TWI627385B - Method and system for measuring object movement - Google Patents

Abstract

An object motion measurement method includes: acquiring, by an image capturing device, a first image and a second image at different time points, wherein the first image and the second image correspond to the same object; The first feature points are paired to the plurality of second feature points in the second image; the transformation matrix is calculated according to the first feature point and the second feature point; the numerical factorization of the transformation matrix is performed; and the numerical factor factorization is performed The results are compared to the transformation matrix model to calculate the motion parameters of 6 degrees of freedom.

Description

Object motion measurement method and system

The present invention relates to an image-based motion measurement method for an object, and more particularly to an object motion measurement method using only one camera.

In general, a camera can measure movement in two dimensions in the real world. If you want to detect three-dimensional movement in the real world, you can set up two cameras, or a camera plus an infrared detection instrument. . However, the use of two cameras is not only costly, but also requires finer corrections, so how to use a camera to measure movement in three dimensions is a topic of interest to those skilled in the art.

Embodiments of the present invention provide an object motion measurement method suitable for use in a computer system. The method includes: acquiring, by the image capturing device, the first image and the second image at different time points, wherein the first image and the second image correspond to the same object; and the plurality of first feature points in the first image Pairing to a plurality of second feature points in the second image; according to the first feature point and the second The feature points are calculated by the transformation matrix; the factorization decomposition is performed on the transformation matrix; and the result of the numerical factorization is compared with the transformation matrix model to calculate the motion parameters of the six degrees of freedom.

In some embodiments, the step of pairing the plurality of first feature points in the first image to the plurality of second feature points in the second image comprises: performing digital image correlation on the first image and the second image (digital Image correlation) algorithm.

In some embodiments, the object motion measurement method further includes: setting a transformation matrix model such as the following equation (1).

H = H _P H _A H _S ...(1)

Where H is the transformation matrix, H _P is the projection transformation matrix, H _A is the affine transformation matrix, and H _S is the similar transformation matrix.

In some embodiments, the step of numerical factorization of the transformation matrix comprises setting a transformation matrix such as equations (2) to (5) below, and calculating parameters K, R, v according to equations (6) to (10) below. , t.

v = H ₁₁ ^-1 h ₂₁ ...(6)

Kt = ( I ₂ - h ₁₂ v ^T ) ^-1 h ₁₂ (7)

t = K ^-1 (1+ v ^T Kt ) h ₁₂ (10).

In some embodiments, the step of comparing the result of the numerical factorization with the transformation matrix model to calculate the motion parameters of the six degrees of freedom comprises: calculating six degrees of freedom according to the following equations (11) to (17) Motion parameters (t _x , t _y , t _z , α, β, θ). Where f is the focal length of the image capturing device, and X ₀ , Y ₀ , and Z ₀ are preset values.

α = f H _P (3,2)...(11)

β =- f H _P (3,1)...(12)

θ =-H _S (1,2)...(13)

In another aspect, an embodiment of the present invention provides an object motion measurement system including an object, an image capture device, and a computer system. The object has a pattern for identification. The image capturing device is configured to capture the first image and the second image corresponding to the object. The computer system is configured to acquire the first image and the second image, and match the plurality of first feature points in the first image to the plurality of second feature points in the second image, and calculate according to the first feature point and the second feature point Out The transformation matrix is subjected to a numerical factorization decomposition of the transformation matrix, and the result of the numerical factorization is compared with the transformation matrix model to calculate the motion parameters of six degrees of freedom.

In some embodiments, the computer system is configured to perform a digital image correlation algorithm on the first image and the second image.

In some embodiments, the computer system is configured to set a transformation matrix model such as equation (1) above.

In some embodiments, the computer system sets the transformation matrix as in equations (2)-(5) above, and calculates the parameters K, R, v, t according to equations (6)-(10) above.

In some embodiments, the computer system calculates motion parameters (t _x , t _y , t _z , α, β, θ) of six degrees of freedom according to equations (11) through (17) above.

The above described features and advantages of the invention will be apparent from the following description.

