CN104657990A - Two-dimensional contour fast registration method - Google Patents

Abstract

The invention relates to a two-dimensional contour fast registration method. The two-dimensional contour fast registration method comprises six major steps: step 1, setting a reference data set and a target data set; step 2, for each point in the target data set, seeking a point with the shortest distance corresponding to the point from reference data set in a centralized manner; step 3, establishing a matching target function; step 4, optimizing the target function, and figuring out an optimal solution of the target function to obtain a new target data set; step 5, performing error analysis and calculation, and if error conditions are met or a maximum number of iterations is reached, going to the step 6, and otherwise, going to step 2, step 6, outputting an error analysis report according to a matching relation after the optimal matching relation is obtained, and realizing two-dimensional contour fast registration. The invention provides the two-dimensional contour fast registration method to realize an ICP (iterative closest point) algorithm, by adopting the method, curve contour registration is efficiently and stably realized, and the method provided by the invention is widely applied to measurement and detection of workpieces after processing, reconstruction of surfaces, identification of three-dimensional objects, calibration of cameras and the like.

Description

A kind of two-dimensional silhouette rapid registering method

Technical field

The present invention relates to a kind of two dimension (2D) profile rapid registering method, refer more particularly to the registration that curved profile is quick, efficient, stable.The invention belongs to Computer Applied Technology field.

Background technology

Iterative closest point algorithms (Iterative Closest Point, ICP) is a kind of method for registering based on free form curved surface that American scholar Besl and Mckay proposed for point set Registration of Measuring Data problem in 1992.This algorithm is on the basis of known two point sets and an initial state assumption corresponding relation, utilizes corresponding point set registration technology to carry out registration, continuous iteration and minimize the algorithm of Image matching error.Compared with the method for registering between corresponding point set, the sharpest edges of ICP algorithm are that it does not need to know the definite corresponding relation between two point sets, but start interative computation based on the corresponding relation of a hypothesis, finally find a corresponding relation optimized and a registration result optimized.ICP algorithm is suitable for registration problems when cannot know point set corresponding relation.The realization of classical ICP algorithm will be used Quaternion Method and ask for the maximum eigenwert of matrix and eigenvalue of maximum characteristic of correspondence vector algorithm, no matter adopts which kind of method to solve the objective function of ICP algorithm, all needs the accuracy considering to solve and speed of convergence.

In prior art, the realization of ICP algorithm has multiple, as singular value decomposition method, Quaternion method, orthogonal matrix method and two Quaternion method, wherein, and most importantly singular value decomposition method and Quaternion method.

Prior art one, based on the method (SVD) of svd.The method, by the relevant nature of the conversion of matrix, directly obtains optimum geometric parameter solution.

Prior art two, based on the calculating kinematic parameter method of hypercomplex number.Rotation matrix and a translation vector unit quaternion matrix represent by the method, then a symmetric matrix is constructed according to the covariance matrix of two point sets, the unit character vector corresponding to eigenvalue of maximum obtaining this matrix is optimum rotation, thus obtains rotation geometry parameter and translation geometric parameter.

Prior art one method implements fairly simple, and result of calculation is also more accurate.The method is owing to being decompose based on SVD, and not all matrix can both carry out SVD decomposition, and for linear and have the data set of singular point not carry out SVD decomposition, therefore the range of application of prior art one has limitation.

Prior art two is owing to being expressed as the function about rotation parameter by translation parameters when tectonic unit's Quaternion Matrix, the calculating therefore for rotation parameter has good precision, but for the calculating of translation parameters, its precision need to improve.

Summary of the invention

1, object: the object of this invention is to provide a kind of two-dimensional silhouette rapid registering method, to improve efficiency and the stability of measurement point string and curved profile registration.

2, technical scheme: the object of the invention is to be achieved through the following technical solutions.

