WO2018214179A1 - Low-dimensional bundle adjustment calculation method and system - Google Patents

Abstract

A low-dimensional bundle adjustment calculation method and system. The method comprises: determining an initial value of a motion parameter; performing optimization calculation on an objective function of the motion parameter to acquire an optimized motion parameter; and calculating coordinates of a three-dimensional scene point according to the optimized motion parameter. By representing depth of field of multiple views as a function of relative motion parameters of every two views, directly restoring motion parameters from multiple views is achieved. The motion parameters are then analyzed to acquire coordinates of a three-dimensional scene point, thereby removing the coordinates of the three-dimensional scene point from a bundle adjustment parameter optimization process, significantly reducing spatial dimensions of parameters. The method is a low-dimensional bundle adjustment method having simple initialization, good robustness, a fast calculation speed and higher calculation precision. The present invention can be used as a core calculation engine for applications such as unmanned vehicle/unmanned aircraft visual navigation, visual three-dimensional reconstruction and augmented reality.

Description

Low-dimensional cluster adjustment calculation method and system Technical field

The present invention relates to the field of computer vision and photogrammetry, and in particular to a low-dimensional cluster adjustment calculation method and system.

Background technique

Bundle Adjustment, which restores 3D scene point coordinates, motion parameters and camera parameters from multiple views, is one of the core technologies in the fields of computer vision and photogrammetry. The goal of the cluster adjustment technique is to minimize the reprojection error of the image points, which can be represented as a nonlinear function of the three-dimensional scene point coordinates, motion parameters, and camera parameters. For the case of m three-dimensional scene points and n views, the parameter space is 3*m+6*n dimensions. Since the number of three-dimensional scene points is usually large, the dimension of the parameter space to be optimized is huge. At present, the mainstream method of cluster adjustment is implemented by a nonlinear optimization algorithm considering the sparseness of the Jacobian matrix to improve the calculation speed. However, the parameter space of the mainstream method has many dimensions and needs to be further improved to adapt. Real-time computing needs.

Summary of the invention

In view of the deficiencies in the prior art, an object of the present invention is to provide a low-dimensional cluster adjustment calculation method and system. The invention expresses the depth of field of multiple views as a function of the relative motion parameters of the two views, and realizes directly recovering the motion parameters from the plurality of views, and then obtaining the coordinates of the three-dimensional scene points from the motion parameters.

A low-dimensional bundling adjustment calculation method according to the present invention includes the following steps:

Step 1: Determine the initial value of the motion parameter;

Step 2: Minimize the objective function of the motion parameter to obtain the optimized motion parameter;

Step 3: Calculate the coordinates of the three-dimensional scene points according to the optimized motion parameters.

Preferably, the step 1 comprises the following steps:

Step 1.1: For the double view of the jth and j+1th views, j=1, 2,..., n-1, the common matching feature point set {j, j+1} on the double view Corresponding image feature points, using a direct linear transformation algorithm to solve the relative pose of the j+1th view relative to the jth view (R _{j, j+1} , t _{j, j+1} );

among them:

n is the number of views participating in the bundle adjustment;

R _j,j+1 is the relative attitude of the j+1th view relative to the jth view;

t _{j, j+1} is the unit relative displacement vector of the j+1th view relative to the jth view, ie ||t _{j, j+1} ||=1;

Calculate the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j-th view coordinate system

And the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j+1th view coordinate system

among them:

i=1,2,...,m ^(j,j+1) ;

m ^{(j, j+1)} represents the number of matching image point pairs in the dual view composed of the jth and j+1th views;

Normalized image point coordinates on the jth view for the i-th matching image point pair corresponding to the common matching feature point set {j, j+1};

Normalized image point coordinates on the j+1th view for the i-th matching image point pair corresponding to the common matching feature point set {j, j+1};

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j-th view coordinate system;

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j+1th view coordinate system;

Step 1.2: Fixed ||T _1,2 ||=1; for the three views of the j-1th, jth, and j+1th views, j=2,3,...,n-1, according to The common matching feature point set {j-1, j, j+1} on the three views, and the scale of the relative displacement ||T _j,j+1 ||/||T _j-1,j || The uniform relative displacement vector T _j,j+1 :

