CN109816705A - A kind of Characteristic points match method lacking skull - Google Patents
A kind of Characteristic points match method lacking skull Download PDFInfo
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Abstract
The invention discloses a kind of Characteristic points match method for lacking skull, this method is directed to skull point cloud model to be registered, extracts the characteristic point of skull first, calculates characteristic sequence, and the rough registration of skull is carried out using the similitude of characteristic sequence；Then pass through the initial point of screening skull point cloud model, the correlation between arbitrary point is concentrated using the spin matrix and translation vector representation initial point of rigid body translation, the solution of rigid body translation is converted into minimization problem and is solved using singular value decomposition method, the rigid body translation spin matrix and translation vector of initial point set are obtained, to realize the thin registration of skull point cloud model sum.The experimental results showed that the method for the present invention has significant raising than existing certain methods in terms of registration accuracy and speed, different resolution may be implemented and lack effective registration of skull.
Description
Technical field
The present invention relates to restoration of facial features technical fields, and in particular to a kind of feature of the different missing skull of resolution ratio
Point method for registering.
Background technique
It is a skill for being restored the skull face appearance of the mankind using the present computer technology means that cranium face, which is restored,
Art, it comes to add soft tissue for skull in conjunction with certain algorithm using the facial soft tissue statistical thickness of the mankind as foundation, with reality
It restores in existing cranium face.Currently used soft tissue adding method mainly includes cranial bone deformation method and two kinds of three-D volumes deformation method, this
Two methods have all referred to skull registration technique, and therefore, skull registration is the important step that cranium face is restored.Currently, cranium
Bone registration technique is led in the authentication of corpse source, mummy Facial restoration, face's plastic operation effect prediction and medical research etc.
Domain has obtained relatively broad application.
Characteristic point is the most basic feature primitive of skull point cloud model, and Feature Points Matching is to need to solve in computer vision
One of basic problem, the one-to-one relationship that characteristic point between match point cloud and to be matched cloud is accurately presented is Dian Yunte
The matched final goal of sign point.Currently, domestic and international researcher proposes much skull point cloud model registration sides based on characteristic point
Method.Such as, Feng Jun etc.[1]Realize that skull is registrated using the characteristic point of full automatic calibration；Diligent Li Xia meter Xi Ding through the ages of heat etc.[2]It adopts
Characteristic point calibration is carried out to three-dimensional cranium sample with a kind of semi-automatic characteristic point scaling method, and realizes the recovery of cranium face；Tong Xin
Dragon[3]A kind of Cranial features point matching process based on subregion statistics variable model is proposed, the accuracy registration of skull is realized；
Zhou C etc.[4]A kind of high-precision skull method for registering is proposed, effective registration of N/D skull may be implemented；Heat diligent ten thousand
Gu Li etc.[5]It proposes based on the corresponding three-dimensional cranium autoegistration method in edge, solves initial attitude and differ biggish skull
Autoregistration problem, but algorithm takes a long time；Tax noon sun etc.[6]It is real using iteration closest approach algorithm and thin plate spline function
It is registrated referring now to skull with unknown skull, but the registration effect to the lower defects with skull of coverage rate and bad.The above
It is for intact skulls point Yun Mo mostly although algorithm achieves higher registration accuracy and speed in terms of skull registration
The registration that type is realized, to the registration effect and bad under missing skull state.
[1] Feng Jun, Chen Yu, Tong Xinlong, wait automatic Calibration [J] optical precision engineering of three-dimensional cranium characteristic point, and 2014,
22(5):1388-1394.
[2] heat diligent Li Xia meter Xi Ding, Geng Guohua, Deng Qingqiong through the ages, waits improved based on characteristic point soft tissue thickness
Cranium face restored method [J] computer application research, 2016,23 (10): 3191-3200.
[3] Tong Xinlong studies the Xi'an [D] based on the Cranial features point matching algorithm of subregion statistics variable model: northwest is big
It learns, 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] heat diligent Li Xia meter Xi Ding, Geng Guohua, Gu Lisongnasierding through the ages waits to be based on the corresponding three-dimensional in edge
Automatic non-rigid registration method [J] the computer application of skull, 2016,36 (11): 3196-3200,3206.