A kind of two-dimensional silhouette rapid registering method of the present invention, it comprises the following steps:

Step one, setting reference data set and target data set;

Step 2, each point concentrated target data, concentrate the point seeking a corresponding with it bee-line in reference data;

Step 3, foundation coupling objective function;

Step 4, objective function to be optimized, to obtain objective function optimum solution, obtain new target data set;

Step 5, carry out error analysis calculation, if meet error condition or reach maximum iteration time, go to step six, otherwise, go to step two;

Step 6, after obtaining Optimum Matching relation, according to this matching relationship output error analysis report.

The rapid registering of two-dimensional silhouette is just achieved by above-mentioned six steps.

Wherein, described in step one, " reference data set " refers to two-dimentional reference data point set, and " target data set " refers to two-dimensional measurement point string, is actual measured value.

Wherein, " bee-line " described in step 2 refers to that obtaining each number of targets strong point by pointwise concentrates corresponding bee-line point in reference data points, each number of targets strong point is made to have a reference data points corresponding with it, its corresponding relation is not also known, but can suppose to there is a corresponding relation, this relation object is similar to rotation and the translation transformation relation of rigid body, therefore, only rotation matrix and translation vector need be solved, just this transformation relation can be obtained;

Wherein, " setting up coupling objective function " described in step 3, " coupling objective function " hypothesis existence target data point set and reference data points collection corresponding relation should be referred to, this corresponding relation is equivalent to rigid body and rotates and translation motion, is namely measurement point string and curved profile registration relation; Described " setting up coupling objective function ", its way sets up coupling objective function based on such corresponding relation according to least square method principle;

Wherein, " being optimized " matching relationship referring to and obtain when making target function value minimum described in step 4 to objective function, then carry out " rigid body translation " according to this relation and obtain new target data point set, certainly, only once and the transformation relation obtained normally can not meet error requirements, need after conversion that the new target data point set that obtains is as the target data point set of next iteration, repeat above step, this is so-called iterative closest point algorithms just.

Wherein, according to the new target data point set that step 4 obtains in step 5, carry out error analysis calculation, if meet error requirements or reach maximum iteration time, then go to step six, otherwise repeat above step until iteration terminates.

3, advantage and effect

The present invention proposes a kind of two-dimensional silhouette rapid registering method to realize ICP algorithm, the method efficiently, stably can realize curved profile registration, and the present invention also can solve linearly and have the registration problems between the data set of singular point.The present invention has wide range of applications, as processed the identification, camera calibration etc. of the measurement and detection of rear workpiece, surperficial reconstruction, three-dimensional body.Meaning of the present invention is to realize 2D measurement point string and quick, efficient, the stable registration of curved profile.

Accompanying drawing explanation

Fig. 1 is iterative closest point algorithms schematic diagram

Fig. 2 is two-dimensional silhouette registration fast method idiographic flow enforcement figure

Code name in figure, symbol description are as follows:

P _i-target data point set, is provided with n data point i=1,2,3 ..., n

Q _i-number of targets strong point P _ibee-line point is concentrated to reference data points;

P _i ¹-target data point set P _ithrough the new target data point set that first time rotates and obtains after translation transformation;

Q _i ¹-number of targets strong point P _i ¹bee-line point is concentrated to reference data points;

P _i ^k-target data the point set that obtains after kth time iterated transform;

Q _i ^k-number of targets strong point P _i ^kbee-line point is concentrated to reference data points.

Embodiment

See Fig. 1, Fig. 2, a kind of two-dimensional silhouette rapid registering method of the present invention, concrete implementation step is as follows:

Step one, existing target data point set P _i(i=1,2 ..., n), be provided with n number of targets strong point, reference data point set from input DXF graphic file, the measurement point data that target data point set is measured from surveying instrument;

