JP7517170B2 - Calibration device and calibration method for line sensor camera - Google Patents

Description

The present invention relates to a calibration device and calibration method for a line sensor camera.

Non-Patent Document 1, an example of conventional technology, discloses a camera calibration method in which an area camera captures images of a planar marker at various positions and orientations to determine external parameters and internal camera parameters for each image.

Patent Document 1, an example of conventional technology, discloses a calibration device and calibration method for a line sensor camera that uses calibration markers to calibrate the internal parameters of the line sensor camera.

Note that Non-Patent Document 2, an example of prior art, is a document that explains lens distortion, which will be described later.

JP 2016-218815 A

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

However, the above conventional technology uses a pinhole camera model, making it difficult to apply to line sensor cameras equipped with lenses that have large distortions (e.g., fisheye lenses).

The present invention has been made in consideration of the above, and aims to enable the calibration of a line sensor camera equipped with a lens with large distortion.

One aspect of the present invention that solves the above-mentioned problems and achieves the object is a calibration device for a line sensor camera that calculates internal and external parameters for calibration of the line sensor camera based on a plurality of images captured by the line sensor camera through a lens of a three-dimensional marker having a plurality of detection points whose two-dimensional coordinates on a two-dimensional plane that is the imaging range of the line sensor camera are known, the calibration device comprising: a lens model selection unit that selects one of a plurality of lens models according to the lens; an image input unit to which the images of the three-dimensional markers, each having a different position and orientation, are input; a measurement coordinate calculation unit that calculates one-dimensional image coordinates on the image of the detection points of the three-dimensional marker for each image; and a line sensor camera that converts the two-dimensional coordinates into the one-dimensional image coordinates. The calibration device for a line sensor camera includes an external parameter calculation unit that inputs known initial values as initial internal parameters in a transformation matrix obtained based on a mathematical model, and calculates initial external parameters from the transformation matrix for each image using a linear solution; and a nonlinear least squares calculation unit that inputs the initial internal parameters and the initial external parameters into an error function that takes lens distortion into account and calculates the internal parameters and the external parameters that minimize the sum of the error function for all the detection points and all the images using a nonlinear solution using iterative calculation, and the nonlinear least squares calculation unit includes a distortion correction calculation unit that corrects the lens distortion.

In the calibration device for a line sensor camera having the above configuration, it is preferable that the three-dimensional marker is L-shaped and the multiple detection points are arranged on the inner surface bent into the L shape.

In the calibration device for a line sensor camera having the above configuration, the mathematical model may use a fisheye lens model.

Alternatively, one aspect of the present invention for solving the above-mentioned problems and achieving the object is a calibration method for a line sensor camera, which calculates internal and external parameters for calibration of the line sensor camera based on a plurality of images captured by the line sensor camera through a lens of a three-dimensional marker having a plurality of detection points whose two-dimensional coordinates on a two-dimensional plane that is the imaging range of the line sensor camera are known, and includes a lens model selection step of selecting one of a plurality of lens models according to the lens, an image input step of inputting the images of the three-dimensional markers each having a different position and orientation, a measurement coordinate calculation step of calculating one-dimensional image coordinates on the image of the detection points of the three-dimensional marker for each image, and a measurement coordinate calculation step of converting the two-dimensional coordinates into the one-dimensional image coordinates. This is a calibration method for a line sensor camera, characterized by comprising: an external parameter calculation step of inputting known initial values as initial internal parameters in a transformation matrix calculated based on a mathematical model of the line sensor camera, and calculating initial external parameters from the transformation matrix for each image using a linear solution; a distortion correction calculation processing step of correcting the lens distortion; and a nonlinear least squares calculation step of inputting the initial internal parameters and the initial external parameters into an error function that takes into account the lens distortion calculated based on the mathematical model, and calculating the internal parameters and the external parameters that minimize the sum of the error function for the total number of detection points and the total number of images using a nonlinear solution using iterative calculation.

In the calibration method for a line sensor camera having the above configuration, it is preferable that the three-dimensional marker is L-shaped and the multiple detection points are arranged on the inner surface of the L-shape.

In the calibration method for a line sensor camera configured as above, a fisheye lens model can be used as the mathematical model.

The present invention makes it possible to calibrate a line sensor camera equipped with a lens that has large distortion.

FIG. 1 is a diagram showing a line sensor camera and an L-shaped marker according to an embodiment. FIG. 2 is a diagram showing a fisheye lens distortion model. FIG. 3 is a diagram showing the configuration of a calibration device for a line sensor camera according to an embodiment. FIG. 4 is a flowchart showing a calibration method for a line sensor camera according to this embodiment.

Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.
However, the present invention should not be construed as being limited to the following embodiments.

<Embodiment>
When performing measurements using a camera, it is essential to determine the camera parameters in advance, such as the focal length, principal point coordinates, and distortion coefficients. This process is called camera calibration.
In the following description, camera calibration will simply be called calibration.

In this embodiment, as in the method described in Non-Patent Document 1, multiple photographing of a marker and calculation of camera parameters by a non-linear optimization method are introduced into the calibration of the line sensor camera.
However, since Non-Patent Document 1 is based on the assumption that an area camera is used, this method cannot be directly introduced into the calibration of a line sensor camera.
For example, with a line sensor camera, the number of dimensions is small, so it is not possible to utilize the orthogonality of the rotation matrix. In addition, since a line sensor camera cannot capture the planar marker used for calibration in a chessboard shape, there is a problem that the focal length and external parameter calculation becomes unstable.
Therefore, in this embodiment, a three-dimensional marker is used for calibration.

In this embodiment, a pinhole camera model and a fisheye lens model are used as the camera model.
However, in this embodiment, since a line sensor camera is used, the two-dimensional plane of the imaging range becomes a one-dimensional image.
Then, by placing a stereoscopic marker on a two-dimensional plane in the imaging range, the rotation can be determined along one axis and the translation can be determined along two dimensions for the external parameters to be determined.

In addition, in the formulas in the following description, non-bold alphabets are scalars, bold lowercase alphabets are vectors, and bold uppercase alphabets are matrices.
Since boldface cannot be used in the document, normal formatting is used, with "(boldface)" added immediately after the relevant alphabet.

FIG. 1 is a diagram showing a line sensor camera 10 and an L-shaped marker 20 according to this embodiment.
In FIG. 1, since the line sensor camera 10 captures only one line, the imaging range is a two-dimensional plane 11 in a 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 expressed by the X axis and the Y axis.
The camera coordinate system (one-dimensional image coordinate system) of the line sensor camera 10 is expressed by a u axis that is perpendicular to an axis w in the optical axis direction of the line sensor camera 10 and parallel to a two-dimensional plane 11 of the imaging range.
If the coordinate of the image coordinate system is defined as u and the coordinate of the camera coordinate system is defined as (x, y), the conversion equation from the camera coordinate system to the image coordinate system is expressed by the following equation (1).

where s is the scaling factor, f is the focal length, and c is the principal point coordinate.
When the coordinates of the object coordinate system are defined as (X, Y), the conversion equation from the object coordinate system to the camera coordinate system is expressed by the following equation (2).

Also, the rotation matrix between the object coordinate system and the camera coordinate system is R (bold) (the rotation axis is 1 and its angle is θ), and the translation vector is t (bold) (a two-dimensional vector whose elements are t ₁ and t ₂ ).
Here, the mathematical model of the pinhole model in the configuration shown in FIG.

Note that u is the position in the camera coordinate system that is actually observed (measurement coordinates in pixel coordinates), and X, Y are the positions in the object coordinate system (true coordinates of the L-shaped marker 20 in the real space (two-dimensional plane 11)).

The above formula (4) 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 formula (4), 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 above equation (2), the distortion can be expressed as in the following equations (5), (6), and (7).
Note that k ₁ to k ₃ are radial distortion coefficients.
Regarding lens distortion, reference is made to Non-Patent Document 2 (especially page 51).

Here, since x′ cannot be substituted directly into equation (7), equation (8) below is substituted into equation (6) above.
Moreover, by substituting the formulas (2), (4), and (5) into the formula (6), the following formula (9) is obtained.

When calibrating this camera model, the error is minimized on the unit focal length plane, and the intrinsic and extrinsic parameters are found using the Levenberg-Marquardt algorithm so that the following equation (10) is minimized.

In the above formula (10), M is the number of times an image is captured, and N is the number of feature points (the number of detected points of the black and white bands 23) obtained in each capture.
The above formula (10) is the sum of the error function based on the above formula (9) for the total number M of captured images and the total number N of detected points.

Here, when calibration was actually performed using a 3D marker, it was found that the use of the 3D marker alone could not completely prevent the solution from becoming unstable.
Here, "unstable" refers to a significant deviation from common knowledge known to experts in camera _calibration , such as "the focal length should not change significantly from the initial value set for the lens" and "the lens distortion coefficients _k1 , _{k2 ,} and _k3 do not become extremely large values, and generally the lens distortion coefficients _k1 , k2, and _k3 often satisfy k1 > _k2 > _k3 ."

