CN106547724A - Theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set - Google Patents

Abstract

The present invention relates to a kind of theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set, it comprises the steps：1st, minimum point set is randomly selected in a cloud；2nd, coordinates computed conversion scaling coefficient lambda；3rd, calculate spacial similarity transformation model spin matrix R；4th, calculate the translation vector t between mapping local coordinate system and world coordinate system；5th, correct point and rough error are counted；6th, judge to perform；7th, export theorem in Euclid space coordinate transformation parameter.Initial value of the present invention without the need for spacial similarity transformation model, according to minimum point set, you can directly obtain theorem in Euclid space coordinate transformation parameter, it is to avoid traditional least square method needs the limitation of initial value.With reference to RANSAC algorithms, in can avoiding control point, rough error calculates the impact for causing to theorem in Euclid space coordinate transformation parameter, is obtained in that high-precision theorem in Euclid space coordinate transformation parameter, the spacial similarity transformation being precisely calculated between coordinate system.

Description

Theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set

Technical field

The present invention relates to spacial similarity transformation Models computed technical field, and in particular to a kind of based on the European of minimum point set Space coordinate conversion parameter acquiring method.

Background technology

Spacial similarity transformation be calculate two coordinate systems between rotation, the optimal transformation of Pan and Zoom, photography survey It is referred to as absolute orientation in amount.Spacial similarity transformation is in geodesic survey, photogrammetric, computer vision, Robot Hand-eye calibration etc. Field has a wide range of applications.With mapping information the reach of science, the daily of people is progressively come in digital earth, smart city Life.The products such as digital map navigation, three-dimensional streetscape, Internet of Things, virtual reality are being altered in steps the life style of people.Space phase It is one of core technology of these technologies and product like conversion, for calculating the transformation relation between different coordinates in real time, sends out Wave important effect.

Traditional spacial similarity transformation Models computed method adopts least square adjustment method.Due to spacial similarity transformation mould Type is nonlinear model, it is therefore desirable to by nonlinear equation linearisation, then carry out least-squares iteration calculating again.In a most young waiter in a wineshop or an inn Before taking advantage of, good initial value is generally required.If initial value is bad, it is easy to cause iteration not restrain, cannot get optimum space phase Like transformation parameter.When between two coordinate systems, rigid transformation is excessive, the ratio that such as there is the very big anglec of rotation or large scale Example scaling, good initial value are often not easy to obtain, and further limit the promotion and application of traditional least-squares iteration method.

The content of the invention

It is an object of the invention to provide a kind of theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set, should Method mainly solves the presence of high rotation angle, long range translation, large scale scaling between world coordinate system and mapping local coordinate system In the case of, theorem in Euclid space coordinate transformation parameter how is directly obtained, the present invention can put down high control point according to two and one is high Process control point, directly calculates spacial similarity transformation equation, obtains accurate reliable theorem in Euclid space coordinate transformation parameter.

To solve above-mentioned technical problem, a kind of theorem in Euclid space coordinate transformation parameter based on minimum point set disclosed by the invention Acquisition methods, it is characterised in that it comprises the steps：

Step 1：Carry out first time RANSAC algorithm iteration process, labelling iterationses I=1, to by coordinate system to be converted The point cloud that constitutes of all coordinate system conversion and control points be marked, each coordinate system conversion and control point one unique sequence of correspondence Row number, carries out stochastic sampling using random () random function to a cloud, randomly selects two and puts down high control point { p_i',p_iI= 1,2 and a vertical control point { z₃',p₃, wherein, { p_i',p_iI=1,2 represent two put down high control point respectively the world sit Mark system and the coordinate surveyed and drawn under local coordinate system, use { z₃',p₃Represent vertical control point respectively in world coordinate system and Bureau of Surveying and Mapping Coordinate under portion's coordinate system, p₁', p₂'、p₁、p₂、p₃It is the column vector of space coordinatess；z₃' it is scalar, represent vertical control point Elevation information under world coordinate system, control point { p₁',p₁, { p₂',p₂, { z₃',p₃It is to solve the problems, such as spacial similarity transformation Required minimum point position information；

Step 2：High control point { p is put down according to two_i',p_iI=1,2, carry out center of gravity calculating；

Then using the flat high control point coordinates after center of gravityWithCoordinates computed changes scaling coefficient lambda；

