and specific numerical values are set according to the size and the complexity of the skull point cloud model during experiments.
Step 2.4, extracting S 1 And S 2 Taking the matched characteristic point pair as a final registration point pair, and calculating a point set S by adopting a quaternion method 1 And S 2 The skull point cloud model U and the skull point cloud model S can be preliminarily aligned through rotation and translation by the rotation matrix and the translation vector of the rigid body transformation, so that the rough registration of the skull point cloud model U and the skull point cloud model S is realized.
Step 3, skull fine registration
After the coarse registration process, the skull point cloud models U and S are basically aligned, and in the fine registration process, initial points of the two skull point cloud models are screened to realize fine registration. The skull fine registration is realized by adopting a point cloud registration algorithm based on SVD, and the algorithm provides a simple and quick skull point cloud registration algorithm aiming at the problem that an ICP algorithm needs to be iterated continuously. When the translation vector t of rigid body transformation is solved, the algorithm solves the translation vector t through the movement of the gravity center of a skull point set, and the calculation of an optimal rotation matrix is carried out in two steps: firstly, constructing a matching matrix by a singular value decomposition method, and then generating a rotation matrix by utilizing the inner product of each left singular vector; the time consumption of the algorithm is greatly improved compared with that of an ICP algorithm under the condition of not influencing the registration precision.
For skull point cloud models U (unknown skull) and S (reference skull) to be registered, the point cloud models of the skull point cloud models U (unknown skull) and S (reference skull) have the same point number N through initial point screening, namely, the corresponding 3D point sets are respectively as follows:
and
wherein
Representing a three-dimensional real space, a i And b j For any point in sets a and B, the method of initial point screening is from the literature: sparse point cloud simplification algorithm [ J ] of Zhang Yuan, gunn China, wei, natural, and so on, retaining geometric features]Computer aided design and graphics bulletins, 2016,28 (9): 1420-1427.
Then point a i And b j The correlation of (d) can be expressed as:
b j ＝Ra i +t (8)
in the formula, R represents a rotation matrix of the rigid body transformation, and t represents a translation vector of the rigid body transformation.
The solution of the rigid body transformation (R, t) can be converted to the minimization problem as follows:
in the formula, the set SE (3) is a euclidean training set of a 3D space, 1= [1,1] T ，||·|| F Is an F norm.
Since the translation vector t can be solved by the movement of the center of gravity of the skull point set, equation (9) can be written in a form that depends only on the rotation matrix R:
wherein R.epsilon.SO (3) is a three-dimensional rotating group, and A 'and B' are defined as:
A'＝[a′ 1 ,...,a′ N ]＝A{I N -(1/N)11 T } (11)
B'＝[b′ 1 ,...,b' N ]＝B{I N -(1/N)11 T } (12)
in the formula I N Is a cell matrix, a' i And b' i Is respectively converted from a to a when the point set is translated in rigid body transformation i And b j The truncated 3D points.
For equation (10), the solution is performed using Singular Value Decomposition (SVD), and then:
in the formula (I), the compound is shown in the specification,
is a left-singular vector matrix of the left,
is a diagonal matrix containing singular values,
is a matrix of right singular vectors,
referring to three-dimensional space, then:
where S is a matrix for avoiding a tiny point cloud matching when a point set contains noise, and diag () represents a diagonal matrix.
By using the formula (13), the rotation matrix R can be obtained from the formula (10) as
R＝VSU T (15)
And further rotating and translating the skull point cloud models U and S according to the calculated rotation matrix R and translation vector t, so that the fine registration of the skull point cloud models U and S can be realized.
Experimental results and analysis:
261 skull point cloud data models are adopted in the experiment to verify the proposed skull registration method. One of 261 skull bones is selected as an unknown skull bone U (as shown in fig. 1), and U is registered with the remaining 260 reference skull bones. Due to the large number of reference calvaria, only some of the reference calvaria S1 to S4 are listed here, as shown in fig. 2.
As can be seen from fig. 1 and 2, the unknown skull U, the reference skull S1 and S2 are all intact skull, whereas the chin of the skull S3 is missing and the teeth and chin of the skull S4 are missing. Initial relative positions of the skull U and a part of the reference skull (S1-S4) are shown in FIG. 3, and it is obvious that the initial relative positions of the skull U and S2 and the skull U and S4 are relatively close, while the initial relative positions of the skull U and S1 and the skull U and S3 are greatly different.