That is, if the parameters that minimize the above equation (10) are found by optimization processing, the parameters may end up being unrealistic values.
Therefore, in this embodiment, the intrinsic parameters and extrinsic parameters are found by the Levenberg-Marquardt method so as to minimize the following equation (11), which is an evaluation function that incorporates expert knowledge such as "the focal length f does not vary greatly from the lens' specified value f0", "the principal point coordinate c is near the image center c0 (although this depends on the camera)", "the lens distortion coefficients _k1 , _k2 , and _{k3 do} not become extremely large numbers", and "the magnitudes of the lens distortion coefficients are often _k1 > _k2 >k3", into the error function based on the above equation (9).

In the above equation (11), _wf is a weighting coefficient of the regularization term for the focal length, _wc is a weighting coefficient of the regularization term for the principal point coordinates, _c0 is a default value of the principal point coordinates, _wk1 is a weighting coefficient of the regularization term for the distortion coefficient _k1 , _wk2 is a weighting coefficient of the regularization term for the distortion coefficient _k2 , and _wk3 is a weighting coefficient of the regularization term for the distortion coefficient _k3 .

By using the above formula (11), not only can the error be reduced, but calibration can also be performed taking into account internal parameters such as the focal length, the position of the principal point coordinates, and the magnitude of the distortion coefficient.
Furthermore, by weighting each internal parameter (here, the focal length, the position of the principal point coordinates, and the magnitude of the distortion coefficient), it is possible to set, as necessary, which parameter among the focal length, the position of the principal point coordinates, and the magnitude of the distortion coefficient is to be given importance, thereby making it possible to incorporate the knowledge of designers and experts.
In addition, in the above formula (11), a squared index called L2 norm is used, but it is also effective to use an absolute value index called L1 norm.

<Fisheye lens model explanation>
FIG. 2 is a diagram showing a fisheye lens distortion model.
The fisheye lens distortion model is different from the pinhole model and is expressed by the following equation (12) using the incidence angle φ of the camera optical axis.
In this case, a model is used in which a distorted image is created from an undistorted image, but it is also possible to use a model in which an undistorted image is created from a distorted image.

The incidence angle φ of the camera optical axis is expressed by the following formula in relation to the coordinate position x' in the normalized coordinate system.

And in the case of a fisheye lens, the following equation (14) can be obtained from the above equations (8) and (12).

The desired internal and external parameters are therefore found by minimizing the error in equation (15) below.

<Calculation of X and Y>
Next, when the above-mentioned internal parameters and external parameters have all been calibrated, X and Y when the measurement coordinate u is obtained are obtained.
This can be achieved by solving the above equation (8) for X and Y. However, since the above equation (8) contains both X and Y, it cannot be solved as it is.
Therefore, at the detection point of the L-shaped marker 20, one of the true coordinates on the two-dimensional plane 11 of X and Y, i.e., one of the true values of X and Y, is 0. By assuming that the value calculated from the parameters obtained in the direction where the true coordinate is 0 is also 0, the following equation (16) is obtained.
Here, x' and x'd are the values defined in equations (5), (6), and (7) above.

Next, a method for determining the external parameters for each shot will be described.
If the transformation matrix representing translation and rotation is expressed by the following equation (17), the transformation matrix can be expressed by the following equation (18) based on the above equation (4).

Expanding and rearranging this gives the following equation (19) for the pinhole model.

<In the case of a fisheye lens>
In the case of a fisheye lens, the following equation (20) should be solved for X.

However, since the above equation (20) contains both X and Y, it cannot be solved as it is.
Therefore, in the case of the L-shaped marker, by taking advantage of the fact that either the true value of X or Y is 0, and assuming that the value calculated using the obtained parameters in the direction where the true value is 0 is also 0, the above equation (16) is obtained.

Here, the normalized image coordinate x' can be found by solving the above equation (5) for φ and substituting it into the following equation (21).

As mentioned above, the values of X and Y can be found analytically in both the pinhole model and the fisheye lens.

<Initial external parameters for fisheye lenses>
Here, a method for determining initial external parameters for each image taken with a fisheye lens will be described.
Normally, in a pinhole model, distortion is very small, so the external parameters are found by ignoring distortion, that is, by assuming a model without distortion.
However, fisheye lenses produce significant distortion that cannot be ignored.
For this reason, the initial external parameters are calculated by using any of the distortion models configured with known values such as those in the following equation (22).

