CN102169579A - Rapid and accurate registration method of dense point cloud model - Google Patents
Rapid and accurate registration method of dense point cloud model Download PDFInfo
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Abstract
The invention discloses a rapid and accurate registration method of a dense point cloud model, comprising the following steps of: realizing the initial registration of a turbine blade dense point cloud model and a CAD (Computer-Aided Design) model through an alignment method; appropriately simplifying the obtained initially registered point cloud data; computing the rotation matrix and the translation matrix of each iteration in an SVD-ICP (Singular Value Decomposition-Iterative Closet Point) algorithm; and finally realizing the accurate registration of a control point set {P} and the CAD model by adopting the SVD-ICP algorithm. In the invention, under the premise of realizing the pre-registration of the point cloud model and the CAD model, the dense point cloud data are simplified; the simplified data are taken as a registered control point set; the total rotation matrix and the translation matrix are computed on the basis of the SVD-ICP algorithm; and the computed total transformation matrixes are applied to the original dense point cloud before the simplification so that the rapid registration of the dense point cloud and the CAD model is realized and the registration accuracy and the registration speed are considered simultaneously.
Description
Technical field
The present invention relates to a kind of coordinate system and unify method, relate in particular to the fast accurate method for registering of a kind of three-dimensional point of density cloud model and cad model, this method is applicable to the registration of the three-dimensional point of density cloud model of field parts such as medical science, Aero-Space, weapons.
Background technology
The registration of turbo blade point cloud model mainly is meant the spatial alternation that the point cloud model of measurement designs a model with respect to CAD, promptly realizes the unification of coordinate system.Current in a lot of fields, size detection and Measurement and analysis technology have crucial effects in raising manufacturing shape, dimensional accuracy with aspect ensuring the quality of products.Common measuring method has three-dimensional coordinates measurement, optical scanning to measure and CT measures.In recent years, along with the development of laser technology, the speed and the precision of optical measurement all are greatly improved, use also more and more widely, the data volume of its acquisition is very huge, though obtained more fully data message, has also brought inconvenience for follow-up Measurement and analysis simultaneously.Such as, the manufacturing accuracy of domestic air mail engine turbine blade is low, qualification rate is low, in order to improve manufacturing accuracy and qualification rate, product is measured, pass through then measurement data and cad model registration, carry out two dimension or three-dimensional variance analysis, relatively draw the deformation rule of product, utilize the reversible deformation technology that the mould of product, processing technology etc. are optimized design, thereby improve the precision and the qualification rate of product.
At present registration Algorithm roughly can be divided three classes: the iteration registration Algorithm, and based on the registration Algorithm of curved surface with based on how much feature registration algorithm.For iterative algorithm, the most representative is iterative closest point algorithms (the iterative closestpoint that Besl etc. proposes, ICP), it is right that algorithm at first utilizes Newton iteration or searching method to seek two groups of closest approaches of putting the cloud correspondences, and adopt Euclidean distance to carry out iteration, thereby obtain three-dimensional rigid body translation as objective function.Though the iterative algorithm degree of accuracy is very high, but there are a lot of limitation, at first be that the time complexity that its iterations causes too much increases, in addition, because the ICP algorithm is had relatively high expectations to 2 relative initial positions of some cloud, initial position between the some cloud can not differ too big, otherwise the convergence direction of ICP is uncertain, and this will cause the degree of accuracy of algorithm and speed of convergence to be affected, even also might be absorbed in locally optimal solution, thereby registration results also is insecure.Can be regarded as with a kind of method based on the registration Algorithm of surface description with based on the registration Algorithm of geometric properties, promptly based on the registration Algorithm of feature, this method registration efficient is higher, and for the cloud data overlapping as the part, applicability is better, but the method is mainly used in the pre-registration of model, and requires model to have tangible geometric properties, and significant limitation is arranged.
Because the precision of iterative algorithm is very high, on the basis of ICP algorithm, there is the people to propose method (the Singular Value Decomposition and Iterative Closest Point algorithm that svd and closest approach iterative algorithm are combined, SVD_ICP), this method is found the solution the transformation problem of two corresponding point sets by svd, progressively iteration realizes registration then, but the speed that the method registration calculates is slower.For the registration of magnanimity cloud data, how under the prerequisite that guarantees registration accuracy, improving registration speed is that the lot of domestic and international scholar is in the problem of making great efforts research.
Summary of the invention
Can not take into account the deficiency of registration accuracy and registration speed in order to overcome prior art, the invention provides a kind of rapid registering method of point of density cloud model, this method has the advantage that guarantees registration accuracy, improves registration speed.
