JP7044016B2 - Line sensor camera calibration device and method - Google Patents

Description

The present invention relates to an apparatus and a method for calibrating a line sensor camera in the field of image processing.

In Non-Patent Document 1 below, as a camera calibration method, it is proposed to obtain an external parameter and an internal parameter of the camera for each shooting by shooting a plane marker in various positions and postures with an area camera.

Further, in Patent Document 1 below, a calibration pattern is projected onto a measurement object, the measurement object is photographed, the photographed image is image-analyzed to extract feature points, and a tertiary feature point is extracted based on the acquired plurality of feature points. In a calibrator, method and program that estimates at least one of the parameters required for the original measurement, if all the parameters are unknown, there is indeterminacy and the values are not uniquely determined, so the evaluation function is regular. It is described that optimization is performed by adding a chemical term.

Further, in Patent Document 2 below, a part of the image area is designated from the target image, an edge is extracted from the designated image area, and the distortion coefficient is calculated based on the coordinates and intensity of the edge position on the image. It is described that the intensity at each edge is used for weighting in the process of calculating the strain coefficient in the imaging parameter measuring method and apparatus and the recording medium.

Further, Patent Document 3 below describes a calibration device and method for a line sensor camera in which the internal parameters of the line sensor camera are calibrated using a calibration marker.

JP-A-2015-36629 Japanese Patent No. 3661073 Japanese Unexamined Patent Publication No. 2016-218815

Z. Zhang. "A Flexible New Technique for Camera Calibration", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22, No. 11, 2000, pp.1330-1334. Richard Szeliski, Toru Tamaki et al., "Computer Vision-Algorithms and Applications-", Kyoritsu Shuppan, 2013, pp.51 C.M. Bishop, "Pattern Recognition and Machine Learning," Springer Japan, 2007, pp.9

The calibration method described in Non-Patent Document 1 is a method in which plane markers are photographed in various positions and orientations, and internal parameters and external parameters of each imaging are solved by a nonlinear optimization method. Since the planar marker is used, it is easy to create a marker, and since multiple shootings are performed, the focal length and the like can be estimated with high accuracy. Due to these characteristics, the method of Non-Patent Document 1 is currently most used as a camera calibration method. However, this method has not been compatible with line sensor cameras. For example, in a line sensor camera, if a plane marker is used as in the method of Non-Patent Document 1, there is a problem that the calculation of the focal length and the like becomes unstable.

Further, the method described in Patent Document 1 is a method of stably obtaining parameters by performing optimization such as adding a regularization term to the evaluation function, but how important each parameter is as a regularization term. No particular consideration was given to prior knowledge such as whether to do so.

Further, what is described in Patent Document 2 is similar to the idea of the present invention in which the regularization is weighted in that the weighting is incorporated into the evaluation function, but the place and the idea of weighting are different from the present invention. In addition, there is a problem that there is no function to directly and stably estimate the value of the parameter.

Further, the device described in Patent Document 3 is a device capable of calibrating by simply taking a plurality of marker images with a line sensor camera having a smaller amount of information than an area camera, but the distortion coefficient becomes extremely large and the focal length becomes extremely large. However, there is a problem that it may occur depending on the captured image that the value is significantly different from the actual value.

Therefore, it is an object of the present invention to provide a calibration device and method for a line sensor camera capable of stably calibrating the line sensor camera.

The calibration device for the line sensor camera according to the first invention, which solves the above problems, is
A three-dimensional marker having a plurality of detection points whose two-dimensional plane coordinates on the two-dimensional plane which is the imaging range of the line sensor camera are known, and
It has a processing unit for calculating internal parameters and external parameters for calibration of the line sensor camera based on a plurality of images of the three-dimensional marker captured by the line sensor camera.
The processing unit
An image input unit in which the images of the three-dimensional markers having different positions and postures are input, and
A measurement coordinate calculation unit that calculates the one-dimensional image coordinates of the detection point of the three-dimensional marker on the image for each image, and the measurement coordinate calculation unit.
For the transformation matrix obtained based on the mathematical model of the line sensor camera that converts the two-dimensional plane coordinates to the one-dimensional image coordinates, input known initial values as the initial internal parameters in the transformation matrix, and use a linear solution method. An external parameter calculation unit that calculates initial external parameters from the transformation matrix for each image,
For an evaluation function obtained by adding a value considering the internal parameters to an error function considering the lens distortion obtained based on the mathematical model, the initial internal parameters and the initial external parameters are input to the evaluation function. Then, the internal parameter and the external parameter, which minimizes the evaluation function obtained by adding the value considering the internal parameter to the sum of the error functions for the total number of the detection points and the total number of the images, were repeatedly calculated. It is characterized by having a non-linear minimum squared part calculated by a non-linear solution method.