Step 3：Rotated come expression of space using quaternary number, according to center of gravity coordinateWithAnd Coordinate Conversion scaling Proportionality coefficient λ, calculates a binary quadratic equation group, obtains Space Rotating quaternion components q₂,q₃, it is shown below：

n₀q₂ ²+n₁q₃q₂+n₂q₃ ²=1

Wherein：

n₀=a²+c²+1 n₁=2ba+2dc n₂=b²+d²+1

Represent seat of the 3rd coordinate system conversion and control point under the mapping local coordinate system of center of gravity Mark；Represent i-th coordinate system conversion and control point, the coordinate under the world coordinate system of center of gravity；

Then, according to Space Rotating quaternion components q₂,q₃, calculate Space Rotating quaternion components q₀,q₁, such as following formula institute Show：q₀=aq₂+bq₃ q₁=cq₂+dq₃

Finally, according to Space Rotating quaternion components q₀,q₁, q₂,q₃, calculate spacial similarity transformation model spin matrix R；

Step 4：High control point { p is put down according to two_i',p_iI=1, and 2 coordinate, Coordinate Conversion scaling coefficient lambda, with And spacial similarity transformation model spin matrix R, directly calculate the translation vector between mapping local coordinate system and world coordinate system t；

Step 5：According to spacial similarity transformation model, the mapping local coordinate of each coordinate system conversion and control point is carried out into sky Between similarity transformation, obtain the coordinate under new world coordinate system, be shown below：

p_i"=λ Rp_i+ t i=1 ..., n

Wherein, the number of n denotation coordinations system conversion and control point, p_iRepresent the Bureau of Surveying and Mapping of i-th coordinate system conversion and control point Portion's coordinate；p_i" world coordinates of the i-th coordinate system conversion and control point of expression after spacial similarity transformation, t is that mapping local is sat Translation vector between mark system and world coordinate system；

Secondly, calculate world coordinates p of each coordinate system conversion and control point through calculating_i" and its original world coordinates p_i' the distance between d_i, it is shown below：

d_i=| p_i”-p_i'|

Relatively apart from d_iWith the size between threshold value σ set in advance, if apart from d_iLess than σ, then illustrate that the coordinate system turns It is correct point to change control point, is put in correct control point set；Otherwise, illustrate that the coordinate system conversion and control point is rough error, be put into In rough error control point set, finally, coordinate system conversion and control in correct control point set and rough error control point set is counted respectively The number of point, the coordinate system conversion and control points that definition is correctly controlled in point set are N_inThe coordinate in point set is controlled with rough error It is that conversion and control is counted as N_out；

Coordinate system conversion and control points N of the step 6. according to correct control point set_inWith coordinate in rough error control point set It is conversion and control points N_out, and current iterationses I, calculate whether meet stopping criterion for iteration, be shown below：

Wherein, β represents confidence level, the iterationses I+1 if iteration continues；

Step 7：In each iteration, two are randomly selected and puts down high control point { p_i',p_iI=1,2 and high process control Point { z₃',p₃A correct control point set and rough error control point set can be all corresponded to, after iteration ends, select correct point most Correct control point set it is corresponding two put down high control point { p_i',p_iI=1,2 and vertical control point { z₃',p₃Counted The theorem in Euclid space coordinate transformation parameter Coordinate Conversion scaling coefficient lambda that calculates, spacial similarity transformation model spin matrix R and Translation vector t between mapping local coordinate system and world coordinate system, as the final theorem in Euclid space coordinate transformation parameter for obtaining.

Beneficial effects of the present invention：

Initial value of the present invention without the need for spacial similarity transformation model, according to minimum point set, you can directly obtain theorem in Euclid space seat Mark conversion parameter, it is to avoid traditional least square method needs the limitation of initial value.With reference to RANSAC algorithms, control point can be avoided Middle rough error calculates the impact for causing to theorem in Euclid space coordinate transformation parameter, is obtained in that high-precision theorem in Euclid space Coordinate Conversion ginseng Number, the spacial similarity transformation being precisely calculated between coordinate system can be geodesic survey, photogrammetric, computer vision, machine The application services such as people's trick calibration.