T _j,j+1 =||T _j,j+1 ||t _j,j+1 ;

among them:

T _1,2 is the relative displacement vector of the second view relative to the first view;

T _j,j+1 is the relative displacement vector of the j+1th view relative to the jth view;

T _j-1,j is the relative displacement vector of the jth view relative to the j-1th view;

m ^{(j-1, j, j+1)} represents the number of common matching image point pairs in the three views composed of the j-1th, jth, and j+1th views;

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j-1, j} on the j-1th and jth views in the j-th view coordinate system;

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} on the j-th and j+1th views in the j-th view coordinate system;

t _j,j+1 is the unit relative displacement vector of the j+1th view relative to the jth view;

Step 1.3: Calculate the absolute pose (R _j+1 , T _j+1 ) of the _j+ 1th view according to the absolute pose (R _j , T _j ) of the jth view:

R _j+1 =R _j,j+1 R _j

T _j+1 =T _j,j+1 +R _j,j+1 T _j

among them:

R _j represents the absolute pose of the jth view;

R _j+1 represents the absolute pose of the j+1th view;

R _j,j+1 is the relative attitude of the j+1th view relative to the jth view;

T _j represents the absolute displacement vector of the jth view;

T _j+1 represents the absolute displacement vector of the j+1th view;

T _j,j+1 is the relative displacement vector of the j+1th view relative to the jth view;

When referring to the first view:

(R ₁ , t ₁ )≡(I ₃ ,0 _3×1 )

among them:

R ₁ represents the absolute posture of the first view;

T ₁ represents the absolute displacement vector of the first view;

I ₃ represents a 3-dimensional unit matrix;

0 _{3 × 1} represents a zero matrix of 3 rows and 1 column.

Preferably, in the step 2, the objective function of the motion parameter is specifically as follows:

The minimum objective function δ(θ) of the motion parameter θ = (R _j , T _j ) _{j = 1, 2, ... n} is given as follows:

e ₃ =[0 0 1] ^T

among them:

θ represents the absolute pose parameter set of all views;

δ(·) means to minimize the objective function;

m ^{(j, k)} represents the number of matching image point pairs in the dual view composed of the jth and kth views;

The normalized image point coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, k} on the jth and kth views on the kth view;

Normalized image point coordinates on the jth view for the i-th matching image point pair corresponding to the common matching feature point set {j, k} on the jth and kth views;

R _j,k is the relative attitude of the kth view relative to the jth view;

T _j,k is the relative displacement vector of the kth view relative to the jth view.

Preferably, the minimum objective function δ(θ) of the motion parameter θ=(R _j , T _j ) _{j=1, 2, . . . n} given in step 2 is: the same three-dimensional scene point to the same view The distance is equal.

Preferably, the step 3 includes the following steps:

According to the optimized motion parameters θ=(R _j ,T _j ) _j=1,2,...n , for the double view composed of the jth and kth views, the coordinates of the three-dimensional scene points are calculated by weighting as follows:

T _j,k =T _k R _j,k T _j

among them:

X _i represents the three-dimensional coordinates of the i-th three-dimensional scene point, and the three-dimensional scene point X _i corresponds to the sth image feature point in the dual view formed by the j-th and k-th views;

Denotes the i-th three-dimensional scene at the points X _i j k web and double web configuration view of view is visible identification function, i.e., when X _i is visible in the view of the dual,

Otherwise, then

R _j represents the absolute pose of the jth view;

T _j,k is the relative displacement vector of the kth view relative to the jth view;

Representing the normalized image point coordinates of the sth matching image point pair corresponding to the common matching feature point set {j, k} on the jth view;

Representing the normalized image point coordinates of the sth matching image point pair corresponding to the common matching feature point set {j, k} on the kth view;

R _k represents the absolute pose of the kth view;

T _j represents the absolute displacement vector of the jth view;

T _k represents the absolute displacement vector of the kth view;

R _j,k represents the relative pose of the kth view relative to the jth view;

T _j,k represents the relative displacement vector of the kth view relative to the jth view.