[6] tax noon sun, Zhou Mingquan, Wu Zhongke wait restoration of facial features method [J] area of computer aided of Registration of Measuring Data to set
Meter and graphics journal, 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] optimization of Zhao Fuqun, Zhou Mingquan skull point cloud model is registrated [J] optical precision engineering, 2017,25 (7):
1927-1933。
Summary of the invention
The object of the present invention is to provide a kind of Characteristic points match methods for lacking skull, solve existing in the prior art
Registration effect when skull point cloud differences in resolution is larger and there is a problem of missing is bad.
In order to realize above-mentioned task, the invention adopts the following technical scheme:
A kind of Characteristic points match method lacking skull, comprising the following steps:
Step 1, feature point extraction is carried out respectively for skull point cloud model U and S to be registered, correspondence obtains feature point set
S1And S2；
Step 2, skull rough registration
Calculate feature point set S1And S2Sequence of attributes at each characteristic point, for S1In each characteristic point s1iIt is corresponding
Sequence of attributes Fs1i, calculate S2In each characteristic point s2jSequence of attributes Fs2jWith Fs1iTonimoto coefficient T1i, pass through threshold value
The mode of screening, determines S1And S2In matched characteristic point pair, to obtain S1And S2Rigid body translation spin matrix and translation vector
Amount, to realize the rough registration of skull point cloud model U and S；
Step 3, skull is carefully registrated
Make skull point cloud model U and S points having the same by initial point screening, corresponding 3D point set be respectively A and
B, using the correlation between arbitrary point in the spin matrix and translation vector representation A and B of rigid body translation, by asking for rigid body translation
Solution is converted to minimization problem and is solved using singular value decomposition method, and rigid body translation spin matrix and the translation of A and B is obtained
Vector, to realize the thin registration of skull point cloud model U and S.
Further, feature point extraction described in step 1, method particularly includes:
For any point p on a skull point cloud modeliIf its k neighbour domain is Nbhd (pi), by appointing in neighborhood
The point p that anticipates can calculate Nbhd (pi) covariance matrix are as follows:
In formula,For Nbhd (pi) average value；
Direction adjustment is carried out to the normal vector of all the points on skull point cloud model, is allowed to meet:
ni·nj<0(i≠j) (2)
In formula, ni、njRespectively indicate the arbitrary point p on skull point cloud modeli、pjNormal vector；
Point piThe principal curvatures k at place1,k2, mean curvature H and Gaussian curvature K respectively indicate are as follows:
In formula, L=fxxN, N=fyyN, M=fxyN, E=fxfx, F=fxfy, G=fyfy, n is point piNormal vector ni, fx、
fyCurved surface z is respectively indicated to the partial differential of x, y；fxx、fyy、fxyRespectively indicate curved surface z to the secondary partial differential of x, to the secondary of y
Partial differential and partial differential is asked to y again after seeking partial differential to x；
S (p) is calculated to extract the characteristic point of skull, its calculating formula of S (p) are as follows:
In formula, k1(p) and k2(p) principal curvatures for being point p；
Any point p in skull point cloud modeli, judge whether it is characterized standard a little are as follows:
If S (pi)>max(S(pi1),S(pi2),...,S(pik)), then point piFor salient point；
If S (pi)<min(S(pi1),S(pi2),...,S(pik)), then point piFor concave point.
Wherein, S (pi)、S(pi1),S(pi2),...,S(pik) it is point pi, point piNeighborhood point pi1,pi2,...,pikRespectively
S (p) value calculated by formula (6)；
Using the salient point and concave point as the characteristic point of skull point cloud model.
Further, the sequence of attributes at each characteristic point described in step 2, by the Gaussian curvature of characteristic point, average song
Rate is constituted.
Further, described in such a way that threshold value is screened, determine S1And S2In matched characteristic point pair, to obtain
S1And S2Rigid body translation spin matrix and translation vector, comprising:
Calculate Tonimoto coefficient T1iMinimum value, if the minimum value be less than setting threshold epsilon, extract its corresponding spy
Sign point is to as matching double points；If continuing S without the point pair for being less than threshold epsilon1In next characteristic point match point search,
Until S1All characteristic points all in S2On searched for until；
Take S1And S2In matched characteristic point pair, as final registration point pair, then using Quaternion Method calculate point set S1
And S2Rigid body translation spin matrix and translation vector.