The calibration device for the line sensor camera according to the second invention, which solves the above problems, is
In the calibration device for the line sensor camera according to the first invention.
The evaluation function is characterized in that the magnitude of the focal length of the lens, the position of the principal point coordinates of the lens, and the magnitude of the distortion coefficient of the lens are each weighted and added to the error function.

The calibration device for the line sensor camera according to the third invention, which solves the above problems, is
In the calibration device for the line sensor camera according to the first or second invention.
The three-dimensional marker has an L-shaped shape, and is characterized in that the plurality of detection points are arranged on an inner surface that is bent into an L-shape.

The calibration device for the line sensor camera according to the fourth invention, which solves the above problems, is
In the calibration device for the line sensor camera according to any one of the first to third inventions.
The mathematical model is characterized by using a pinhole camera model.

The method for calibrating the line sensor camera according to the fifth invention, which solves the above problems, is
Calibration of the line sensor camera based on a plurality of images taken by the line sensor camera of a three-dimensional marker having a plurality of detection points whose two-dimensional plane coordinates are known on the two-dimensional plane which is the imaging range of the line sensor camera. A line sensor camera calibration method that calculates internal and external parameters for the camera.
An image input step in which the images of the three-dimensional markers having different positions and postures are input, and
A measurement coordinate calculation step of calculating the one-dimensional image coordinates of the detection point of the three-dimensional marker on the image for each image, and
For the transformation matrix obtained based on the mathematical model of the line sensor camera that converts the two-dimensional plane coordinates to the one-dimensional image coordinates, input known initial values as the initial internal parameters in the transformation matrix, and use a linear solution method. An external parameter calculation step of calculating the initial external parameters from the transformation matrix for each image, and
For an evaluation function obtained by adding a value considering the internal parameters to an error function considering the lens distortion obtained based on the mathematical model, the initial internal parameters and the initial external parameters are input to the evaluation function. Then, the internal parameter and the external parameter, which minimizes the evaluation function obtained by adding the value considering the internal parameter to the sum of the error functions for the total number of the detection points and the total number of the images, were repeatedly calculated. It is characterized by having a non-linear minimum square step calculated by a non-linear solution method.

The method for calibrating the line sensor camera according to the sixth invention for solving the above problems is as follows.
In the calibration method of the line sensor camera according to the fifth aspect of the invention.
The evaluation function is characterized in that the size of the focal length of the lens, the position of the principal point coordinates of the lens, and the size of the distortion coefficient of the lens are each weighted and added to the error function.

The method for calibrating the line sensor camera according to the seventh invention, which solves the above problems, is
In the calibration method of the line sensor camera according to the fifth or sixth invention.
The three-dimensional marker is characterized by using an L-shaped marker in which the plurality of detection points are arranged on an inner surface bent into an L-shape.

The method for calibrating the line sensor camera according to the eighth invention for solving the above problems is as follows.
In the calibration method of the line sensor camera according to any one of the fifth to seventh inventions.
A pinhole camera model is used as the mathematical model.

According to the calibration device and method for the line sensor camera according to the present invention, the line sensor camera can be calibrated in a stable manner.

It is a schematic block diagram which shows an example of embodiment of the calibration apparatus of the line sensor camera which concerns on this invention. It is a flowchart explaining the calibration method of the line sensor camera carried out by the apparatus shown in FIG. This is an example of an image obtained by photographing an L-shaped marker. This is another example of an image obtained by photographing an L-shaped marker.