For example, when using an orthogonal projection model, substituting the orthogonal projection equation (22) above into equation (8) above gives the following equation (23).

Using the above formulas (23), (20), and (21), we obtain the following formula (24).

The initial external parameters can be obtained by singular value decomposition of the above equation.

Here, by utilizing the property that the scale can reduce the order by one, the transformation matrix can be solved by formulating three or more simultaneous equations.
In reality, the L-shaped marker 20 has three or more coordinates, but in this case, the equations and the number of unknowns do not match, so the least squares method is used.
If the squared error is E and the error vector occurring at each measurement point is e (in bold), the following equation (25) is obtained.
It should be noted that "T" is the symbol representing a transposed matrix.

The vector for minimizing the squared error E is the eigenvector corresponding to the smallest eigenvalue of B ^T B (in bold).
Therefore, when singular value decomposition is used to find the eigenvector that is the solution, the two upper expressions of the following expression (26) are obtained.
where U (bold) is the left singular matrix, V (bold) is the right singular matrix, Σ (bold) is the singular value matrix, and I (bold) is the identity matrix.
As a result, B ^T B (bold) can be expressed by the following formula (26).

From this result, it can be seen that the eigenvectors are the same as the right singular vectors of the right singular matrix V (in bold), and the eigenvalues are the same as the squares of the singular values.
From this, the transformation matrix can be obtained by using singular value decomposition.

To obtain actual external parameters, normalization is performed at t ₂ because the scale is indefinite and t ₂ >0, and the rotation and translation parameters are obtained using (cos θ) ² +(sin θ) ² =1 due to the nature of the rotation matrix.

In this way, even in the case of a line sensor camera, if the measurement coordinate u, true coordinates X, Y, focal length f, and principal point coordinate c are obtained, a solution can be found by a linear solution method.
In reality, the focal length f and the principal point coordinate c are not known at first, so the initial external parameters are obtained by inputting appropriate values.
Then, finally, by using these initial external parameters as initial values and solving the above equation (11) by the Levenberg-Marquardt method, the final internal parameters and external parameters can be obtained.

Next, the calibration device and calibration method for a line sensor camera according to the present invention, which performs the above-mentioned calculations, will be described below with reference to Figures 4 and 3.

FIG. 3 is a diagram showing the configuration of a calibration device 30 for a line sensor camera according to this embodiment.
The calibration device 30 shown in FIG. 3 is a calibration device for the line sensor camera 10, and includes a memory unit 31, an image input unit 32, a measurement coordinate calculation unit 33, an external parameter calculation unit 34, a nonlinear least squares calculation unit 35, and a lens model selection unit 36.
The nonlinear least squares calculation unit 35 includes a distortion correction calculation unit 350 .

The line sensor camera 10 is a camera in which imaging elements such as CCDs (Charge-Coupled Devices) are arranged in a one-dimensional line, and captures an image of an object in a one-dimensional line.

The L-shaped marker 20 is a three-dimensional marker in an L-shape, which is bent at 90° at its center 21 and is a rigid body having a black and white band 23 on its inner surface 22 of the bend.
The black and white bands 23 are arranged symmetrically around the center 21 and are arranged so that they alternate between black and white along the longitudinal direction of the inner surface 22, and the width of the black and white of the black and white bands 23 is known, in other words, the multiple detection points of the black and white bands 23 are known in two-dimensional plane coordinates on the two-dimensional plane 11.
When using a planar marker as in the method of Non-Patent Document 1 mentioned above, the focal length becomes unstable. However, in this embodiment, an L-shaped marker 20 is used for calibration, making it possible to accurately calculate the focal length.

In this embodiment, an L-shaped three-dimensional marker is used as the calibration marker, but as long as it is possible to give depth to multiple detection points and it is possible to ensure that either the X or Y true coordinate of all detection points on the two-dimensional plane 11 is 0, the calibration marker is not limited to the L-shaped three-dimensional marker.
For example, in the case of a rectangular parallelepiped or a right-angled triangular prism, the black and white bands 23 shown in FIG. 1 may be provided on the outer surfaces of two sides that sandwich the right angle.