Preferably, the low-dimensional bundling adjustment calculation method considers a situation in which the camera has been calibrated, and assumes that a matching image point pair between the views has been determined.

A low-dimensional bundling adjustment computing system according to the present invention includes a computer readable storage medium storing a computer program, the computer program being executed by a processor to implement the steps of the low-dimensional bundling adjustment calculation method described above.

Compared with the prior art, the present invention has the following beneficial effects:

The invention is a low-dimensional bundle adjustment method with simple initialization, good Lubang, faster calculation speed and higher calculation precision. The invention can be used as a core calculation engine for unmanned/undulous visual navigation, visual three-dimensional reconstruction, augmented reality and the like.

DRAWINGS

Further features of the present invention, by way of a detailed description of non-limiting embodiments, The purpose and advantages will become more apparent:

1 is a flow chart showing the steps of a low dimensional bundling adjustment method provided in accordance with the present invention.

detailed description

The invention will now be described in detail in connection with specific embodiments. The following examples are intended to further understand the invention, but are not intended to limit the invention in any way. It should be noted that a number of changes and modifications may be made by those skilled in the art without departing from the inventive concept. These are all within the scope of protection of the present invention.

The present invention expresses the depth of field as a function of the motion parameters, thereby eliminating the coordinates of the three-dimensional scene points from the parameter optimization process of the bundle adjustment. For the case of m three-dimensional scene points and n views, the parameter space is 6*n dimensions. Compared with the current mainstream methods, the bundle adjustment method proposed by the present invention greatly reduces the dimension of the parameter space.

The present invention contemplates situations where the camera has been calibrated and assumes that matching image point pairs between views have been determined.

The following is an explanation of the general form of the generation:

Assume that n is the number of views adjusted by the bundle, which are sequentially numbered as view 1, view 2, ... view n;

(R _i , T _i ) represents the absolute pose of the i-th view;

R _i represents the absolute pose of the i-th view;

T _i =||T _i ||t _i represents the absolute displacement vector of the i-th view;

t _i represents the unit absolute displacement vector of the i-th view, ie ||t _i ||=1;

θ represents the absolute pose parameter set of all views;

Representing the relative pose of the kth view relative to the jth view;

T _j,k ≡T _k -R _jk T _j represents a relative displacement vector of the kth view with respect to the jth view;

T _j,k =||T _j,k ||t _j,k ,t _j,k is the unit relative displacement vector of the kth view relative to the jth view, ie ||t _j,k ||=1 ;

(R _j,k , t _j,k ) represents the relative pose of the kth view relative to the jth view;

{j} represents all feature point sets on the jth view;

{j,k} denotes a set of common matching feature points on the jth and kth views, {j,k,...} and so on, representing a set of common matching feature points on three or more views;

(j, k) represents a dual view of the jth and kth views;

m ^{(j, k)} represents the number of matching image point pairs in the dual view composed of the jth and kth views;

The normalized image point coordinates of the i-th matching image point pair in the double view composed of the jth and kth views, respectively, in the jth view and the kth view, that is, the first two components are calibrated The image point coordinates, the third component is 1.

A low-dimensional bundle adjustment method according to the present invention includes the following steps:

Step 1: Determine the initial value of the motion parameter;

Step 2: Minimize the objective function of the motion parameter to obtain the optimized motion parameter;

Step 3: Calculate the coordinates of the three-dimensional scene points according to the optimized motion parameters.

The individual steps are described in detail below.

The step 1 includes the following steps:

Step 1.1: For the double view of the jth and j+1th views, j=1, 2,..., n-1, the common matching feature point set {j, j+1} on the double view Corresponding image feature points, using Direct Linear Transformation (DLT) algorithm, solve the relative pose of the j+1th view relative to the jth view (R _{j, j+1} , t _{j, j+1} );

among them:

n is the number of views participating in the bundle adjustment;

R _j,j+1 is the relative attitude of the j+1th view relative to the jth view;

t _{j, j+1} is the unit relative displacement vector of the j+1th view relative to the jth view, ie ||t _{j, j+1} ||=1;

Calculate the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j-th view coordinate system