Step 2, get target data point concentrate 1 P _i(x _i, y _i), concentrate searching point in reference data points make a P _iarrive distance is the shortest, and namely calculating reference point concentrates corresponding point make minimum, in this way the point that can find correspondence is concentrated in reference point to each point in target data.Suppose existence rotation matrix and a translation vector, target data point set P _i(x _i, y _i) obtain a new new data point set by this conversion corresponding relation between these two point sets is $\left(\begin{array}{c}{x}_i^1\\ y_i^1\end{array}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)+\left(\begin{array}{c}{b}_1\\ b_2\end{array}\right),$ Wherein, θ, b ₁, b ₂for undetermined coefficient, matrix $\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)$ For rotation matrix, vector $\left(\begin{array}{c}{b}_1\\ b_2\end{array}\right)$ For translation vector;

Step 3, solve undetermined coefficient θ, b according to the corresponding relation in step 2 ₁, b ₂, resolution principle should make the number of targets strong point after conversion to P _i(x _i, y _i) corresponding to reference data points the quadratic sum of distance minimum, set up about independent variable θ, b according to this principle ₁, b ₂objective function:

$f=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[{(x_i^{\′}-\cos {\mathrm{\θx}}_i-\sin {\mathrm{\θy}}_i-b_1)}^2+{(y_i^{\′}+\sin {\mathrm{\θx}}_i-\cos {\mathrm{\θy}}_i-b_2)}^2];$

Step 4, objective function to be optimized, to obtain objective function optimum solution.If function f gets minimum value, then the local derviation numerical value of f to each unknowm coefficient equals zero, and so can set up following three equations:

$\begin{array}{c}\frac{\∂f}{\∂\mathrm{\θ}}=2\mathrm{\Σ}[(x_i^{\′}-\cos {\mathrm{\θx}}_i-\sin \mathrm{\θ}{y}_i-b_1)(\sin \mathrm{\θx}-\cos {\mathrm{\θy}}_i)+\\ (y_i^{\′}+\sin {\mathrm{\θx}}_i-\cos {\mathrm{\θy}}_i-b_2)(\cos {\mathrm{\θx}}_i+\sin {\mathrm{\θy}}_i)]=0\end{array}$

$\frac{\∂f}{{\∂b}_1}=-2\mathrm{\Σ}(x_i^{\′}-\cos {\mathrm{\θx}}_i-\sin {\mathrm{\θy}}_i-b_1)$

$\frac{\∂f}{{\∂b}_2}=-2\mathrm{\Σ}(y_i^{\′}+\sin {\mathrm{\θx}}_i-\cos {\mathrm{\θy}}_i-b_2)$

These three equations are solved, obtains

$b_1=\frac{\mathrm{\Σ}{x}_i^{\′}-\cos \mathrm{\θ\Σ}{x}_i-\sin \mathrm{\θ\Σ}{y}_i}{n}$

$b_2=\frac{\mathrm{\Σ}{y}_i^{\′}+\sin \mathrm{\θ\Σ}{x}_i-\cos \mathrm{\θ\Σ}{y}_i}{n}$

If $X^{\′}=\frac{\mathrm{\Σ}{x}_i^{\′}}{n},Y^{\′}=\frac{\mathrm{\Σ}{y}_i^{\′}}{n},X=\frac{\mathrm{\Σ}{x}_i}{n},Y=\frac{\mathrm{\Σ}{y}_i}{n},$ Obtain:

Σ{(Yx _i-Xy _i)+[(y′ _i-Y′)x _i-(x′ _i-X′)y _i]cosθ+[(x′ _i-X′)x _i+(y′ _i-Y′)y _i]sinθ}＝0

Because Y Σ is x _i-X Σ y _i=0, so

[n(X′Y-XY′)+Σ(x _iy′ _i-x′ _iy _i)]cosθ-[n(ZZ′+YY′)-Σ(x′ _ix _i+y′ _iy _i)]sinθ＝0

Thus try to achieve

$\mathrm{\θ}=\arctan =\frac{[n(X^{\′}Y-{\mathrm{XY}}^{\′})+\mathrm{\Σ}(x_i{y}_i^{\′}-x_i^{\′}{y}_i)]}{[n({\mathrm{ZZ}}^{\′}+{\mathrm{YY}}^{\′})-\mathrm{\Σ}(x_i^{\′}{x}_i+y_i^{\′}+y_i)]}$

θ is substituted into b ₁, b ₂can in the hope of b ₁, b ₂.