Further, in the spin matrix and translation vector representation A and B using rigid body translation between arbitrary point
The solution of rigid body translation is converted to minimization problem and is solved using singular value decomposition method, obtains A's and B by correlation
Rigid body translation spin matrix and translation vector, comprising:
Any point a in point set AiWith any point b in point set BjCorrelation indicate are as follows:
bj=Rai+t (8)
In formula, R indicates that the spin matrix of rigid body translation, t indicate the translation vector of rigid body translation；
The solution of rigid body translation (R, t) can be converted to following minimization problem:
In formula, set SE (3) is the euclidean training group an of 3d space, 1=[1,1 ..., 1]T, | | | |FIt is one
A F norm；
Formula (9) can be write as the form for only relying upon spin matrix R:
In formula, R ∈ SO (3) is a three-dimensional rotation group, and A' and B' are respectively defined as:
A'=[a '1,...,a'N]=A { IN-(1/N)11T} (11)
B'=[b '1,...,b'N]=B { IN-(1/N)11T} (12)
In formula, INIt is a cell matrix, a 'iWith b 'iIt is when point set is in rigid body translation translation respectively from aiAnd bjIn delete
The 3D point subtracted, i, j=1,2 ..., N, N indicate the quantity at the midpoint point set A or B；
In formula (10), is solved using singular value decomposition (SVD) method, is then had here:
In formula,It is a left singular vector matrix,It is the diagonal matrix comprising singular value,It is a right singular vector matrix,Refer to three-dimensional space, then can calculate:
In formula, S is one for avoiding the matched matrix of tiny dots cloud when concentrating Noise, and diag () indicates diagonal
Matrix；
Using formula (13), can acquire spin matrix R from formula (10) is
R=VSUT (15)
To obtain the rigid body translation spin matrix R and translation vector t of A and B.
The present invention has following technical characterstic compared with prior art:
A unknown skull is registrated with 260 known skulls in the experiment of the method for the present invention, has found one most
Skull is referred to be similar, the results showed that is somebody's turn to do the skull method for registering based on characteristic point than existing certain methods in registration accuracy
There is significant raising in terms of speed；The present invention is a kind of quickly accurate skull method for registering, and different resolutions may be implemented
Effective registration of rate and missing skull.
Detailed description of the invention
Fig. 1 is unknown skull U；
(a), (b), (c) and (d) of Fig. 2 is respectively to refer to skull S 1, S2, S3 and S4；
(a), (b), (c) and (d) of Fig. 3 is respectively the initial relative position of U and S1, U and S2, U and S3 and U and S4；
(a), (b), (c) and (d) that Fig. 4 is is respectively a front surface and a side surface of U and S1 registration result, U and S2 registration result
A front surface and a side surface, a front surface and a side surface of a front surface and a side surface of U and S3 registration result and U and S4 registration result；
Fig. 5 is the overall flow figure of the method for the present invention.
Specific embodiment
The present invention provides a kind of Characteristic points match methods for lacking skull, first extraction skull point cloud or spy concave or convex
Point is levied, and calculates the characteristic sequence of characteristic point, to realize the rough registration of skull；Then using based on singular value decomposition
The point cloud registration algorithm of (singular value decomposition, SVD) realizes the thin registration of skull, is achieved in unknown
The final accurate matching of skull and reference skull.Skull can be realized without being iterated in point cloud registration algorithm based on SVD
Thin registration, therefore in the case where guaranteeing registration accuracy, the registration speed of the algorithm has significantly than iteration closest approach algorithm
Raising.Specific method of the present invention are as follows:
Step 1, feature point extraction is carried out respectively for skull point cloud model U and S to be registered, method particularly includes:
For skull point cloud model, point thereon shows convex recessed or flat feature in regional area, this
A little salient points and concave point are the characteristic point for the skull point cloud model to be extracted.The specific extraction process of characteristic point is as follows:
For any point p on a skull point cloud modeliIf its k neighbour domain is Nbhd (pi), then piNormal direction
Amount is the normal vector for the tangent plane that the place has adjoint point to be fitted.Here, piNormal vector niUsing principal component analysis
(principal component analysis, PCA) method solves.