100‧‧‧Object motion measurement system

110‧‧‧ objects

111‧‧‧ pattern

120‧‧‧Image capture device

130‧‧‧ computer system

X, Y, Z‧‧‧ axes

210, 220‧‧‧ objects

t _x , t _y , t _z , α, β, θ‧‧‧ exercise parameters

310‧‧‧planar coordinate system

311‧‧‧ objects

320‧‧‧Projection Center

330‧‧‧Image coordinate system

340‧‧‧ main axis

410‧‧‧ first image

420‧‧‧second image

411~413‧‧‧ first feature point

421~423‧‧‧second feature point

510, 520‧‧‧ procedures

511, 512, 521~523, 530‧‧ steps

611, 612‧‧‧ rolling mill

621, 622‧‧ label

631, 632‧‧‧ image capture device

701~705‧‧‧Steps

FIG. 1 is a schematic diagram showing an object motion measurement system according to an embodiment.

2A to 2D are schematic views showing various movements of an object in a three-dimensional space according to an embodiment.

FIG. 3 is a schematic diagram of a three-dimensional coordinate system and an image coordinate system according to an embodiment.

FIG. 4 is a schematic diagram showing an image before and after an object is moved according to an embodiment.

FIG. 5 is a flow chart showing the establishment of a forward model and a reverse model according to an embodiment.

FIG. 6 is a schematic diagram showing a method for measuring the motion of an applied object in a rolling system according to an embodiment.

FIG. 7 is a flow chart showing a method of measuring an object motion according to an embodiment.

The terms "first", "second", "etc." used in this document are not intended to mean the order or the order, and are merely to distinguish between elements or operations described in the same technical terms.

1 is a schematic diagram showing an object motion measurement system according to an embodiment. Referring to FIG. 1, the object motion measurement system 100 includes an object 110, an image capture device 120, and a computer system 130. The object 110 has a pattern 111 for identification. The pattern 111 in FIG. 1 is merely an example, and the present invention does not limit the size, color, texture, content, and the like of the pattern 111. This pattern 111 may be originally formed on the object 110 (consisting of the color and shape of the object 110 itself), or may be additionally formed on the object 110 (for example, by printing, drawing, pasting a sticker having the pattern 111, etc.). The pattern 111 must have sufficient features whereby the movement of the object 110 can be recognized. The image capturing device 120 is, for example, a digital camera, a camera, a photographic lens, or other device having an image sensor for capturing an image corresponding to the object 110. Computer department The system 130 can perform an object motion measurement method to calculate the motion of the object 110 in three-dimensional space.

In general, the computer system 130 acquires the first image and the second image at different time points through the image capturing device 120, and pairs the plurality of first feature points in the first image to the plurality of the second image. The second feature point calculates a transformation matrix according to the first feature point and the second feature point. The computer system 130 also performs numerical factorization on the transformation matrix, and compares the result of the numerical factorization with the transformation matrix model to calculate the motion parameters of six degrees of freedom. Each step will be described in detail below.

The movement of the object in three dimensions must first be described. 2A-2D are schematic diagrams showing various movements of an object in a three-dimensional space, according to an embodiment. In FIGS. 2A to 2D, the X axis extends in the horizontal direction, the Y axis extends in the vertical direction, and the Z axis is incident on the paper surface (which is also equal to the optical axis of the image capturing device). The movement of three-dimensional space can be divided into at least two categories: planar motion (Fig. 2A) and off-plane motion (Fig. 2B to Fig. 2D). In FIG. 2A, the object is moved in the XY plane, and the conversion relationship between the object 210 before the motion and the object 220 after the motion is a similar transformation, and three motion parameters (t _x , t _y , θ can be used. To describe, where t _x represents the displacement on the X axis, t _y represents the displacement on the Y axis, and θ represents the angle of rotation about the Z axis. In Figure 2B, the object is moved in the Z-axis, the relationship between the object after the object 210 before movement and the movement 220 can be used to represent the motion parameter t _z, t _z is a Z-axis displacement. In Fig. 2C, the object is rotated about the Y axis, and the relationship between the object 210 before the motion and the object 220 after the motion can be expressed by the motion parameter β, which is the angle of rotation about the Y axis. In Fig. 2D, the object is rotated about the X axis, and the relationship between the object 210 before the motion and the object 220 after the motion can be represented by the motion parameter α, which is the angle of rotation about the X axis. Thus, in this embodiment, the movement of the object in three dimensions can be represented by six motion parameters (t _x , t _y , t _z , α, β, θ).