The registration process of the unknown skull U and a certain reference skull S is as follows: firstly, extracting characteristic points of a skull U and a skull S, and realizing coarse registration of the skull based on the characteristic points; and then, realizing fine registration of the skull by adopting a point cloud registration algorithm based on SVD. By registering the unknown skull U with 260 reference skull S1-S260, a most similar reference skull S1 of U is found (as shown in FIG. 2 (a)), and the registration result of U with partial reference skull S1-S4 is shown in FIG. 4.
Fig. 4 shows the front and side of the registration result of the unknown skull U with the reference skull S1-S4. Obviously, the unknown skull U is successfully registered with the reference skull S1, and the registration with the rest of the skull fails, and the results of the failed registration are shown in fig. 4 (b) -4 (d).
In order to further verify the performance of the skull registration method, a hierarchical skull registration method [7 ] is adopted]And an optimized skull registration method [8] The cranium shown in fig. 1 and 2 was registered. The hierarchical skull registration method comprises the steps of firstly realizing coarse registration through matching of skull characteristic regions, and then realizing fine skull registration by adopting an improved ICP algorithm. The method can realize skull registration with larger resolution difference, but has poor registration effect on the missing skull and consumes longer time in the process of extracting the characteristic region. The optimized skull registration method comprises the steps of firstly realizing coarse skull registration based on regions through the steps of region division, region registration, solving combination coefficients, rigid body transformation and the like, and then realizing fine skull registration by adopting an ICP (inductively coupled plasma) algorithm. The method has poor registration effect on the skull with large resolution difference, and is mainly caused by the requirement on the number of regional point clouds in regional registration. Specific registration results of these three registration methods are shown in table 1.
TABLE 1 skull registration results of the three registration methods
As can be seen from table 1, the proposed feature point-based skull registration algorithm has the best registration performance in the case that the resolution difference between the unknown skull and the reference skull is large and there is skull missing. And a better registration result cannot be obtained by singly adopting the coarse registration algorithm or the fine registration algorithm. Also, with documents [7] Compared with the registration method, the registration accuracy and the registration speed are respectively improved by about 20 percent and 30 percent, and the method is comparable to the literature [8] Compared with the registration method, the registration accuracy and the registration speed are respectively improved by about 10 percent and 20 percent. This is because the algorithm extracts point features of the skull, so point matching at the coarse registration stage takes less time; in the fine registration stage, the method is realized by adopting a point cloud registration algorithm based on SVD, and when solving the translation vector of rigid body transformation, the solution is carried out through the movement of the gravity center of a skull point set; and the calculation of the optimal rotation matrix is realized by constructing a matching matrix form, so that the time consumption of the algorithm can be further greatly reduced, and the registration precision is improved. Therefore, the point cloud registration method based on the feature points is an effective skull registration method, and can solve the problems of different resolutions and the rapid and accurate registration of the skull with the deficiency.
Claims (5)
1. A method for registering characteristic points of a missing skull, which is characterized by comprising the following steps:
step 1, respectively extracting characteristic points of skull point cloud models U and S to be registered to correspondingly obtain a characteristic point set S 1 And S 2 ；
Step 2, coarse skull registration
Computing a feature point set S 1 And S 2 Sequence of attributes at each feature point, for S 1 Each feature point s in 1i Corresponding attribute sequence
ComputingS 2 Each feature point s in 2j Property sequence of
And
of (2) Tonimoto coefficient T 1i Determining S by means of threshold screening 1 And S 2 To obtain S 1 And S 2 The rigid body transforms a rotation matrix and a translation vector to realize coarse registration of the skull point cloud model U and the skull point cloud model S;
step 3, skull fine registration
The skull point cloud model U and the skull point cloud model S have the same point number through initial point screening, the corresponding 3D point sets are respectively A and B, the correlation between any points in the A and the B is represented by using a rotation matrix and a translation vector of rigid body transformation, the solution of the rigid body transformation is converted into a minimization problem, a singular value decomposition method is adopted for solution, the rotation matrix and the translation vector of the rigid body transformation of the A and the B are obtained, and therefore the fine registration of the skull point cloud model U and the skull point cloud model S is achieved.