Description of the drawings

Fig. 1 is the flow chart of the present invention；

Specific embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail：

The present invention is directed to the more situation in control point in current practical engineering application, with reference to conventional elimination of rough difference technology RANSAC, proposes a kind of theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set, can be in RANSAC iteration mistakes Cheng Zhong, random minima point set calculate spacial similarity transformation model parameter, and final model parameter calculation result is not thick in receptor site cloud Poor impact, highly reliable, high precision, the method, as shown in figure 1, it comprises the steps：

Step 1：Minimum point set is randomly selected in a cloud：

Carry out first time RANSAC algorithm iteration process, labelling iterationses I=1, to being owned by coordinate system to be converted The point cloud that coordinate system conversion and control point is constituted is marked, each coordinate system conversion and control point one unique serial number of correspondence, Stochastic sampling is carried out using random () random function to a cloud, two is randomly selected and is put down high control point { p_i',p_iI=1,2 and One vertical control point { z₃',p₃(above-mentioned two puts down high control point { p_i',p_iI=1,2 and vertical control point { z₃',p₃} Constitute minimum point set), wherein, { p_i',p_iI=1,2 represent two put down high control point respectively world coordinate system and mapping local Coordinate under coordinate system, uses { z₃',p₃Represent seat of the vertical control point respectively under world coordinate system and mapping local coordinate system Mark, p₁', p₂'、p₁、p₂、p₃The column vector of equal space coordinatess；z₃' it is scalar, represent vertical control point under world coordinate system Elevation information, control point { p₁',p₁, { p₂',p₂, { z₃',p₃It is to solve the problems, such as the minimum point position required for spacial similarity transformation Information；

Step 2：Coordinates computed changes scaling coefficient lambda：

High control point { p is put down according to two_i',p_iI=1,2, center of gravity calculating is carried out, is shown below：

Wherein,WithThe survey of the world coordinates and center of gravity of center of gravity is represented respectively Local coordinate is painted, wherein, x_i'、y_i' and z_i' for space original coordinates under world coordinate system, x_i、y_iAnd z_iTo survey and draw local coordinate The lower space original coordinates of system, T represent the transposition of vector, p_c' for the barycentric coodinates column vector under world coordinate system, p_cFor Bureau of Surveying and Mapping Barycentric coodinates column vector under portion's coordinate system；

Then using the flat high control point coordinates after center of gravityWithCoordinates computed changes scaling coefficient lambda, such as Shown in following formula：

Step 3：Calculate spacial similarity transformation model spin matrix R：

According to center of gravity coordinateWithAnd Coordinate Conversion scaling coefficient lambda, calculate a binary quadratic equation Group, obtains Space Rotating quaternion components q₂,q₃, it is shown below：

n₀q₂ ²+n₁q₃q₂+n₂q₃ ²=1

Wherein：

n₀=a²+c²+1 n₁=2ba+2dc n₂=b²+d²+1

Represent seat of the 3rd coordinate system conversion and control point under the mapping local coordinate system of center of gravity Mark；Represent i-th coordinate system conversion and control point, the coordinate under the world coordinate system of center of gravity；

Then, rotated come expression of space using quaternary number, according to Space Rotating quaternion components q₂,q₃, calculate Space Rotating Quaternion components q₀,q₁, it is shown below：q₀=aq₂+bq₃q₁=cq₂+dq₃

Finally, according to Space Rotating quaternion components q₀,q₁, q₂,q₃, spacial similarity transformation model spin matrix R is calculated, It is shown below：

Step 4：Calculate the translation vector t between mapping local coordinate system and world coordinate system：

High control point { p is put down according to two_i',p_iI=1, and 2 coordinate, Coordinate Conversion scaling coefficient lambda, and space Similarity transformation model spin matrix R, directly calculates the translation vector t between mapping local coordinate system and world coordinate system, as follows Shown in formula：

T=p_c'-λRp_c

Wherein, p_c' for the barycentric coodinates column vector under world coordinate system, p_cTo survey and draw the barycentric coodinates under local coordinate system Column vector；