Next, the correspondence between the three-dimensional coordinate system and the image coordinate system will be described. 3 is a schematic diagram depicting a three-dimensional coordinate system and an image coordinate system, in accordance with an embodiment. Please refer to FIG. 3. FIG. 3 illustrates a planar coordinate system 310, a projection center 320 (also referred to as a mirror core), and an image coordinate system 330. Both the planar coordinate system 310 and the image coordinate system 330 are coordinate systems on the XY plane. Planar coordinate system 310 represents the plane in which object 311 is located, projection center 320 represents the center of the lens in image capture device 120, and image coordinate system 330 represents the plane formed by the optical sensing array in image capture device 120. The vertical distance between the projection center 320 and the image coordinate system 330 is the focal length f of the image capturing device 120. The principal axis 340 is a line parallel to the Z axis and passing through the projection center 320. The main axis 340 intersects the coordinate points (p _x , p _y ) on the image coordinate system 330 and intersects the planar coordinate system 310. The coordinate point (X ₀ , Y ₀ ). The coordinates are described here in a homogeneous representation. The coordinates of the object 311 in three-dimensional space are vectors X=[X _i ,Y _i ,Z _i ,1] ^T , and the coordinates of the projection center 320 in the three-dimensional space are vectors [X ₀ , Y ₀ , -Z ₀ , 1]. ^T. After optical imaging, the projection of the object 311 on the image coordinate system 330 is represented as a vector x ₁ , and the vector x ₁ and the vector X have the following equation (1), where the vector And the matrix K are expressed as equations (2) and (3), respectively.

Here, Z _i =0 is set, so the vector X can be reduced by one dimension, and the equation (1) can be rewritten as the following equation (4), wherein the matrix L ₁ and the vector X _P are expressed as equations (5) and (6), respectively. Thus, vector x ₁ can be expressed as equation (7) below, where vector x ₁ has been normalized such that the third element in vector x ₁ is one.

x ₁ = KL ₁ X _p ...(4)

X _p =[ X _i Y _i 1] ^T ...(6)

If the object 311 is moving, it is assumed that the coordinates of the object on the image coordinate system 330 after the motion is represented as a vector x ₂ . Then, the vector x ₂ and the vector X have the relationship of the following equation (8), wherein the matrix R and the vector t are expressed as equations (9) and (10), respectively.

R = Rot ( α ) Rot ( β ) Rot ( θ )...(9)

t =[ t _x t _y t _z ] ^T ...(10)

The matrix R represents the displacement formed after the angles of α, β, and θ are respectively rotated on the X, Y, and Z axes. Since Z _i =0 is set, the vector X can be reduced by one dimension, and the equation (8) can be rewritten as the following equation (11), where the matrix L _{2 is} expressed as the following equation (12).

x ₂ = KL ₂ X _p ...(11)

According to the equation (4) and the equation (12), the relationship between the vector x ₁ and the vector x ₂ can be written as the following equation (13), wherein the size of the transformation matrix H is 3 x 3, expressed as the following equation (14).

x ₂ = H x ₁ ...(13)

Referring to FIG. 1 and FIG. 4, the image capturing device 120 obtains the first image 410 and the second image 420 before and after the object is moved, where the first image 410 corresponds to the object before the movement, and the second image 420 is Corresponds to the object after the move. The computer system 130 finds two feature points that are paired with each other in the first image 410 and the second image 420 according to a digital image correlation algorithm. For example, the first feature points 411 - 413 in the first image 410 are respectively paired to the second feature points 421 - 423 in the second image 420 . Each set of paired feature points can be substituted into equation (13) to provide a set of solutions. Since there are 9 unknowns in the transformation matrix H, at least 9 pairs of matching feature points are needed, according to the paired feature points. The transformation matrix H can be calculated. It should be noted that the present invention does not limit the specific content of the above-mentioned digital image association algorithm, and those skilled in the art can adopt any conventional algorithm.

After calculating the transformation matrix H, it is necessary to calculate the above six degrees of freedom motion parameters (t _x , t _y , t _z , α , β , θ). However, to complete this step, it is necessary to start from the camera projection theory, and then obtain the forward model and the inverse model, and then compare the forward model with the inverse model. FIG. 5 is a flow chart showing the establishment of a forward model and a reverse model, according to an embodiment. Referring to FIG. 5, the process 510 of establishing a forward model includes steps 511, 512. In step 511, the transformation matrix H is derived, which has been described as equations (1)-(14) above. In step 512, the transformation matrix H is factorized to obtain a plurality of matrix internal parameters. The process 520 of creating a reverse model includes steps 521-523. In step 521, a digital image association algorithm is executed to obtain feature points that are paired with each other. In step 522, the transformation matrix H is calculated from these feature points. In step 523, the transformation matrix H is subjected to numerical factorization to obtain a plurality of matrix internal parameters. In step 530, the matrix internal parameters are compared to calculate a motion parameter of 6 degrees of freedom. Steps 521 to 522 have been explained above, and steps 512, 523 and 530 will be explained below.