Nbhd (p can be calculated by any point p in neighborhoodi) covariance matrix are as follows:
In formula,For Nbhd (pi) average value.
So, piNormal vector niIt is exactly the corresponding feature vector of minimal eigenvalue of covariance matrix X.To ensure a little
The consistency in normal vector direction carries out direction adjustment to the normal vector of all the points on skull point cloud model here, is allowed to meet:
ni·nj<0(i≠j) (2)
In formula, njIndicate the arbitrary point p on skull point cloud modeljNormal vector.
For point pi, because there are a curved surface z=f (x, y) to approach piNeighborhood point cloud, it is possible to use point piAnd
The curvature of the local surface of its neighborhood point fitting characterizes its curvature.So, point piThe principal curvatures k at place1,k2, mean curvature H with
And Gaussian curvature K is respectively indicated are as follows:
In formula, L=fxxN, N=fyyN, M=fxyN, E=fxfx, F=fxfy, G=fyfy, n is point piNormal vector ni, fx、
fyCurved surface z is respectively indicated to the partial differential of x, y；fxx、fyy、fxyRespectively indicate curved surface z to the secondary partial differential of x, to the secondary of y
Partial differential and partial differential is asked to y again after seeking partial differential to x.
Next, calculating S (p) to extract the characteristic point of skull, its calculating formula of S (p) is
In formula, k1(p) and k2(p) with the principal curvatures of as point p, pass through formula (3) and calculate.
For any point p in skull point cloudi, judge whether it is characterized standard a little are as follows:
If S (pi)>max(S(pi1),S(pi2),...,S(pik)), then point piFor salient point；
If S (pi)<min(S(pi1),S(pi2),...,S(pik)), then point piFor concave point.
Wherein, S (pi1),S(pi2),...,S(pik) it is point piNeighborhood point pi1,pi2,...,pikIt is calculated respectively by formula (6)
S (p) value.
It is just extracted characteristic point skull point cloud model or concave or convex using the above method, is based on these characteristic points, connects
Get off the rough registration of skull can be realized.
Step 2, skull slightly matches
Skull point cloud model U (unknown skull) to be registered for two and S (referring to skull), it is assumed that extracted to its
Its feature point set is respectively S1And S2.So to S1In any point s1i, its Gaussian curvature K is calculated first1iAnd mean curvature H1i,
Obtain sequence of attributesThen point s is found again1iIn S2In match point.
Search characteristics point set S1And S2Match point specific step is as follows:
Step 2.1, feature point set S is calculated first1And S2Sequence of attributes at each characteristic pointWherein, i
=1,2 .., n1, j=1,2 .., n2, n1And n2Respectively indicate S1And S2In characteristic point number；The attribute of each characteristic point
Sequence is made of the Gaussian curvature of this feature point, average curvature.
Step 2.2, for S1In each characteristic point s1iCorresponding sequence of attributesCalculate S2In each characteristic point s2j
Sequence of attributesWithTonimoto coefficient T1i:
In above formula, C and D respectively indicate characteristic point s1i, characteristic point s2jSequence of attributes vector, T indicate Tonimoto system
Number.
Step 2.3, Tonimoto coefficient T is calculated1iMinimum value, if the minimum value be less than setting threshold epsilon, extract it
Corresponding characteristic point is to as matching double points；If continuing S without the point pair for being less than threshold epsilon1In next characteristic point match point
Search, until S1All characteristic points all in S2On searched for until；Wherein threshold epsilon is integer, when specific value is according to experiment
The size of skull point cloud model, the setting of complexity situation.
Step 2.4, S is extracted1And S2In matched characteristic point pair, as final registration point pair, then use Quaternion Method
Calculate point set S1And S2The spin matrix and translation vector of rigid body translation can be by skull point cloud model U by rotation and translation
It is tentatively aligned with S, is achieved in the rough registration of skull point cloud model U and S.