Step 5：The correct point of statistics and rough error：

Spacial similarity transformation model parameter λ is calculated, after R and t, according to spacial similarity transformation model, by each coordinate system The mapping local coordinate of conversion and control point carries out spacial similarity transformation, obtains the coordinate under new world coordinate system, such as following formula institute Show：

p_i"=λ Rp_i+ t i=1 ..., n

Wherein, the number of n denotation coordinations system conversion and control point, p_iRepresent the Bureau of Surveying and Mapping of i-th coordinate system conversion and control point Portion's coordinate；p_i" world coordinates of the i-th coordinate system conversion and control point of expression after spacial similarity transformation, t is that mapping local is sat Translation vector between mark system and world coordinate system；

Secondly, calculate world coordinates p of each coordinate system conversion and control point through calculating_i" and its original world coordinates p_i' the distance between d_i, it is shown below：

d_i=| p_i”-p_i'|

Relatively apart from d_iWith the size between threshold value σ set in advance, if apart from d_iLess than σ, then illustrate that the coordinate system turns It is correct point to change control point, is put in correct control point set (inliers set)；Otherwise, illustrate the coordinate system conversion and control Point is rough error, is put in rough error control point set (outliers set), finally, counts correct control point set and rough error respectively The number of coordinate system conversion and control point in control point set, the correct coordinate system conversion and control controlled in point set of definition are counted and are N_inThe coordinate system conversion and control points controlled with rough error in point set are N_out；

Step 6：Judge to perform：

According to the coordinate system conversion and control points N of correct control point set_inWith coordinate system conversion in rough error control point set Control points N_out, and current iterationses I, calculate whether meet stopping criterion for iteration, be shown below：

Wherein, β represents confidence level, the iterationses I+1 if iteration continues；

Step 7：Output theorem in Euclid space coordinate transformation parameter：

In each iteration, two are randomly selected and puts down high control point { p_i',p_iI=1,2 and vertical control point { z₃', p₃A correct control point set and rough error control point set can be all corresponded to, after iteration ends, selection is correctly put most correct Corresponding two of control point set puts down high control point { p_i',p_iI=1,2 and vertical control point { z₃',p₃Calculated Theorem in Euclid space coordinate transformation parameter Coordinate Conversion scaling coefficient lambda, spacial similarity transformation model spin matrix R and Bureau of Surveying and Mapping Translation vector t between portion's coordinate system and world coordinate system, as the final theorem in Euclid space coordinate transformation parameter for obtaining.

In above-mentioned technical proposal, the confidence level β is 0.99.Threshold value σ takes engineering experience value 1, the unit of threshold value σ with The adopted unit of world coordinates is consistent.

Spacial similarity transformation model has seven parameters, and its minimum point set is two and puts down high control point and a high process control Point.The present invention realizes high-precision spacial similarity transformation, provides good initial value for traditional spacial similarity transformation solution, is The minimum point set of RANSAC algorithms selects to provide technical support.

The content that this specification is not described in detail belongs to prior art known to professional and technical personnel in the field.

Claims (6)

1. a kind of theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set, it is characterised in that it includes following step Suddenly：

Step 1：Carry out first time RANSAC algorithm iteration process, labelling iterationses I=1, to the institute by coordinate system to be converted There is the point cloud that coordinate system conversion and control point is constituted to be marked, each coordinate system conversion and control point one unique sequence of correspondence Number, stochastic sampling is carried out using random () random function to a cloud, two is randomly selected and is put down high control point { p_i',p_iI=1, 2 and a vertical control point { z₃',p₃, wherein, { p_i',p_iI=1,2 represent two put down high control point respectively in world coordinates System and the coordinate surveyed and drawn under local coordinate system, use { z₃',p₃Represent vertical control point respectively in world coordinate system and mapping local Coordinate under coordinate system, p₁', p₂'、p₁、p₂、p₃The column vector of equal space coordinatess；z₃' it is scalar, represent that vertical control point is alive Elevation information under boundary's coordinate system, control point { p₁',p₁, { p₂',p₂, { z₃',p₃It is to solve the problems, such as needed for spacial similarity transformation The minimum point position information wanted；

Step 2：High control point { p is put down according to two_i',p_iI=1,2, carry out center of gravity calculating；

Then using the flat high control point coordinates after center of gravityWithCoordinates computed changes scaling coefficient lambda；