The present invention realizes that the above-mentioned purpose technical solution may further comprise the steps:
Step 1
Choose on measurement point cloud model and the cad model any three groups of corresponding point respectively to (P
1, Q
1), (P
2, Q
2), (P
3, Q
3), P wherein
1, P
2, P
3Not on same plane.Order
Make vector v
3And w
3,
Make vector vector v
2And w
2,
v
1, v
2And v
3Constitute orthogonal coordinate system, be expressed as unit vector
In like manner
Any point P in the measurement point cloud model
iTransform to corresponding point Q
iRelational expression be: Q
i=RP
i+ T, wherein R=[w] [v]
-1, T=Q
1-[w] [v]
-1P
1
Step 2
The point of density cloud model that utilizes the uniform sampling method that step 1 is obtained is reduced to 10000-50000 point, and { P} seeks point set corresponding with it on the cad model { P ' } as the control point set with the some cloud after simplifying.
Step 3
{ P} is as the registration control points collection with control point set that step 2 obtains, calculate the rotation matrix and the translation matrix of per step iteration in the SVD_ICP algorithm: the utilization singular value decomposition method, the calculation control point set is with respect to the translation and the rotation matrix of cad model, and detailed process is as follows:
1) utilizes formula
With
Ask for the barycenter p and the p ' of two point sets { P} and { P ' }.
2) according to formula q
i=p
i-p and q '
i=p '
i-p ' calculates in two point sets { P} and { P ' } each point with respect to the displacement of its barycenter.
3) according to formula
Ask for matrix H, and by formula H=U Λ V
TMatrix H is carried out svd, and wherein U is the left singular matrix of H, and V is the right singular matrix of H, and the two is 3 * 3 orthogonal matrix.
4) according to formula R=VU
TAnd T=p '-Rp calculates the rotation matrix R of i step iteration
iWith the translation matrix T
i
Step 4
{ the accurate registration of P} and cad model, method is as follows: try to achieve every iteration rotation matrix R once according to step 3 to adopt the SVD_ICP algorithm to realize the control point set
iWith the translation matrix T
iThereby, utilize formula R
z=R
i* R
I-1* ... .*R
1And T
z=R
i* T
I-1+ T '
iTry to achieve control point set { the rotation matrix R that P} is total with respect to cad model
zWith the translation matrix T
z, R wherein
zBe 3 * 3 matrix, T
zIt is 3 * 1 matrix.By formula Q
i=R
zP
i+ T
z, P wherein
iBe any point in the point cloud model, Q
iFor after the conversion with P
iCorresponding point; R
zAnd T
zOriginal point cloud model before being applied to simplify is realized itself and the fast accurate registration of cad model.
The invention has the beneficial effects as follows: under the prerequisite that realizes point cloud model and the pre-registration of cad model, by intensive cloud data is simplified, with the data after simplifying as the registration control points collection, on the basis of SVD_ICP algorithm, calculate and try to achieve total rotation matrix and translation matrix, original point of density cloud before then total transformation matrix of trying to achieve being applied to simplify, realize the rapid registering of itself and cad model, taken into account registration accuracy and registration speed.
The present invention is further described below in conjunction with accompanying drawing and example.
Description of drawings
Fig. 1 is the schematic flow sheet of the method for the invention.
Fig. 2 is certain turbo blade point of density cloud model and cad model.
Fig. 3 is that the difference of point of density cloud model is simplified figure as a result, and wherein Fig. 3 (a) is the figure as a result that is reduced to 139240 points, and Fig. 3 (b) is the structural drawing that is reduced to 23206 points.
Fig. 4 is turbo blade point of density cloud model and cad model registration process figure as a result, and wherein Fig. 4 (a) is the pre-registration result of two models, and Fig. 4 (b) is that essence is joined figure as a result.
Embodiment
Below in conjunction with certain turbo blade point of density cloud model (counting 1392396) and cad model (referring to Fig. 2), elaborate operation steps of the present invention.
Step 1
Realize the initial registration of turbo blade point of density cloud model and cad model by the method for alignment, choose on measurement point cloud model and the cad model any three groups of corresponding point respectively (P
1, Q
1), (P
2, Q
2), (P
3, Q
3), P wherein
1, P
2, P
3Not on same plane.Order
Make vector v
3And w
3,
Make vector vector v
2And w
2,
v
1, v
2And v
3Constitute orthogonal coordinate system, be expressed as unit vector
In like manner
Any point P in the measurement point cloud model
iTransform to corresponding point Q
iRelational expression be: Q
i=RP
i+ T, wherein R=[w] [v]
-1, T=Q
1-[w] [v]
-1P
1The results are shown in Figure 4 (a).
Step 2
The initial registration cloud data that is obtained by step 1 is carried out suitable simplification, the point of density cloud model that utilizes the uniform sampling method that step 1) is obtained is reduced to 10000-50000 point, { P} seeks point set corresponding with it on the cad model { P ' } as the control point set with the some cloud after simplifying.The results are shown in Figure 3.