θ, b will be obtained ₁, b ₂value, be then updated to equation $\left(\begin{array}{c}{x}_i^1\\ y_i^1\end{array}\right)=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)+\left(\begin{array}{c}{b}_1\\ b_2\end{array}\right)$ In, just can obtain new target data point set

Step 5, the target data point set that step 4 is obtained be updated to equation in carry out error analysis, if error σ is not less than specified value, then will step 2 is returned, if the target data point that obtains is after kth time iteration as new target data point set corresponding bee-line point is concentrated to be to reference data points so repeat down, until error meets the demands or iterations reaches maximum requirement, then go to step six;

Step 6, the data point finally obtained and reference point to be made comparisons one by one, obtain the error of each point and output error analysis report, thus obtain the error analysis report of whole two-dimensional silhouette curve registration.

The present invention can be applicable to process in the measurement and detection technology of rear workpiece, first a registration mode is found according to datum mark in measurement and detection process, then the error of other measurement points and reference point is calculated according to this mode and output error is reported, and then obtain Error analysis of machining report, to processing, there is certain directive function.The present invention is not limited to measure and detects and in registration technology field, also can be applicable to the reconstruction on surface, the identification of three-dimensional body, the demarcation etc. of camera.

Claims (6)

1. a two-dimensional silhouette rapid registering method, is characterized in that: it comprises the following steps:

Step one, setting reference data set and target data set;

Step 2, each point concentrated target data, concentrate the point seeking a corresponding with it bee-line in reference data;

Step 3, foundation coupling objective function;

Step 4, objective function to be optimized, to obtain objective function optimum solution, obtain new target data set;

Step 5, carry out error analysis calculation, if meet error condition or reach maximum iteration time, go to step six, otherwise, go to step two;

Step 6, after obtaining Optimum Matching relation, according to this matching relationship output error analysis report, achieve the rapid registering of two-dimensional silhouette.

2. a kind of two-dimensional silhouette rapid registering method according to claim 1, is characterized in that: " reference data set " refers to two-dimentional reference data point set described in step one, " target data set " refers to two-dimensional measurement point string, is actual measured value.

3. a kind of two-dimensional silhouette rapid registering method according to claim 1, it is characterized in that: " bee-line " described in step 2 refers to that obtaining each number of targets strong point by pointwise concentrates corresponding bee-line point in reference data points, each number of targets strong point is made to have a reference data points corresponding with it, its corresponding relation is not known, but suppose to there is a corresponding relation, this relation object is similar to rotation and the translation transformation relation of rigid body, therefore, only rotation matrix and translation vector need be solved, just this transformation relation can be obtained.

4. a kind of two-dimensional silhouette rapid registering method according to claim 1, it is characterized in that: " setting up coupling objective function " described in step 3, " coupling objective function " hypothesis existence target data point set and reference data points collection corresponding relation should be referred to, this corresponding relation is equivalent to rigid body and rotates and translation motion, is namely measurement point string and curved profile registration relation; Described " setting up coupling objective function ", its way sets up coupling objective function based on such corresponding relation according to least square method principle.

5. a kind of two-dimensional silhouette rapid registering method according to claim 1, it is characterized in that: " being optimized " matching relationship referring to and obtain when making target function value minimum described in step 4 to objective function, then carry out " rigid body translation " according to this relation and obtain new target data point set, certainly, only once and the transformation relation obtained normally can not meet error requirements, need the new target data point set that obtains after conversion as the target data point set of next iteration, repeat above step, this is so-called iterative closest point algorithms just.

6. a kind of two-dimensional silhouette rapid registering method according to claim 1, it is characterized in that: according to the new target data point set that step 4 obtains in step 5, carry out error analysis calculation, if meet error requirements or reach maximum iteration time, then go to step six, otherwise repeat above step until iteration terminates.