Step 3, skull is carefully registrated
By rough registration process, skull point cloud model U and S is substantially aligned, in thin registration process, to the two craniums
Bone point cloud model carries out the screening of initial point, to realize thin registration.Skull is carefully registrated real using the point cloud registration algorithm based on SVD
Existing, which proposes that a kind of simple, quick skull point cloud registering is calculated aiming at the problem that ICP algorithm needs to carry out continuous iteration
Method.The algorithm is solved when solving the translation vector t of rigid body translation by the movement of the center of gravity of skull point set, and is most preferably revolved
The calculating of torque battle array is carried out in two steps: singular value decomposition method is constructed into a matching matrix first, it is then unusual using each left side
The inner product of vector generates spin matrix；In the case where not influencing registration accuracy, the time-consuming of the algorithm has substantially than ICP algorithm
The raising of degree.
For skull point cloud model U (unknown skull) to be registered and S (referring to skull), they are made by initial point screening
Point cloud model points N having the same, i.e., corresponding 3D point set is respectively as follows:WithWhereinIndicate three-dimensional real number space, aiAnd bjIt is described for the arbitrary point in set A and B
Initial point screening method from document: Zhang Yuhe, Geng Guohua, Wei Xiaoran, wait retain geometrical characteristic dispersion point cloud letter
Change algorithm [J] CAD and graphics journal, 2016,28 (9): 1420-1427.
Then point aiAnd bjCorrelation may be expressed as:
bj=Rai+t (8)
In formula, R indicates that the spin matrix of rigid body translation, t indicate the translation vector of rigid body translation.
The solution of rigid body translation (R, t) can be converted to following minimization problem:
In formula, set SE (3) is the euclidean training group an of 3d space, 1=[1,1 ..., 1]T, | | | |FIt is one
A F norm.
Since translation vector t can be solved by the movement of the center of gravity of skull point set, formula (9) can be write as only according to
Rely in the form of spin matrix R:
In formula, R ∈ SO (3) is a three-dimensional rotation group, and A' and B' are respectively defined as:
A'=[a '1,...,a′N]=A { IN-(1/N)11T} (11)
B'=[b '1,...,b'N]=B { IN-(1/N)11T} (12)
In formula, INIt is a cell matrix, a 'iWith b 'iIt is when point set is in rigid body translation translation respectively from aiAnd bjIn delete
The 3D point subtracted.
For formula (10), is solved using singular value decomposition (SVD) method, is then had here:
In formula,It is a left singular vector matrix,It is the diagonal matrix comprising singular value,It is a right singular vector matrix,Refer to three-dimensional space, then can calculate:
In formula, S is one for avoiding the matched matrix of tiny dots cloud when concentrating Noise, and diag () indicates diagonal
Matrix.
Using formula (13), can acquire spin matrix R from formula (10) is
R=VSUT (15)
Skull point cloud model U and S are further rotated according to the spin matrix R and translation vector t calculated above
And translation, the thin registration of skull point cloud model U and S can be realized.
Experimental result and analysis:
Mentioned skull method for registering is verified in experiment using 261 skull point cloud data models.It is chosen from 261 skulls
One is used as unknown skull U (as shown in Figure 1), and U is registrated with remaining 260 with reference to skull.Due to reference skull number
It measures more, only lists part here with reference to 1~S4 of skull S, as shown in Figure 2.
By Fig. 1 and Fig. 2 as it can be seen that unknown skull U, with reference to skull S 1 and S2 being complete skull, and the chin of skull S 3
There are missing, the tooth and chin of skull S 4 are lacked.Skull U and part refer to the initial relative position of skull (S1~S4) such as
Shown in Fig. 3, it is clear that the initial relative position of skull U and S2 and skull U and S4 relatively, and skull U and S1 and skull U
It differs greatly with the initial relative position of S3.
Unknown skull U and a certain registration process with reference to skull S are as follows: extract the characteristic point of skull U and S first, and be based on
The rough registration of this feature point realization skull；Then the thin registration of skull is realized using the point cloud registration algorithm based on SVD.Passing through will
Unknown skull U is registrated with 260 with reference to 1~S260 of skull S, has found a most similar reference skull S 1 of U (such as
Shown in Fig. 2 (a)), U is as shown in Figure 4 with reference to the registration result of 1~S4 of skull S with part.