As described below, the memory unit 31 stores the selected lens model, image data from the line sensor camera 10, measurement coordinate data (measurement coordinate u) on the image of the black and white band 23 of the L-shaped marker 20 in each shot, the lens initial value, the true coordinates X, 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 coordinate c, and distortion coefficients _k1 to _k3 ), and external parameters of the line sensor camera 10 in each shot (rotation θ, translation _t1 , _t2 ).
It should be noted that the distortion coefficients differ between the pinhole camera model and the fisheye lens model.
Examples of the storage unit 31 include storage devices such as a random access memory (RAM), a hard disk drive (HDD), and a solid state drive (SSD).

The lens model selection unit 36 selects one of the multiple lens models in the above formula (22) and stores the selected lens model in the storage unit 31.

The image input unit 32 receives image data of the L-shaped marker 20 acquired by the line sensor camera 10 and stores the input image data in the memory unit 31.

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, calculates the measurement coordinate u (one-dimensional image coordinate) on the image of the black and white band 23 (detection point) of the L-shaped marker 20 for each capture, and stores it in the memory unit 31 as measurement coordinate data.
The coordinates of the black and white band 23 (detection point) of the L-shaped marker 20 on the image are detected by image processing such as binarization or edge detection.

The external parameter calculation unit 34 uses the above-mentioned formula to calculate the external parameters of the line sensor camera 10 for each shot from the measurement coordinate u, lens initial value, and true coordinates X, Y of the black and white band 23 (detection point) of the L-shaped marker 20 for each shot calculated by the measurement coordinate calculation unit 33, and stores the parameters in the memory unit 31.

The nonlinear least squares calculation unit 35 uses the measurement coordinate u for each image captured calculated by the measurement coordinate calculation unit 33, the lens initial value, the true coordinates X, Y of the black and white band 23 (detection point) of the L-shaped marker 20, and the external parameters of the line sensor camera 10 for each image captured calculated by the external parameter calculation unit 34 to calculate the final internal parameters of the line sensor camera 10 and the external parameters of the line sensor camera 10 for each image captured by the Levenberg-Marquardt method using the above-mentioned equation (11).The nonlinear least squares calculation unit 35 then stores the results in the memory unit 31.
Incidentally, since distortion cannot be ignored in a fisheye lens as described above, the distortion correction calculation section 350 of the nonlinear least squares calculation section 35 performs calculations to correct the distortion.

Figure 4 is a flowchart showing the calibration method for the line sensor camera according to this embodiment.

(Step S1)
In the lens model selection step, the lens model selection unit 36 selects one of the multiple lens models of the above formula (22), and the selected lens model is stored in the storage unit 31.

(Step S2)
In the image input process, the image input unit 32 sets the line sensor camera 10 in various positions and orientations (positions and orientations in which at least one of the rotation angle θ around the w axis and the positions _t1 , _t2 in directions parallel to the u axis and v axis are different, and which allow the entire three-dimensional marker to be captured) relative to the L-shaped marker 20, which has a fixed position, and images are captured at each position and orientation and stored in the memory unit 31.
The position of the L-shaped marker 20 is fixed, so that installation error is not included.

(Step S3)
In the measurement coordinate calculation process, the measurement coordinate calculation unit 33 performs a detection process of the black and white band 23 (detection point) of the L-shaped marker 20 for each captured image, calculates the measurement coordinate u (one-dimensional image coordinate) on the image of the black and white band 23 (detection point) of the L-shaped marker 20, and stores it in the memory unit 31 as measurement coordinate data.

(Step S4)
In the external parameter calculation step, the external parameter calculation unit 34 sets the focal length f to the manufacturer's published value, the principal point coordinate c to half the total number of pixels, and the distortion coefficients _k1 to _k3 to all 0 as lens initial values that become the initial internal parameters of the line sensor camera 10, and calculates initial external parameters for each captured image by linear solution using the above-mentioned equations, and stores them in the memory unit 31.
It should be noted that the distortion coefficients differ between the pinhole camera model and the fisheye lens model.

(Step S5)
In the distortion correction calculation process, since distortion cannot be ignored in a fisheye lens as described above, the distortion correction calculation unit 350 performs calculations to correct lens distortion (distortion correction calculation unit 350).

(Step S6)
In the nonlinear least squares calculation step, the nonlinear least squares calculation unit 35 uses the above-mentioned initial internal parameters and the initial extrinsic parameters calculated in step S4 as initial values to calculate final internal parameters and extrinsic parameters for each captured image using the above-mentioned equation (11) by the Levenberg-Marquardt method, and stores the final internal parameters and extrinsic parameters in the memory unit 31.