2. The method for registering the characteristic points of the missing skull as claimed in claim 1, wherein the characteristic point extraction in step 1 is specifically carried out by:
for any point p on a skull point cloud model i Let k be Nbhd (p) i ) Nbhd (p) can be calculated from any point p in the neighborhood i ) The covariance matrix of (a) is:
in the formula (I), the compound is shown in the specification,
is Nbhd (p) i ) Average value of (d);
and (3) carrying out direction adjustment on normal vectors of all points on the skull point cloud model to ensure that the normal vectors meet the following requirements:
n i ·n j <0(i≠j) (2)
in the formula, n i 、n j Respectively representing arbitrary points p on the skull point cloud model i 、p j The normal vector of (a);
point p i Main curvature k of 1 ,k 2 The mean curvature H and the gaussian curvature K are respectively expressed as:
wherein L = f xx n，N＝f yy n，M＝f xy n，E＝f x f x ，F＝f x f y ，G＝f y f y N is a point p i Normal vector n of i ，f x 、f y Respectively representing partial differential of a curved surface z to x and y; f. of xx 、f yy 、f xy Respectively representing the second partial differential of the curved surface z to x, the second partial differential of y, and partial differential of y after partial differential of x is solved;
and calculating S (p) to extract the characteristic points of the skull, wherein the calculation formula of S (p) is as follows:
in the formula, k 1 (p) and k 2 (p) is the principal curvature of point p;
at any point p in the skull point cloud model i Judging whether it is a feature pointThe standard of (2) is:
if S (p) i )>max(S(p i1 ),S(p i2 ),...,S(p ik ) P) then point p i Is a salient point;
if S (p) i )<min(S(p i1 ),S(p i2 ),...,S(p ik ) P) then point p i Are pits.
Wherein, S (p) i )、S(p i1 ),S(p i2 ),...,S(p ik ) Is a point p i Point p i Is a neighborhood point p i1 ,p i2 ,...,p ik Values of S (p) calculated by the formulas (6), respectively;
and taking the convex points and the concave points as the characteristic points of the skull point cloud model.
3. The method for registering the characteristic points of the missing skull according to claim 1, wherein the attribute sequence at each characteristic point in the step 2 is composed of gaussian curvature and mean curvature of the characteristic point.
4. The method for registering the characteristic points of the missing skull according to claim 1, wherein the S is determined by means of threshold screening 1 And S 2 To obtain S 1 And S 2 The rigid body transformation rotation matrix and translation vector of (2), comprising:
calculating the Tonimoto coefficient T 1i If the minimum value is smaller than the set threshold epsilon, extracting a corresponding characteristic point pair as a matching point pair; if no point pairs smaller than the threshold value epsilon exist, continuing S 1 Searching for matching point of next characteristic point until S 1 All feature points of (2) are in S 2 Until the search is finished;
get S 1 And S 2 Taking the matched characteristic point pair as a final registration point pair, and calculating a point set S by adopting a quaternion method 1 And S 2 The rotation matrix and the translation vector of the rigid body transformation.
5. The method for registering the characteristic points of the missing skull as claimed in claim 1, wherein the method for representing the correlation between any points in A and B by using the rotation matrix and the translation vector of the rigid body transformation, and converting the solution of the rigid body transformation into a minimization problem and performing the solution by using a singular value decomposition method to obtain the rotation matrix and the translation vector of the rigid body transformation of A and B comprises the following steps:
any point a in the point set A i And any one point B in the point set B j The correlation of (d) is expressed as:
b j ＝Ra i +t (8)
in the formula, R represents a rotation matrix of rigid body transformation, and t represents a translation vector of the rigid body transformation;
the solution of the rigid body transformation (R, t) can be converted to a minimization problem as follows:
in the formula, the set SE (3) is a euclidean training set of 3D space, 1= [1, 1., 1=] T ，||·|| F Is an F norm;
equation (9) can be written in a form that depends only on the rotation matrix R:
wherein R.epsilon.SO (3) is a three-dimensional rotating group, and A 'and B' are defined as:
A'＝[a' 1 ,...,a' N ]＝A{I N -(1/N)11 T } (11)
B'＝[b' 1 ,...,b' N ]＝B{I N -(1/N)11 T } (12)
in the formula I N Is a cell matrix, a' i And b' i Is respectively from a when the point set is translated in rigid body transformation i And b j N, N represents the number of points in point set a or B;
in equation (10), the solution is obtained by Singular Value Decomposition (SVD), and thus:
in the formula (I), the compound is shown in the specification,
is a left-singular vector matrix of the left,
is a diagonal matrix containing singular values,
is a matrix of right singular vectors,
referring to three-dimensional space, then:
wherein, S is a matrix for avoiding matching of tiny point clouds when the point set contains noise, and diag () represents a diagonal matrix;
by using the formula (13), the rotation matrix R can be obtained from the formula (10) as
R＝VSU T (15)
Thereby obtaining a rigid transformation rotation matrix R and a translation vector t of A and B.
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