Fig. 4 gives a front surface and a side surface of unknown skull U and the registration result with reference to 1~S4 of skull S.Obviously, unknown cranium
Bone U is registrated successfully with reference to skull S 1, failure is registrated with remaining skull, shown in failure registration result such as Fig. 4 (b)~4 (d).
In order to further verify the performance of the skull method for registering, then be respectively adopted stratification skull method for registering [7] and
A kind of skull method for registering of optimization[8]Fig. 1 and skull shown in Fig. 2 are registrated.Stratification skull method for registering is logical first
Rough registration is realized in the matching for crossing Cranial features region, then realizes that skull is carefully registrated using a kind of improved ICP algorithm.This method
The biggish skull registration of differences in resolution may be implemented, but it is bad to the registration effect of missing skull, and in characteristic area
It is taken a long time during extraction.And the skull method for registering optimized then passes through region division, region registration, solution combination first
Coefficient and rigid body translation and etc. realize the skull rough registration based on region, carefully matching for skull is then realized using ICP algorithm again
It is quasi-.This method is bad to the registration effect of the biggish skull of differences in resolution, mainly due to region registration in region point cloud
Number requirement caused by.The specific registration result of these three method for registering is as shown in table 1.
The skull registration result of 1 three kinds of method for registering of table
Seen from table 1, the case where larger in the differences in resolution of unknown skull and reference skull, and there are Skull defects
Under, the skull registration Algorithm based on characteristic point of proposition has best registration performance.And individually use this paper rough registration algorithm
Or thin registration Algorithm, it cannot obtain preferable registration result.Moreover, with document[7]Method for registering compare, registration accuracy
About 20% and 30% is respectively increased with speed, with document[8]Method for registering compare, registration accuracy and speed are respectively increased
About 10% and 20%.This is because the extraction of this paper algorithm is the point feature of skull, therefore matches and consume in the point in rough registration stage
When it is shorter；And in the carefully registration stage, it is realized using the point cloud registration algorithm based on SVD, in the translation vector for solving rigid body translation
When, it is solved by the movement of skull point set center of gravity；And the calculating of best spin matrix is real by way of constructing matching matrix
It is existing, the time-consuming of algorithm can be further substantially reduced, registration accuracy is improved.Therefore it says, the point cloud based on characteristic point of proposition is matched
Quasi- method is a kind of effective skull method for registering, can solve resolution ratio it is different and exist missing skull it is quick, smart
Really registration.
Claims (5)
1. a kind of Characteristic points match method for lacking skull, which comprises the following steps:
Step 1, feature point extraction is carried out respectively for skull point cloud model U and S to be registered, correspondence obtains feature point set S1With
S2；
Step 2, skull rough registration
Calculate feature point set S1And S2Sequence of attributes at each characteristic point, for S1In each characteristic point s1iCorresponding category
Property sequenceCalculate S2In each characteristic point s2jSequence of attributesWithTonimoto coefficient T1i, sieved by threshold value
The mode of choosing, determines S1And S2In matched characteristic point pair, to obtain S1And S2Rigid body translation spin matrix and translation vector
Amount, to realize the rough registration of skull point cloud model U and S；
Step 3, skull is carefully registrated
Make skull point cloud model U and S points having the same by initial point screening, corresponding 3D point set is respectively A and B, benefit
With the correlation in the spin matrix and translation vector representation A and B of rigid body translation between arbitrary point, the solution of rigid body translation is turned
It is changed to minimization problem and is solved using singular value decomposition method, obtain the rigid body translation spin matrix and translation vector of A and B
Amount, to realize the thin registration of skull point cloud model U and S.