Step 512 is described herein. First, it must convert the matrix H solution is the product of three matrices, such as the following equation (15), wherein the projection matrix _P H (Project) transformation matrix, the matrix H _A is provided imitation (Affine) transformation matrix, and the matrix H _S is a similar transformation matrix.

H = H _P H _A H _S ...(15)

All of the above three matrices have their own special format, so the conversion matrix H in equation (14) needs to be rewritten to conform to the format of the three matrices. The transformation matrix H repeats as shown in the following equation (16).

Equation (16) can be simplified to the following equation (17).

Where matrix I ₂ is a second-order identity matrix, p = [ p _x p _y ], R ₂ = [ r ₁₁ r ₁₂ ; r ₂₁ r ₂₂ ], q = [- X ₀ - Y ₀ ], r = [ r ₃₁ r ₃₂ ] ^T , z = t _z + Z ₀ . The following equation (18) can be obtained by calculating the inverse matrix in equation (17).

The key to factorization is to first disassemble the second matrix according to equation (19) below.

Therefore, the above equation (18) can be rewritten as the following equation (20), where α = ( r ^T R ₂ ^-1 ) ^T , β = - r ^T R ₂ ^-1 t + z .

The first two matrices to the right of the equation (20) can be rewritten according to equation (21), where v = ( α ^T ( f I ₂ + pα ^T ) ^-1 ) ^T

Therefore, equation (20) can be rewritten as equation (23) below.

The first matrix to the right of the equal sign of equation (23) already has the form of matrix H _P , and the next four matrices must be processed. The second and third matrices are first merged as equation (24) below, and the fourth and fifth matrices can be combined as in equation (25) below. The matrix of equations (24), (25) may incorporate a matrix as in equation (26).

Then, the matrix in equation (26) can be disassembled into two matrices in the following equation (27).

The matrix on the left in equation (27) has the form of matrix H _A and the right has the form of matrix H _S . The transformation matrix H can be written in the form of the following equation (28), and the equation (28) corresponds to the equation (29).

The following is a brief description of how to calculate the six motion parameters, in which the values in equation (28) are calculated first. After 3 each coordinate conversion parameter of the six motion parameters in FIG. Are substituted into equation (29), and with equation (28) respectively, can be found in the matrix H _P the vector v can be expressed as the following equation (30).

That is, if the value of the vector v is known, the motion parameters α, β can be calculated. On the other hand, the second matrix H _A in equation (28) can be normalized to the following equation (31).

Substituting the above six motion parameters with the parameters converted by each coordinate in Fig. 3 into equation (29) and according to the first approximation (1+ x ) ^-1 1- x , the following equation (32) and equation (33) can be obtained.

If the matrix K/d is known, plus the motion parameters α, β have been calculated, the motion parameter t _z can be obtained after substituting into equation (33).

The motion parameters (t _x , t _y , θ) of the plane motion are included in the matrix H _S . If the matrix H _S is known, and the matrix R ₂ can be expressed as the following equation (34), the motion parameter θ, that is, θ = - R ₂ (1, 2 ) can be obtained.

Furthermore, the following equation (35) can be obtained from the equations (28) and the matrix H _S in equation (29), from which the motion parameters t _x , t _y can be obtained.

Referring back to Figure 5, step 512 has been detailed above. The above paragraph assumes that the values in equation (28) are calculated first, and in actual operation these values are calculated by step 523, and step 523 will be explained here. After obtaining the nine values in the transformation matrix H, the goal is to decompose the transformation matrix H into three matrices H _P , H _A and H _S . First, the three matrices can be multiplied first, as in equation (36) below.

The purpose of the numerical factorization is to find the parameters K, R, v, t. Since it is a homogeneous representation, the parameters in equation (36) can be scaled so that H(3,3)=1, after scaling, as in the following equation (37), where the parameters H ₁₁ , h ₁₂ , h ₂₁ For example, the following equations (38) ~ (40).

According to the above relationship, v ^T H ₁₁ = h ₁₂ ^{T can} be obtained, and v = H ₁₁ ^-1 h ₂₁ can be obtained to obtain the parameter v. On the other hand, since h ₁₂ (1+ v ^T Kt )= Kt , Kt = ( I ₂ - h ₁₂ v ^T ) ^-1 h ₁₂ can be obtained, and Kt is obtained. The above equation (38) can be rewritten as the following equation (41), since v ^T Kt is known, so it can be calculated from H ₁₁ R.