When making measurements using a camera, it is essential to obtain camera parameters such as the focal length, principal point coordinates, and distortion coefficient of the camera in advance, and obtaining this is called camera calibration. Hereinafter, camera calibration is simply referred to as calibration.

In the present invention, as in the method of Non-Patent Document 1, the camera parameter calculation by the multiple shooting of the marker and the nonlinear optimization method is introduced into the calibration of the line sensor camera. However, since the method of Non-Patent Document 1 is premised on an area camera, this method cannot be directly introduced into the calibration of a line sensor camera. For example, in a line sensor camera, the number of dimensions is small, so the orthogonality of the rotation matrix cannot be utilized, and since the line sensor camera cannot take a chessboard-like image of a plane marker for calibration, the focal length and external parameters are calculated. The problem is that it becomes unstable. Therefore, in the present invention, a three-dimensional marker is used for calibration.

Further, in the present invention, a pinhole camera model is used as the camera model. However, in the present invention, since the line sensor camera is used, the three-dimensional space of the imaging range becomes a two-dimensional image in the normal area camera, whereas the two-dimensional plane of the imaging range becomes the one-dimensional image in the line sensor camera. Become. Then, by installing the three-dimensional marker on the two-dimensional plane of the imaging range, the external parameters to be obtained can be set to one axis for rotation and two dimensions for translation.

Here, the apparatus configuration of the present invention is shown in FIG. 1, and the mathematical model in the configuration shown in FIG. 1 is shown in the following equation (1). The details of the apparatus configuration of the present invention shown in FIG. 1 will be described later.

Further, in the following equations (1) to (17), the alphabet that is not bold (bold) is a scalar, and the lowercase alphabet of bold (bold) is a vector, and the bold alphabet (bold). The uppercase alphabet is a matrix. In addition, since bold type (bold type) cannot be used in the document, the normal format is used and "(bold type)" is added immediately after the corresponding alphabet.

In FIG. 1, since the line sensor camera 10 captures only one line, the imaging range is the two-dimensional plane 11 in the three-dimensional space. The object coordinate system (two-dimensional plane coordinate system) of the L-shaped marker 20 on the two-dimensional plane 11 is represented by the X-axis and the Y-axis, and the camera coordinate system (one-dimensional image coordinate system) of the line sensor camera 10 is represented by a line. It is represented by a u-axis orthogonal to the axis w in the optical axis direction of the sensor camera 10 and parallel to the two-dimensional plane 11 of the imaging range. The rotation matrix between the object coordinate system and the camera coordinate system is R (bold body) (the axis of rotation is one axis and its angle is θ), and the translation vector is t (bold body) (two-dimensional vector whose elements are t). ₁ , t ₂ ).

Here, s is a scaling coefficient, f is a focal distance, c is a principal point coordinate, u is a position in an actually observed camera coordinate system (measured coordinates in pixel coordinates), and X and Y are positions in an object coordinate system (L). It is the true value coordinates in the real space (two-dimensional plane 11) of the character marker 20.

The above equation (1) is a mathematical model for converting the object coordinates (two-dimensional plane coordinates) of the L-shaped marker 20 into the camera coordinates (one-dimensional image coordinates) of the line sensor camera 10. However, in the above equation (1), the distortion of the lens of the line sensor camera 10 is not taken into consideration. Therefore, if (x, y) is defined as in the following equation (2), the strain can be expressed as in the following equations (3) to (5). Note that k ₁ to k ₃ are radial distortion coefficients. Further, regarding the distortion of the lens, Non-Patent Document 2 (particularly, page 51) is referred to.

I would like to expand the above equations (1) to (5), but since x "cannot be substituted into equation (5) as it is, the following equation (5)'is substituted into equation (4). Equations (1) to (3) Is also substituted into the equation (4) to obtain the following equation (6).

When calibrating with this camera model, the error in the unit focal length plane will be minimized, and the internal and external parameters will be minimized by the Levenberg-Marquardt method so that the following equation (7) is minimized. Will be sought.