2. the Characteristic points match method of missing skull as described in claim 1, which is characterized in that characteristic point described in step 1
It extracts, method particularly includes:
For any point p on a skull point cloud modeliIf its k neighbour domain is Nbhd (pi), by any one in neighborhood
Point p can calculate Nbhd (pi) covariance matrix are as follows:
In formula,For Nbhd (pi) average value；
Direction adjustment is carried out to the normal vector of all the points on skull point cloud model, is allowed to meet:
ni·nj<0(i≠j) (2)
In formula, ni、njRespectively indicate the arbitrary point p on skull point cloud modeli、pjNormal vector；
Point piThe principal curvatures k at place1,k2, mean curvature H and Gaussian curvature K respectively indicate are as follows:
In formula, L=fxxN, N=fyyN, M=fxyN, E=fxfx, F=fxfy, G=fyfy, n is point piNormal vector ni, fx、fyPoint
Not Biao Shi curved surface z to the partial differential of x, y；fxx、fyy、fxyRespectively indicate curved surface z to the secondary partial differential of x, to the secondary partially micro- of y
Divide and partial differential is asked to y again after seeking partial differential to x；
S (p) is calculated to extract the characteristic point of skull, its calculating formula of S (p) are as follows:
In formula, k1(p) and k2(p) principal curvatures for being point p；
Any point p in skull point cloud modeli, judge whether it is characterized standard a little are as follows:
If S (pi)>max(S(pi1),S(pi2),...,S(pik)), then point piFor salient point；
If S (pi)<min(S(pi1),S(pi2),...,S(pik)), then point piFor concave point.
Wherein, S (pi)、S(pi1),S(pi2),...,S(pik) it is point pi, point piNeighborhood point pi1,pi2,...,pikPass through respectively
S (p) value that formula (6) calculates；
Using the salient point and concave point as the characteristic point of skull point cloud model.
3. the Characteristic points match method of missing skull as described in claim 1, which is characterized in that each spy described in step 2
Sequence of attributes at sign point, is made of the Gaussian curvature of characteristic point, average curvature.
4. the Characteristic points match method of missing skull as described in claim 1, which is characterized in that described to be screened by threshold value
Mode, determine S1And S2In matched characteristic point pair, to obtain S1And S2Rigid body translation spin matrix and translation vector,
Include:
Calculate Tonimoto coefficient T1iMinimum value, if the minimum value be less than setting threshold epsilon, extract its corresponding characteristic point
To as matching double points；If continuing S without the point pair for being less than threshold epsilon1In next characteristic point match point search, until S1
All characteristic points all in S2On searched for until；
Take S1And S2In matched characteristic point pair, as final registration point pair, then using Quaternion Method calculate point set S1And S2
Rigid body translation spin matrix and translation vector.
5. the Characteristic points match method of missing skull as described in claim 1, which is characterized in that described utilizes rigid body translation
Spin matrix and translation vector representation A and B in correlation between arbitrary point, the solution of rigid body translation is converted into minimum
Problem is simultaneously solved using singular value decomposition method, and the rigid body translation spin matrix and translation vector of A and B is obtained, comprising:
Any point a in point set AiWith any point b in point set BjCorrelation indicate are as follows:
bj=Rai+t (8)
In formula, R indicates that the spin matrix of rigid body translation, t indicate the translation vector of rigid body translation；
The solution of rigid body translation (R, t) can be converted to following minimization problem:
In formula, set SE (3) is the euclidean training group an of 3d space, 1=[1,1 ..., 1]T, | | | |FIt is a F
Norm；
Formula (9) can be write as the form for only relying upon spin matrix R:
In formula, R ∈ SO (3) is a three-dimensional rotation group, and A' and B' are respectively defined as:
A'=[a'1,...,a'N]=A { IN-(1/N)11T} (11)
B'=[b'1,...,b'N]=B { IN-(1/N)11T} (12)
In formula, INIt is a cell matrix, a'iAnd b'iIt is when point set is in rigid body translation translation respectively from aiAnd bjIn delete
3D point, i, j=1,2 ..., N, N indicate the quantity at the midpoint point set A or B；
In formula (10), is solved using singular value decomposition (SVD) method, is then had here:
In formula,It is a left singular vector matrix,It is the diagonal matrix comprising singular value,It is a right singular vector matrix,Refer to three-dimensional space, then can calculate:
In formula, S is one for avoiding the matched matrix of tiny dots cloud when concentrating Noise, and diag () is indicated to angular moment
Battle array；
Using formula (13), can acquire spin matrix R from formula (10) is
R=VSUT (15)
To obtain the rigid body translation spin matrix R and translation vector t of A and B.
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