According to the analysis results of equations (33) and (34) above, the matrix The matrix R is represented by the following equations (42) and (43), respectively, wherein the variables x, y, z, and r are expressed as equations (44) to (47), respectively.

The variables that need to be calculated in equations (42) and (43) are x, y, z, θ , and the matrix R provides four sets of solutions. Specifically, these four variables can be calculated by the following equation (48).

After calculating the above four variables x, y, z, θ , we can find the matrix. With the matrix R, the matrix K can be calculated by the following equation (49).

Finally, the parameter t can be calculated by the following equation (50).

t = K ^-1 (1+ v ^T Kt ) h ₁₂ ...(50)

According to the above calculation, four parameters K, R, v, and t can be calculated, and thus the numerical factorization of the transformation matrix H is completed.

Referring back to Figure 5, step 530 is explained next. First, to simplify the calculation, p _x = p _y =0 can be set. In addition, the focal length f is known, and the parameters X ₀ , Y ₀ , Z ₀ can be obtained by means of correction or other measurement, that is, the parameters X ₀ , Y ₀ , Z ₀ can be regarded as preset values. The invention does not limit how to obtain the parameters X ₀ , Y ₀ , Z ₀ . According to the above equation (30), since the value of the vector v is known, the motion parameters α and β can be calculated, and the following equations (51) and (52) can be referred to.

α = f H _P (3,2)...(51)

β =- f H _P (3,1)...(52)

Next, the matrix R ₂ can be taken from the matrix H _S , so the motion parameter θ can be calculated according to the following equation (53).

θ =-H _S (1,2)...(53)

After the above equation (35) is developed, the following equations (54) and (55) are obtained, whereby the motion parameters t _x and t _y can be calculated.

Finally, according to equation (33) yields the following equation (56), thereby to calculate the motion parameters t _z.

In this way, in the embodiment of the present invention, only one image capturing device is needed to calculate the motion parameters of six degrees of freedom.

In some embodiments, the object motion measurement method described above may be Used in steel mills. 6 is a schematic diagram showing a method of measuring an applied object motion in a rolling system according to an embodiment. Referring to FIG. 6, the rolling system includes rolling mills 611 and 612, and the rolling mills 611 and 612 are respectively provided with labels 621 and 622. The labels 621, 622 have a specific pattern for identification. The image capturing devices 631 and 632 are configured to acquire images of the tags 621 and 622, respectively, and transmit the images to the computer system 130.

The rolling mills 611, 612 are used to extrude a material, for example by extruding a steel blank into a steel strip, and then forming a steel coil. According to the rolling theory, the thickness of the exit of the rolling delay is determined by the balance between the rigidity of the material and the rigidity of the rolling mill. When the material is squeezed, a reaction force of the rolling mill is applied to cause the rolls to move toward a large gap (small rigidity). In this embodiment, the computer system 130 can determine whether the rolling mills 611, 612 are displaced according to the above-described object motion measurement method, thereby evaluating the maintenance effect and the rolling problem of the equipment. It should be noted that FIG. 6 is only an example. The labels 621 and 622 and the image capturing devices 631 and 632 may be disposed at any suitable position. For example, in some embodiments, only one image capturing device may be used. The displacement on the two rolls is detected. In some embodiments, the rolling mills 611, 612 may also be H-type rolling mills or any other rolling mill, and the invention is not limited thereto. For example, an H-roll mill has four rolls, two horizontal rolls and two vertical rolls, the horizontal roll controls the rolling of the web, and the vertical roll controls the rolling of the wings. Due to the structure of the H-shaped steel itself, the rigidity in the vertical direction is large, and the rigidity in the horizontal direction is small. Therefore, when the gap is not properly controlled, the phenomenon of bending left and right is likely to occur. In order to understand the direction of the vertical roll, and whether the gap management is in line with expectations, in some embodiments, the label can be attached to the roller advancement screw and the image can be captured. Calculate the motion parameters of 6 degrees of freedom.