In the above equation (7), M is the number of times the image is taken, and N is the number of feature points (the number of detected points of the black and white band 23) acquired in each picture. The above equation (7) is the sum of the error functions based on the above equation (6) for the total number M of the captured images and the total number N of the detection points.

Here, when the calibration was actually performed using the steric marker, it was found that the solution could not be completely prevented from becoming unstable just by using the steric marker. Unstable here means that "the focal length should not change significantly from the initial value set for the lens", "the distortion coefficients k ₁ , k ₂ , k ₃ of the lens do not become extremely large values, and In addition, the distortion coefficients k ₁ , k ₂ , and k ₃ of the lens are generally k ₁ > k ₂ > k ₃ "from the general knowledge known to those who are experts in camera calibration. It means that it deviates greatly.

That is, if the parameter that minimizes the above equation (7) is obtained by the optimization process, the parameter may have an unrealistic value. Therefore, in this embodiment, the error function based on the above equation (6) is that "the focal length f does not change significantly from the specified value f ₀ of the lens" and "the principal point coordinate c is the image center c ₀ (depending on the camera)". "The distortion coefficient of the lens k ₁ , k ₂ , k ₃ is not an extremely large number", "The magnitude of the distortion coefficient of the lens is k ₁ > k ₂ > k ₃ " It was decided to obtain the internal and external parameters by the Lebenberg Marcart method so that the evaluation function (the following equation (8)) that introduced the knowledge of experts such as "many" is minimized.

In the above equation (8), w _f is the weighting coefficient of the regularization term of the focal distance, w _c is the weighting coefficient of the regularization term of the main point coordinates, c ₀ is the default value of the main point coordinates, and w _k 1 is the distortion coefficient k. ₁ is the weighting coefficient of the regularized term, w _k2 is the weighting coefficient of the regularized term of the strain coefficient k ₂ , and w _k 3 is the weighting coefficient of the regularized term of the strain coefficient k ₃ .

By using the above equation (8), not only the error is small, but also calibration can be performed in consideration of internal parameters such as the size of the focal length, the position of the principal point coordinates, and the size of the strain coefficient. In addition, by weighting each internal parameter (here, the size of the focal length, the position of the principal point coordinates, the size of the strain coefficient), the size of the focal length, the position of the principal point coordinates, and the size of the strain coefficient are weighted. Of these, which parameter is important can be set as needed, which can introduce the knowledge of designers and experts. Although the square index called the L2 norm is used in the above equation (8), it is also effective to use the absolute value index called the L1 norm.

Next, when all the above-mentioned internal and external parameters have been calibrated (calibrated), X and Y when the measurement coordinates u are obtained are obtained. This may be solved by solving the above equation (6) in the form of X and Y, but since the above equation (6) includes both X and Y, it cannot be solved as it is. Therefore, at the detection point of the L-shaped marker 20, the fact that either of the true value coordinates on the two-dimensional plane 11 of X and Y is 0 is utilized, and the parameters obtained in the direction in which the true value coordinates become 0 are used. The calculated value is also assumed to be 0 and solved. As a result, the above equation (6) became the following equations (9) and (10), and the values of X and Y could be obtained analytically. Here, x'and x'are the values defined by the above equations (3) to (5).

Next, a method of obtaining external parameters for each shooting will be described. Assuming that the transformation matrix representing translation and rotation is the following equation (11), the transformation matrix can be expressed by the following equation (12) based on the above equation (1).

When this is expanded and organized, the following equation (13) is obtained.

Here, the transformation matrix can be solved by constructing three or more simultaneous equations by utilizing the property that the scale can reduce the order by one. Actually, the coordinates of the L-shaped marker 20 are three or more points, but in this case, the equation and the number of unknowns do not match. Therefore, the least squares method is used. The squared error is E, the error vector generated at each measurement point is e (bold body), the number of coordinates of the marker is n, and the squared error E is expressed by the following equation (15) using the matrix expressed by the following equation (14). be able to. Note that " ^T " is a symbol representing a transposed matrix.