In this embodiment, one line sensor camera 10 and one L-shaped marker 20 are used, and by following the above procedure, it is possible to determine internal parameters of the line sensor camera 10, such as the focal length f, the principal point coordinate c, and the distortion coefficients _k1 to _k3 , as well as external parameters of the L-shaped marker 20, such as the rotation θ and the translations _t1 and _t2 , for each shot.
It should be noted that the distortion coefficients differ between the pinhole camera model and the fisheye lens model.

As described above, according to this embodiment, it is possible to calibrate a line sensor camera equipped with a lens that has a large distortion, such as a fisheye lens.

The present invention is not limited to the above-described embodiment, but also includes various modifications in which components are added, deleted, or converted from the above-described configuration.

REFERENCE SIGNS LIST 10 Line sensor camera 11 Two-dimensional plane 20 L-shaped marker 21 Center 22 Inner surface 23 Black and white band 30 Calibration device 31 Storage unit 32 Image input unit 33 Measurement coordinate calculation unit 34 External parameter calculation unit 35 Nonlinear least squares calculation unit 36 Lens model selection unit 350 Distortion correction calculation unit

Claims (6)

1. A calibration device for a line sensor camera, the device calculating internal parameters and external parameters for calibration of the line sensor camera based on a plurality of images captured by the line sensor camera through a lens of a three-dimensional marker having a plurality of detection points whose two-dimensional coordinates on a two-dimensional plane that is an imaging range of the line sensor camera are known, the device comprising:
a lens model selection unit that selects one of a plurality of lens models according to the lens;
an image input unit to which the images of the three-dimensional markers each having a different position and orientation are input;
a measurement coordinate calculation unit that calculates one-dimensional image coordinates on the image of the detection point of the stereoscopic marker for each of the images;
an external parameter calculation unit that inputs known initial values as initial internal parameters in a transformation matrix obtained based on a mathematical model of the line sensor camera that transforms the two-dimensional plane coordinates into the one-dimensional image coordinates, and calculates initial external parameters from the transformation matrix for each of the images by a linear solution;
a nonlinear least squares calculation unit that inputs the initial internal parameters and the initial external parameters into an error function that takes into account the lens distortion obtained based on the mathematical model, and calculates the internal parameters and the external parameters that minimize a sum of the error function for all the detection points and all the images by a nonlinear solution using iterative calculation,
The calibration device for a line sensor camera, wherein the nonlinear least squares calculation unit has a distortion correction calculation unit that corrects the distortion of the lens. 2. The line sensor camera calibration device according to claim 1,
A calibration device for a line sensor camera, wherein the three-dimensional marker is L-shaped, and the plurality of detection points are arranged on the inner surface of the L-shape. 3. The calibration device for a line sensor camera according to claim 1,
13. A calibration device for a line sensor camera, wherein the mathematical model uses a fisheye lens model. A method for calibrating a line sensor camera, comprising the steps of: calculating internal and external parameters for calibration of the line sensor camera based on a plurality of images captured by the line sensor camera through a lens of a three-dimensional marker having a plurality of detection points whose two-dimensional coordinates on a two-dimensional plane that is an imaging range of the line sensor camera, the method comprising:
a lens model selection step of selecting one of a plurality of lens models according to the lens;
an image input step of inputting images of the three-dimensional markers each having a different position and orientation;
a measurement coordinate calculation step of calculating one-dimensional image coordinates on the image of the detection point of the stereoscopic marker for each of the images;
an external parameter calculation step of inputting known initial values as initial internal parameters in a transformation matrix obtained based on a mathematical model of the line sensor camera that transforms the two-dimensional plane coordinates into the one-dimensional image coordinates, and calculating initial external parameters from the transformation matrix for each of the images by a linear solution;
a distortion correction calculation processing step for correcting the distortion of the lens;
and a nonlinear least squares calculation step of inputting the initial internal parameters and the initial external parameters into the error function, for an error function taking into account lens distortion obtained based on the mathematical model, and calculating, by a nonlinear solution using iterative calculation, the internal parameters and the external parameters that minimize the sum of the error function for all of the detection points and all of the images. 5. The method for calibrating a line sensor camera according to claim 4,
A calibration method for a line sensor camera, characterized in that the three-dimensional marker is L-shaped and the multiple detection points are arranged on the inner surface of the L-shape. 6. The method for calibrating a line sensor camera according to claim 4, further comprising:
A calibration method for a line sensor camera, comprising the steps of: (a) detecting a position of a fisheye lens;

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