Step 3
The reduced data that obtains with step 2 calculates rotation and translation matrix in per step iteration in the SVD_ICP algorithm, with formula as the registration control points collection
Be objective function, the calculation control point set is with respect to the transformation matrix of cad model, and detailed process is as follows: 1. according to the method for search closest approach, try to achieve on the cad model and control point set { point set that P} is corresponding { P ' }, utilize formula
With
Ask for the barycenter p and the p ' of two point sets.2. according to formula q
i=p
i-p and q '
i=p '
i-p ' calculates 2 displacements of concentrating each point with respect to its barycenter.3. according to formula
Ask for matrix H, and by formula H=U Λ V
TMatrix H is carried out svd, and wherein U is the left singular matrix of H, and V is the right singular matrix of H, and the two is 3 * 3 orthogonal matrix.4. according to formula R=VU
TAnd T=p '-Rp calculates rotation matrix R and translation matrix T.
Step 4
Can utilize formula R then in the hope of the transformation matrix R and the T in per step in the iterative process by step 3
z=R
i* R
I-1* ... ..*R
1And T
z=R
i* T
I-1+ T '
i, the calculation control point set is with respect to total transformation matrix R of cad model
zAnd T
zThe total transformation matrix R that tries to achieve
zAnd T
zBy formula Q
i=R
zP
i+ T
zBe applied to original point of density cloud model, just realized the accurate registration fast of itself and cad model, see Fig. 4 (b).
Rapid registering according to above-mentioned steps realization intensive cloud data of turbo blade and cad model carries out three-dimensional variance analysis to the result behind the registration, and registration time when statistics is simplified the result as the reference mark with difference and deviation result are as table
1, shown in the table 2.
The used time statistical form of the different reference mark of table 1 registration
The three-dimensional deviation statistics table of table 2
By table 1, data result carries out accurate registration with the data after simplifying as the reference mark as can be seen in the table 2, and its registration speed is greatly improved.From three-dimensional deviation result, to compare with the result who carries out registration before the simplification, its deviation changes very little, can guarantee the accuracy requirement of registration.
In a word, can under the prerequisite that guarantees registration accuracy, realize the fast accurate registration of intensive cloud data and cad model according to above-mentioned steps.
Claims (1)
1. the fast accurate method for registering of point of density cloud model is characterized in that comprising the steps:
Step 1
Choose on measurement point cloud model and the cad model any three groups of corresponding point respectively to (P
1, Q
1), (P
2, Q
2), (P
3, Q
3), P wherein
1, P
2, P
3Not on same plane; Order
Make vector v
3And w
3,
Make vector vector v
2And w
2,
v
1, v
2And v
3Constitute orthogonal coordinate system, be expressed as unit vector
In like manner
Any point P in the measurement point cloud model
iTransform to corresponding point Q on the cad model
iRelational expression be: Q
i=RP
i+ T, wherein R=[w] [v]
-1, T=Q
1-[w] [v]
-1P
1
Step 2
The point of density cloud model that utilizes the uniform sampling method that step 1 is obtained is reduced to 10000-50000 point, and { P} seeks point set corresponding with it on the cad model { P ' } as the control point set with the some cloud after simplifying;
Step 3
The control point set that obtains with step 2 P} calculates the rotation matrix and the translation matrix of per step iteration in the SVD_ICP algorithm as the registration control points collection:
1) utilizes formula
With
Ask for the barycenter p and the p ' of two point sets { P} and { P ' };
2) according to formula q
i=p
i-p and q '
i=p '
i-p ' calculates in two point sets { P} and { P ' } each point with respect to the displacement of its barycenter;
3) according to formula
Ask for matrix H, and by formula H=U Λ V
TMatrix H is carried out svd, and wherein U is the left singular matrix of H, and V is the right singular matrix of H, and the two is 3 * 3 orthogonal matrix;
4) according to formula R=VU
TAnd T=p '-Rp calculates the rotation matrix R of i step iteration
iWith the translation matrix T
i
Step 4
{ the accurate registration of P} and cad model, method is as follows: try to achieve every iteration rotation matrix R once according to step 3 to adopt the SVD_ICP algorithm to realize the control point set
iWith the translation matrix T
iThereby, utilize formula R
z=R
i* R
I-1* ... ..*R
1And T
z=R
i* T
I-1+ T '
iTry to achieve control point set { the rotation matrix R that P} is total with respect to cad model
zWith the translation matrix T
z, R wherein
zBe 3 * 3 matrix, T
zIt is 3 * 1 matrix; By formula Q
i=R
zP
i+ T
z, P wherein
iBe any point in the point cloud model, Q
iFor after the conversion with P
iCorresponding point; R
zAnd T
zOriginal point cloud model before being applied to simplify is realized itself and the fast accurate registration of cad model.
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