The vector for minimizing the square error E is the ^eigenvector corresponding to the minimum eigenvalue of BTB (bold body). Therefore, singular value decomposition is used to obtain the eigenvector to be the solution. This is given by the following equation (16). Here, U (bold form) is a left singular matrix, V (bold form) is a right singular matrix, Σ (bold form) is a singular value matrix, and I (bold form) is an identity matrix. As a result, the ^BTB (bold body) can be expressed by the following equation (17).

From this result, it can be seen that the eigenvector is the same as the right singular vector of the right singular matrix V (bold), and the eigenvalue is the same as the square of the singular value. From this, the transformation matrix can be obtained by using the singular value decomposition.

To make it an actual external parameter, the scale is indefinite and t ₂ > 0, so normalization is performed at t ₂ , and due to the nature of the rotation matrix, (cos θ) ² + (sin θ) ² = 1 is used for rotation. And find the translation parameters.

As described above, even with the line sensor camera, if the measurement coordinates u, the true value coordinates X and Y, the focal length f, and the principal point coordinates c are known, the solution can be obtained by the linear solution method. Actually, since the focal length f and the principal point coordinates c are not known at first, the initial external parameters are obtained by inputting appropriate values. Finally, the final internal and external parameters can be obtained by solving the equation (8) by the Levenberg-Marquart method with this initial external parameter as the initial value.

Next, the calibration device and method of the line sensor camera according to the present invention for performing the above calculation will be described below with reference to FIGS. 1 and 2.

[Example 1]
The device of this embodiment is a calibration device of the line sensor camera 10, and as shown in FIG. 1, has an L-shaped marker 20 and a processing system 30, and the processing system 30 has a storage unit 31 and an image input. It has a unit 32, a measurement coordinate calculation unit 33, an external parameter calculation unit 34, and a non-linear minimum square unit 35.

In the line sensor camera 10, an image pickup device such as a CCD (Charge-Coupled Device) is arranged in a one-dimensional linear shape, and an image of an object to be imaged is captured in the one-dimensional linear shape.

The L-shaped marker 20 is a three-dimensional marker having an L-shaped shape, and is formed of a rigid body that is bent at 90 ° at the center 21 and has a black-and-white band 23 on the bent inner surface 22. The black-and-white band 23 is arranged symmetrically about the center 21 and alternately arranged in black and white along the longitudinal direction of the inner surface 22, and the black-and-white width of the black-and-white band 23 is known. That is, a plurality of detection points by the black-and-white band 23 are known in the two-dimensional plane coordinates on the two-dimensional plane 11. When a plane marker is used as in the method of Non-Patent Document 1 described above, the focal length becomes unstable, but in this embodiment, the L-shaped marker 20 is used for calibration, and the focal length is accurately set. It can be calculated.

Although an L-shaped three-dimensional marker is used in this embodiment, it is possible to give depth to a plurality of detection points, and the true X and Y on the two-dimensional plane 11 of all the detection points are true. If either of the value coordinates can be set to 0, the marker is not limited to the L-shaped solid marker. For example, in a rectangular parallelepiped or a right-angled triangular prism, a black-and-white band 23 as shown in FIG. 1 may be provided on the outer surfaces of two sides sandwiching the right angle.

In the processing system 30, in the storage unit 31, as will be described later, image data from the line sensor camera 10, measurement coordinate data (measurement coordinates u) on the image of the black and white band 23 of the L-shaped marker 20 in each shooting, and a lens. Initial values, true value coordinates X and Y of the black and white band 23 of the L-shaped marker 20, internal parameters of the line sensor camera 10 (focal length f, principal point coordinates c, distortion coefficient k ₁ to k ₃ ), and lines in each shooting. The external parameters (rotation θ, translation t ₁ , t ₂ ) of the sensor camera 10 are stored. As the storage unit 31, a storage device such as a RAM (Random Access memory), an HDD (Hard Disk Drive), or an SSD (Solid State Drive) can be used.

Further, in the image input unit 32, the image data of the L-shaped marker 20 acquired by the line sensor camera 10 is input from the line sensor camera 10, and the input image data is stored in the storage unit 31.