And the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j+1th view coordinate system

among them:

i=1,2,...,m ^(j,j+1) ;

m ^{(j, j+1)} represents the number of matching image point pairs in the dual view composed of the jth and j+1th views;

Normalized image point coordinates on the jth view for the i-th matching image point pair corresponding to the common matching feature point set {j, j+1};

Normalized image point coordinates on the j+1th view for the i-th matching image point pair corresponding to the common matching feature point set {j, j+1};

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j-th view coordinate system;

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j+1th view coordinate system;

Step 1.2: Without loss of generality, fixed ||T _1,2 ||=1; for three views of the j-1th, jth, and j+1th views, j=2,3,..., n-1, according to a common set of matching feature points on the three views {j-1, j, j + 1}, the calculation of the relative displacement of the scale _{|| T j, j + 1 ||} / || T j-1, _j ||, to obtain a uniform displacement relative displacement vector T _j,j+1 :

T _j,j+1 =||T _j,j+1 ||t _j,j+1 ;

among them:

T _1,2 is the relative displacement vector of the second view relative to the first view;

T _j,j+1 is the relative displacement vector of the j+1th view relative to the jth view;

T _j-1,j is the relative displacement vector of the jth view relative to the j-1th view;

m ^{(j-1, j, j+1)} represents the number of common matching image point pairs in the three views composed of the j-1th, jth, and j+1th views;

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j-1, j} on the j-1th and jth views in the j-th view coordinate system;

Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} on the j-th and j+1th views in the j-th view coordinate system;

t _j,j+1 is the unit relative displacement vector of the j+1th view relative to the jth view;

Step 1.3: Calculate the absolute pose (R _j+1 , T _j+1 ) of the _j+ 1th view according to the absolute pose (R _j , T _j ) of the jth view:

R _j+1 =R _j,j+1 R _j

T _j+1 =T _j,j+1 +R _j,j+1 T _j

among them:

R _j represents the absolute pose of the jth view;

R _j+1 represents the absolute pose of the j+1th view;

R _j,j+1 is the relative attitude of the j+1th view relative to the jth view;

T _j represents the absolute displacement vector of the jth view;

T _j+1 represents the absolute displacement vector of the j+1th view;

T _j,j+1 is the relative displacement vector of the j+1th view relative to the jth view;

When referring to the first view:

(R ₁ , t ₁ )≡(I ₃ ,0 _3×1 )

among them:

R ₁ represents the absolute posture of the first view;

T ₁ represents the absolute displacement vector of the first view;

I ₃ represents a 3-dimensional unit matrix;

0 _{3 × 1} represents a zero matrix of 3 rows and 1 column;

It should be noted:

- In step 1.1, the value of j is j = 1, 2, ..., n-1;

- In step 1.2, the value of j is j = 2, 3, ..., n-1;

- In step 1.3, the value of j is j = 1, 2, ..., n-1.

In the step 2, the objective function of the motion parameter is specifically as follows:

Under the premise that the distances from the same three-dimensional scene point to the same view are equal _, the minimum objective function δ(θ) of the motion parameter θ=(R _j , T _j ) _{j=1, 2, . . . n} is given as follows:

e ₃ =[0 0 1] ^T

among them:

θ represents the absolute pose parameter set of all views;

δ(·) means to minimize the objective function;

m ^{(j, k)} represents the number of matching image point pairs in the dual view composed of the jth and kth views;

The normalized image point coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, k} on the jth and kth views on the kth view;

Normalized image point coordinates on the jth view for the i-th matching image point pair corresponding to the common matching feature point set {j, k} on the jth and kth views;

R _j,k is the relative attitude of the kth view relative to the jth view;

T _j,k is the relative displacement vector of the kth view relative to the jth view;

Since the initial value of the motion parameter obtained in step 1 has been optimized by step 2, an optimized value of the motion parameter is obtained. Therefore, step 3 is calculated based on the optimized value of the motion parameter. Specifically, the step 3 includes the following steps:

According to the optimized motion parameters θ=(R _j ,T _j ) _j=1,2,...n , for the double view composed of the jth and kth views, the coordinates of the three-dimensional scene points are calculated by weighting as follows:

T _j,k =T _k -R _j,k T _j

among them:

X _i represents the three-dimensional coordinates of the i-th three-dimensional scene point, and the three-dimensional scene point X _i corresponds to the sth image feature point in the dual view formed by the j-th and k-th views;

Denotes the i-th three-dimensional scene at the points X _i j k web and double web configuration view of view is visible identification function, i.e., when X _i is visible in the view of the dual,

Otherwise, then

R _j represents the absolute pose of the jth view;

T _j,k is the relative displacement vector of the kth view relative to the jth view;

Representing the normalized image point coordinates of the sth matching image point pair corresponding to the common matching feature point set {j, k} on the jth view;

Representing the normalized image point coordinates of the sth matching image point pair corresponding to the common matching feature point set {j, k} on the kth view;

R _k represents the absolute pose of the kth view;

T _j represents the absolute displacement vector of the jth view;

T _k represents the absolute displacement vector of the kth view;

R _j,k represents the relative pose of the kth view relative to the jth view;

T _j,k represents the relative displacement vector of the kth view relative to the jth view.

The specific embodiments of the present invention have been described above. It is to be understood that the invention is not limited to the specific embodiments described above, and various changes or modifications may be made by those skilled in the art without departing from the scope of the invention. The features of the embodiments and the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (7)

1. A low-dimensional cluster adjustment calculation method, comprising the following steps:

   Step 1: Determine the initial value of the motion parameter;

   Step 2: Minimize the objective function of the motion parameter to obtain the optimized motion parameter;

   Step 3: Calculate the coordinates of the three-dimensional scene points according to the optimized motion parameters.
2. The low-dimensional bundling adjustment calculation method according to claim 1, wherein the step 1 comprises the following steps:

   Step 1.1: For the double view of the jth and j+1th views, j=1, 2,..., n-1, the common matching feature point set on the dual view {j, j+1 } corresponding image feature points, using the direct linear transformation algorithm to solve the relative pose of the j+1th view relative to the jth view (R _{j, j+1} , t _{j, j+1} );

   among them:

   n is the number of views participating in the bundle adjustment;

   R _j,j+1 is the relative attitude of the j+1th view relative to the jth view;

   t _{j, j+1} is the unit relative displacement vector of the j+1th view relative to the jth view, ie ||t _{j, j+1} ||=1;

   Calculate the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j-th view coordinate system

   

   And the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j+1th view coordinate system

   

   

   

   among them:

   i=1,2,...,m ^(j,j+1) ;

   m ^{(j, j+1)} represents the number of matching image point pairs in the dual view composed of the jth and j+1th views;

   

   Normalized image point coordinates on the jth view for the i-th matching image point pair corresponding to the common matching feature point set {j, j+1};

   

   Normalized image point coordinates on the j+1th view for the i-th matching image point pair corresponding to the common matching feature point set {j, j+1};

   

   Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j-th view coordinate system;

   

   Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} in the j+1th view coordinate system;

   Step 1.2: Fixed ||T _1,2 ||=1; for the three views of the j-1th, jth, and j+1th views, j=2,3,...,n-1 Calculate the scale of relative displacement based on the common matching feature point set {j-1, j, j+1} on the three views ||T _j,j+1 ||/||T _j-1,j || , to obtain a uniform displacement vector T _j,j+1 :

   

   T _j,j+1 =||T _j,j+1 ||t _j,j+1 ;

   among them:

   T _1,2 is the relative displacement vector of the second view relative to the first view;

   T _j,j+1 is the relative displacement vector of the j+1th view relative to the jth view;

   T _j-1,j is the relative displacement vector of the jth view relative to the j-1th view;

   m ^{(j-1, j, j+1)} represents the number of common matching image point pairs in the three views composed of the j-1th, jth, and j+1th views;

   

   Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j-1, j} on the j-1th and jth views in the j-th view coordinate system;

   

   Representing the three-dimensional coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, j+1} on the j-th and j+1th views in the j-th view coordinate system;

   t _j,j+1 is the unit relative displacement vector of the j+1th view relative to the jth view;

   Step 1.3: Calculate the absolute pose (R _j+1 , T _j+1 ) of the _j+ 1th view according to the absolute pose (R _j , T _j ) of the jth view:

   R _j+1 =R _j,j+1 R _j

   T _j+1 =T _j,j+1 +R _j,j+1 T _j

   among them:

   R _j represents the absolute pose of the jth view;

   R _j+1 represents the absolute pose of the j+1th view;

   R _j,j+1 is the relative attitude of the j+1th view relative to the jth view;

   T _j represents the absolute displacement vector of the jth view;

   T _j+1 represents the absolute displacement vector of the j+1th view;

   T _j,j+1 is the relative displacement vector of the j+1th view relative to the jth view;

   When referring to the first view:

   (R ₁ , t ₁ )≡(I ₃ ,0 _3×1 )

   among them:

   R ₁ represents the absolute posture of the first view;

   T ₁ represents the absolute displacement vector of the first view;

   I ₃ represents a 3-dimensional unit matrix;

   0 _{3 × 1} represents a zero matrix of 3 rows and 1 column.
3. The low-dimensional bundle adjustment calculation method according to claim 1, wherein in the step 2, the objective function of the motion parameter is specifically as follows:

   The minimum objective function δ(θ) of the motion parameter θ = (R _j , T _j ) _{j = 1, 2, ... n} is given as follows:

   

   e ₃ =[0 0 1] ^T

   

   

   among them:

   θ represents the absolute pose parameter set of all views;

   δ(·) means to minimize the objective function;

   m ^{(j, k)} represents the number of matching image point pairs in the dual view composed of the jth and kth views;

   

   The normalized image point coordinates of the i-th matching image point pair corresponding to the common matching feature point set {j, k} on the jth and kth views on the kth view;

   

   Normalized image point coordinates on the jth view for the i-th matching image point pair corresponding to the common matching feature point set {j, k} on the jth and kth views;

   R _j,k is the relative attitude of the kth view relative to the jth view;

   T _j,k is the relative displacement vector of the kth view relative to the jth view.
4. The low-dimensional bundling adjustment calculation method according to claim 3, wherein the motion parameter θ=(R _j , T _j ) _{j=1, 2, . . .} The premise of the objective function δ(θ) is that the distances of the same three-dimensional scene points to the same view are equal.
5. The low-dimensional bundle adjustment calculation method according to claim 1, wherein the step 3 comprises the following steps:

   According to the optimized motion parameters θ=(R _j ,T _j ) _j=1,2,...n , for the double view composed of the jth and kth views, the coordinates of the three-dimensional scene points are calculated by weighting as follows:

   

   

   T _j,k =T _k -R _j,k T _j

   

   among them:

   X _i represents the three-dimensional coordinates of the i-th three-dimensional scene point, and the three-dimensional scene point X _i corresponds to the sth image feature point in the dual view formed by the j-th and k-th views;

   

   Denotes the i-th three-dimensional scene at the points X _i j k web and double web configuration view of view is visible identification function, i.e., when X _i is visible in the view of the dual,

   

   Otherwise, then

   

   R _j represents the absolute pose of the jth view;

   T _j,k is the relative displacement vector of the kth view relative to the jth view;

   

   Representing the normalized image point coordinates of the sth matching image point pair corresponding to the common matching feature point set {j, k} on the jth view;

   

   Representing the normalized image point coordinates of the sth matching image point pair corresponding to the common matching feature point set {j, k} on the kth view;

   R _k represents the absolute pose of the kth view;

   T _j represents the absolute displacement vector of the jth view;

   T _k represents the absolute displacement vector of the kth view;

   R _j,k represents the relative pose of the kth view relative to the jth view;

   T _j,k represents the relative displacement vector of the kth view relative to the jth view.
6. The low-dimensional bundling adjustment calculation method according to claim 1, wherein the low-dimension bundling adjustment calculation method considers a situation in which the camera has been calibrated, and assumes that a matching image point pair between the views has been determined.
7. A low-dimensional bundle adjustment computing system comprising a computer readable storage medium storing a computer program, wherein the computer program is executed by a processor to implement the low dimension of any one of claims 1 to 6. The steps of the cluster adjustment calculation method.

Images