Step 3：Rotated come expression of space using quaternary number, according to center of gravity coordinateWithAnd Coordinate Conversion scaling Coefficient lambda, calculates a binary quadratic equation group, obtains Space Rotating quaternion components q₂,q₃, it is shown below：

n₀q₂ ²+n₁q₃q₂+n₂q₃ ²=1

$m_0{q_2}^2+m_1{q}_3{q}_2+m_2{q_3}^2=\stackrel{\‾}{{z_3}^{\′}}$

Wherein：

$m_0=(a^2-c^2-1)\mathrm{\λ}\stackrel{\‾}{z_3}-2a\mathrm{\λ}\stackrel{\‾}{x_3}+2ac\mathrm{\λ}\stackrel{\‾}{y_3}$

$m_1=2\left(\right(1+bc+ad)\mathrm{\λ}\stackrel{\‾}{y_3}+(c-b)\mathrm{\λ}\stackrel{\‾}{x_3}+\left(ba-dc\right)\mathrm{\λ}\stackrel{\‾}{z_3})$

$m_2=(b^2-d^2+1)\mathrm{\λ}\stackrel{\‾}{z_3}+2d\mathrm{\λ}\stackrel{\‾}{x_3}+2bd\mathrm{\λ}\stackrel{\‾}{y_3}$

n₀=a²+c²+1 n₁=2ba+2dc n₂=b²+d²+1

$\begin{array}{cccc}a=\frac{\stackrel{\‾}{{z_i}^{\′}}+\mathrm{\λ}\stackrel{\‾}{z_i}}{\stackrel{\‾}{{x_i}^{\′}}-\mathrm{\λ}\stackrel{\‾}{x_i}}& b=-\frac{\stackrel{\‾}{{y_i}^{\′}}+\mathrm{\λ}\stackrel{\‾}{y_i}}{\stackrel{\‾}{{x_i}^{\′}}-\mathrm{\λ}\stackrel{\‾}{x_i}}& c=-\frac{\stackrel{\‾}{{y_i}^{\′}}-\mathrm{\λ}\stackrel{\‾}{y_i}}{\stackrel{\‾}{{x_i}^{\′}}-\mathrm{\λ}\stackrel{\‾}{x_i}}& d=-\frac{\stackrel{\‾}{{z_i}^{\′}}-\mathrm{\λ}\stackrel{\‾}{z_i}}{\stackrel{\‾}{{x_i}^{\′}}-\mathrm{\λ}\stackrel{\‾}{x_i}}\end{array}$

Represent coordinate of the 3rd coordinate system conversion and control point under the mapping local coordinate system of center of gravity；Represent i-th coordinate system conversion and control point, the coordinate under the world coordinate system of center of gravity；

Then, according to Space Rotating quaternion components q₂,q₃, calculate Space Rotating quaternion components q₀,q₁, it is shown below：q₀ =aq₂+bq₃ q₁=cq₂+dq₃

Finally, according to Space Rotating quaternion components q₀,q₁, q₂,q₃, calculate spacial similarity transformation model spin matrix R；

Step 4：High control point { p is put down according to two_i',p_iI=1, and 2 coordinate, Coordinate Conversion scaling coefficient lambda, Yi Jikong Between similarity transformation model spin matrix R, directly calculate mapping local coordinate system and world coordinate system between translation vector t；

Step 5：According to spacial similarity transformation model, the mapping local coordinate of each coordinate system conversion and control point is carried out into space phase Like converting, the coordinate under new world coordinate system is obtained, is shown below：

p_i"=λ Rp_i+ t i=1 ..., n

Wherein, the number of n denotation coordinations system conversion and control point, p_iRepresent that the mapping local of i-th coordinate system conversion and control point is sat Mark；p_i" world coordinates of the i-th coordinate system conversion and control point of expression after spacial similarity transformation, t is mapping local coordinate system Translation vector and world coordinate system between；

Secondly, calculate world coordinates p of each coordinate system conversion and control point through calculating_i" and its original world coordinates p_i' it Between apart from d_i, it is shown below：

d_i=| p_i”-p_i'|

Relatively apart from d_iWith the size between threshold value σ set in advance, if apart from d_iLess than σ, then the coordinate system conversion control is illustrated System point is correct point, is put in correct control point set；Otherwise, illustrate that the coordinate system conversion and control point is rough error, be put into rough error In control point set, finally, coordinate system conversion and control point in correct control point set and rough error control point set is counted respectively Number, the coordinate system conversion and control points that definition is correctly controlled in point set are N_inThe coordinate system controlled with rough error in point set turns Change points are controlled for N_out；