Further, the measurement coordinate calculation unit 33 detects the black-and-white band 23 (detection point) of the L-shaped marker 20 from the image data captured by the line sensor camera 10, and the black-and-white band 23 (detection point) of the L-shaped marker 20 in each shooting. ), The measurement coordinates u (one-dimensional image coordinates) on the image are obtained and stored in the storage unit 31 as the measurement coordinate data. The coordinates on the image of the black and white band 23 (detection point) of the L-shaped marker 20 are detected by performing image processing such as binarization processing and edge detection.

Further, in the external parameter calculation unit 34, the measurement coordinates u in each shooting calculated by the measurement coordinate calculation unit 33, the initial lens value, and the true value coordinates X and Y of the black and white band 23 (detection point) of the L-shaped marker 20 are used. Using the above-mentioned equations (11) to (17), the external parameters of the line sensor camera 10 in each shooting are obtained and stored in the storage unit 31.

Further, in the non-linear minimum squared unit 35, the measured coordinates u in each shooting calculated by the measured coordinate calculation unit 33, the initial value of the lens, the true value coordinates X, Y of the black and white band 23 (detection point) of the L-shaped marker 20, and the outside. Using the external parameters of the line sensor camera 10 for each shooting obtained by the parameter calculation unit 34, the above-mentioned equation (8) is used for the final internal parameters of the line sensor camera 10 and the external parameters of the line sensor camera 10 for each shooting. ) Is calculated by the Levenberg-Markart method and stored in the storage unit 31.

Next, the calibration method of the line sensor camera according to the present invention will be described with reference to FIG. 2 together with FIG.

(Step S1)
In the image input process, at least one of various positions and postures (rotation angle θ around the w-axis and positions t1 and t2 parallel to the u-axis and v-axis is different from the L-shaped marker 20 whose position is fixed. In addition, the line sensor camera 10 is installed so that the entire three-dimensional marker can be photographed (position and posture), images at each position and posture are captured, and stored in the storage unit 31 (image input unit 32). An example of the captured image is shown in FIGS. 3A and 3B. Since the position of the L-shaped marker 20 is fixed, the installation error is not included.

(Step S2)
In the measurement coordinate calculation step, the black-and-white band 23 (detection point) of the L-shaped marker 20 is detected for each captured image, and the measurement coordinates u (detection point) of the black-and-white band 23 (detection point) of the L-shaped marker 20 are performed. (One-dimensional image coordinates) is calculated and stored as measurement coordinate data in the storage unit 31 (measurement coordinate calculation unit 33).

(Step S3)
In the external parameter calculation process, the focal length f is the manufacturer's published value, the principal point coordinate c is half the total number of pixels, and the distortion coefficients k ₁ to k ₃ are set as the lens initial values that are the initial internal parameters of the line sensor camera 10. All are set to 0, and the initial external parameters are calculated by the linear solution method using the above-mentioned equations (11) to (17) for each captured image and stored in the storage unit 31 (external parameter calculation unit 34).

(Step S4)
In the nonlinear least squares step, the above-mentioned initial internal parameters and the initial external parameters calculated in step S3 are used as initial values, and the above-mentioned equation (8) is used for each photographed image, and the final result is obtained by the Levenberg-Marquart method. Internal and external parameters are calculated and stored in the storage unit 31 (nonlinear least squares unit 35).

In this embodiment, one line sensor camera 10 and one L-shaped marker 20 are used, and the focal length f, the principal point coordinates c, and the distortion coefficients k ₁ to k ₃ of the line sensor camera 10 are internally determined by the above procedure. In addition to obtaining the parameters, it is possible to obtain external parameters such as the rotation θ of the L-shaped marker 20 and the parallel movements t ₁ and t ₂ for each shooting.

As described above, in this embodiment, by using a nonlinear solution method that minimizes the evaluation function that considers not only the error function but also the value of the internal parameter, the internal parameter including the distortion of the lens and the external parameter are stable. Moreover, it is possible to calculate at the same time. In addition, by introducing a weighting coefficient when considering the value of the internal parameter, it is possible to introduce expert knowledge such as which internal parameter is important, and it is possible to perform calibration more appropriately. Become.