7 is a flow chart showing a method of measuring an object motion according to an embodiment. Referring to FIG. 7, in step 701, the first image and the second image are respectively acquired by the image capturing device at different time points. In step 702, a plurality of first feature points in the first image are paired to a plurality of second feature points in the second image. In step 703, a conversion matrix is calculated according to the first feature point and the second feature point. In step 704, a numerical factorization is performed on the transformation matrix. In step 705, the result of the factorization is compared with the transformation matrix model to calculate the motion parameters of six degrees of freedom. The steps in Fig. 7 have been described in detail above, and will not be described again here. It should be noted that the steps in FIG. 7 can be implemented as multiple codes or circuits, and the present invention is not limited thereto. In addition, the method of FIG. 7 can be used in conjunction with the above embodiments, or can be used alone. In other words, other steps can be added between the steps of FIG.

In another aspect, the present invention also proposes a computer program product, which can be written by any programming language and/or platform. When the computer program product is loaded into a computer system and executed, the above-mentioned Object motion measurement method.

Although the present invention has been disclosed in the above embodiments, it is not intended to limit the present invention, and any one of ordinary skill in the art can make some changes and refinements without departing from the spirit and scope of the present invention. The scope of the invention is defined by the scope of the appended claims.

Claims (10)

An object motion measurement method is applicable to a computer system, comprising: acquiring a first image and a second image at different time points through an image capturing device, wherein the first image and the second image are corresponding to the same image Pairing the plurality of first feature points in the first image with the plurality of second feature points in the second image; calculating a conversion matrix according to the first feature points and the second feature points Performing a numerical factorization on the transformation matrix; and comparing the result of the factorization with a transformation matrix model to calculate a motion parameter of six degrees of freedom. The method for measuring an object motion according to claim 1, wherein the step of pairing the plurality of first feature points in the first image to the plurality of second feature points in the second image comprises: The first image and the second image perform a digital image correlation algorithm. The object motion measurement method according to claim 1, further comprising: setting the transformation matrix model as the following equation (1): H = H _P H _A H _S (1) where H is the conversion The matrix, H _P is the projection transformation matrix, H _A is the affine transformation matrix, and H _S is the similar transformation matrix. The method for measuring the motion of an object according to claim 3, wherein the step of decomposing the transformation matrix by the numerical factor comprises: setting the transformation matrix as the following equations (2) to (5); Calculate the parameters K, R, v, t according to the following equations (6) to (10): v = H ₁₁ ^-1 h ₂₁ (6) t = K ^-1 (1+ v ^T Kt ) h ₁₂ (10). The method for measuring an object motion according to claim 4, wherein the step of comparing the result of the factorization with the transformation matrix model to calculate the motion parameter of the six degrees of freedom comprises: according to the following equation (11)~(17) Calculate the motion parameters of the six degrees of freedom (t _x , t _y , t _z , α , β , θ): α = f H _P (3, 2)... (11) β = - f H _P (3,1)...(12) θ =-H _S (1,2)...(13) Where f is the focal length of the image capturing device, and X ₀ , Y ₀ , and Z ₀ are preset values. An object motion measurement system includes: an object having a pattern for identification; an image capture device for capturing a first image and a second image corresponding to the object; a computer system for Obtaining the first image and the second image, and pairing the plurality of first feature points in the first image to the plurality of second feature points in the second image, according to the first feature points and the The second feature point calculates a transformation matrix, performs a numerical factorization on the transformation matrix, and compares the result of the factorization with a transformation matrix model to calculate a motion parameter of 6 degrees of freedom. The object motion measurement system of claim 6, wherein the computer system is configured to perform a digital image correlation algorithm on the first image and the second image. The object motion measurement system according to claim 6, wherein the computer system is configured to set the transformation matrix model as the following equation (1): H = H _P H _A H _S (1) where H For the transformation matrix, H _P is a projection transformation matrix, H _A is an affine transformation matrix, and H _S is a similar transformation matrix. The object motion measurement system according to claim 8, wherein the computer system sets the conversion matrix as the following equations (2) to (5), The computer system calculates the parameters K, R, v, t according to the following equations (6) to (10): v = H ₁₁ ^-1 h ₂₁ (6) Kt = ( I ₂ - h ₁₂ v ^T ) ^{- 1} h ₁₂ ...(7) t = K ^-1 (1+ v ^T Kt ) h ₁₂ (10). The object motion measurement system according to claim 9, wherein the computer system calculates the motion parameters (t _x , t _y , t _z , of the six degrees of freedom according to the following equations (11) to (17) . α, β, θ): α = f H P (3,2) ... (11) β = - f H P (3,1) ... (12) θ = -H S (1,2) ... (13) Where f is the focal length of the image capturing device, and X ₀ , Y ₀ , and Z ₀ are preset values.