Step 6：According to the coordinate system conversion and control points N of correct control point set_inTurn with coordinate system in rough error control point set Change control points N_out, and current iterationses I, calculate whether meet stopping criterion for iteration, be shown below：

$k=log(1-\mathrm{\β})/\log \[1-{\left(\frac{N_{in}}{N_{in}+N_{out}}\right)}^3\]$

Wherein, β represents confidence level, the iterationses I+1 if iteration continues；

Step 7：In each iteration, two are randomly selected and puts down high control point { p_i',p_iI=1,2 and vertical control point {z₃',p₃A correct control point set and rough error control point set can be all corresponded to, after iteration ends, selection is correctly put most Corresponding two of correct control point set puts down high control point { p_i',p_iI=1,2 and vertical control point { z₃',p₃Calculated Theorem in Euclid space coordinate transformation parameter Coordinate Conversion scaling coefficient lambda out, spacial similarity transformation model spin matrix R and survey The translation vector t between local coordinate system and world coordinate system is painted, as the final theorem in Euclid space coordinate transformation parameter for obtaining.

2. theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set according to claim 1, its feature exist In：In the step 2, high control point { p is put down according to two_i',p_iI=1,2, carry out center of gravity calculating；It is shown below：

$\begin{array}{cc}\stackrel{\‾}{{p_i}^{\′}}={p_i}^{\′}-{p_c}^{\′}& \stackrel{\‾}{p_i}=p_i-p_c\end{array}$

$\begin{array}{ccc}{p_c}^{\′}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{p_i}^{\′}& p_c=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{p}_i& n=2\end{array}$

Wherein,WithThe Bureau of Surveying and Mapping of the world coordinates and center of gravity of center of gravity is represented respectively Portion's coordinate, wherein, x_i'、y_i' and z_i' for space original coordinates under world coordinate system, x_i、y_iAnd z_iTo survey and draw under local coordinate system Space original coordinates, T represent the transposition of vector, p_c' for the barycentric coodinates column vector under world coordinate system, p_cSit for mapping local Barycentric coodinates column vector under mark system；

Then using the flat high control point coordinates after center of gravityWithCoordinates computed changes scaling coefficient lambda, such as following formula It is shown：

$\begin{array}{cc}\mathrm{\λ}=\sqrt{{\stackrel{\‾}{{p_i}^{\′}}}^T\stackrel{\‾}{{p_i}^{\′}}/{\stackrel{\‾}{p_i}}^T\stackrel{\‾}{p_i}}& i=1or2\end{array}.$

3. theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set according to claim 1, its feature exist In：

In the step 3, according to Space Rotating quaternion components q₀,q₁, q₂,q₃, calculate spacial similarity transformation model spin matrix R, is shown below：

$R=\left(\begin{array}{ccc}{q}_0^2+q_1^2-q_2^2-q_3^2& 2(q_1{q}_2-q_0{q}_3)& 2(q_1{q}_3+q_0{q}_2)\\ 2(q_1{q}_2+q_0{q}_3)& q_0^2-q_1^2+q_2^2-q_3^2& 2(q_2{q}_3-q_0{q}_1)\\ 2(q_1{q}_3-q_0{q}_2)& 2(q_2{q}_3+q_0{q}_1)& q_0^2-q_1^2-q_2^2+q_3^2\end{array}\right).$

4. theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set according to claim 1, its feature exist In：In the step 4, high control point { p is put down according to two_i',p_iI=1, and 2 coordinate, Coordinate Conversion scaling coefficient lambda, with And spacial similarity transformation model spin matrix R, directly calculate the translation vector between mapping local coordinate system and world coordinate system T, is shown below：

T=p_c'-λRp_c

Wherein, p_c' for the barycentric coodinates column vector under world coordinate system, p_cFor survey and draw local coordinate system under barycentric coodinates arrange to Amount.

5. theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set according to claim 1, its feature exist In：The confidence level β is 0.99.

6. theorem in Euclid space coordinate transformation parameter acquisition methods based on minimum point set according to claim 1, its feature exist In：Threshold value σ is 1, and the unit unit adopted with world coordinates of threshold value σ is consistent.