10 Line sensor camera 20 L-shaped marker 23 Black and white band 30 Processing system 31 Storage unit 32 Image input unit 33 Measurement coordinate calculation unit 34 External parameter calculation unit 35 Non-linear least squares unit

Claims (8)

A three-dimensional marker having a plurality of detection points whose two-dimensional plane coordinates on the two-dimensional plane which is the imaging range of the line sensor camera are known, and
It has a processing unit for calculating internal parameters and external parameters for calibration of the line sensor camera based on a plurality of images of the three-dimensional marker captured by the line sensor camera.
The processing unit
An image input unit in which the images of the three-dimensional markers having different positions and postures are input, and
A measurement coordinate calculation unit that calculates the one-dimensional image coordinates of the detection point of the three-dimensional marker on the image for each image, and the measurement coordinate calculation unit.
For the transformation matrix obtained based on the mathematical model of the line sensor camera that converts the two-dimensional plane coordinates to the one-dimensional image coordinates, input known initial values as the initial internal parameters in the transformation matrix, and use a linear solution method. An external parameter calculation unit that calculates initial external parameters from the transformation matrix for each image,
For the evaluation function obtained by adding the value considering the internal parameters to the error function considering the lens distortion obtained based on the mathematical model, the initial internal parameters and the initial external parameters are input to the evaluation function. Then, the internal parameter and the external parameter, which minimizes the evaluation function obtained by adding the value considering the internal parameter to the sum of the error functions for the total number of the detection points and the total number of the images, were repeatedly calculated. A line sensor camera calibration device characterized by having a non-linear minimum squared portion calculated by a non-linear solution method. In the calibration device for the line sensor camera according to claim 1,
The evaluation function is a line sensor characterized in that the magnitude of the focal length of the lens, the position of the principal point coordinates of the lens, and the magnitude of the distortion coefficient of the lens are each weighted and added to the error function. Camera calibration device. In the calibration device for the line sensor camera according to claim 1 or 2.
The three-dimensional marker has an L-shaped shape, and is a calibration device for a line sensor camera, characterized in that the plurality of detection points are arranged on an inner surface bent into an L-shape. In the calibration device for the line sensor camera according to any one of claims 1 to 3.
The mathematical model is a calibration device for a line sensor camera, which is characterized by using a pinhole camera model. Calibration of the line sensor camera based on a plurality of images taken by the line sensor camera of a three-dimensional marker having a plurality of detection points whose two-dimensional plane coordinates are known on the two-dimensional plane which is the imaging range of the line sensor camera. A line sensor camera calibration method that calculates internal and external parameters for the camera.
An image input step in which the images of the three-dimensional markers having different positions and postures are input, and
A measurement coordinate calculation step of calculating the one-dimensional image coordinates of the detection point of the three-dimensional marker on the image for each image, and
For the transformation matrix obtained based on the mathematical model of the line sensor camera that converts the two-dimensional plane coordinates to the one-dimensional image coordinates, input known initial values as the initial internal parameters in the transformation matrix, and use a linear solution method. An external parameter calculation step of calculating the initial external parameters from the transformation matrix for each image, and
For the evaluation function obtained by adding the value considering the internal parameters to the error function considering the lens distortion obtained based on the mathematical model, the initial internal parameters and the initial external parameters are input to the evaluation function. Then, the internal parameter and the external parameter, which minimizes the evaluation function obtained by adding the value considering the internal parameter to the sum of the error functions for the total number of the detection points and the total number of the images, were repeatedly calculated. A line sensor camera calibration method comprising a non-linear minimum square step calculated by a non-linear solution method. In the calibration method of the line sensor camera according to claim 5,
As the evaluation function, a line sensor characterized in that the size of the focal length of the lens, the position of the principal point coordinates of the lens, and the size of the distortion coefficient of the lens are each weighted and added to the error function. How to calibrate the camera. In the calibration method of the line sensor camera according to claim 5 or 6.
A method for calibrating a line sensor camera, which comprises using as the three-dimensional marker an L-shaped marker in which the plurality of detection points are arranged on an inner surface bent into an L-shape. The method for calibrating a line sensor camera according to any one of claims 5 to 7.
A method for calibrating a line sensor camera, which comprises using a pinhole camera model as the mathematical model.

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