JP6622503B2 - Camera model parameter estimation apparatus and program thereof - Google Patents

Description

  The present invention relates to a camera model parameter estimation apparatus and program for estimating a camera model parameter of a camera system composed of a photographing camera and a camera platform.

  In recent years, various research and development including 3D image processing has been actively performed using images taken by a multi-viewpoint camera. One of the important technologies for realizing these is camera calibration. Here, the camera calibration is to obtain camera parameters of the photographing camera. The camera parameters include external parameters indicating the position and orientation of the photographing camera, and internal parameters specific to the photographing camera such as a focal length.

  Camera calibration methods can be roughly divided into two. In the first method, feature points are extracted from a photographed image of a photographing camera by image analysis, and camera calibration is performed from the positional relationship of the feature points. This first method has an advantage that an electronic device such as a sensor is unnecessary. Here, the first method is classified into strong calibration and weak calibration, but both methods have problems. In the strong calibration, the calibration pattern is photographed and the camera is calibrated. However, since the calibration pattern needs to be reflected in the photographed image, the photographed image can be greatly restricted. In weak calibration, it is necessary to perform extraction, association, bundle adjustment, and the like of feature points, and depending on the captured image, these processes may not be successful and camera calibration may not be performed properly. In addition, since the first method requires complicated processing such as feature point extraction and numerical calculation, high-speed processing, particularly real-time processing, may be difficult while ensuring sufficient accuracy.

  Because of the above problems, the second method is considered. In the second method, information such as pan and tilt of the camera platform is physically measured using a sensor, and camera calibration is performed using the information. In this second method, it is necessary to calculate the camera model parameters in advance using the calibration pattern, but only simple calculation processing using the camera model parameters and sensor values (pan, tilt, etc.) is necessary. Since the camera parameters can be obtained, real-time processing is also possible. Furthermore, the second method has no restrictions or dependence on the photographed image at the time of use, and can calibrate the camera reliably.

  Here, as a second technique, there is known a technique for performing camera calibration for one photographing camera for the purpose of CG (Computer Graphics) synthesis in a virtual studio (Patent Document 1, Non-Patent Document 1). ). In these conventional techniques, a plurality of calibration patterns having different feature point intervals and sizes are prepared, and a calibration pattern suitable for the zoom range is selected even when the photographing camera is zoomed greatly from wide angle to telephoto. Then, the conventional technique extracts feature points from the selected calibration pattern, and performs camera model parameter estimation and camera calibration using the coordinates of the extracted feature points and information such as pan and tilt acquired by the sensor. .

Japanese Patent No. 4960941

Hidehiko Okubo and 4 others, Consideration of high-precision camera calibration in virtual studios, FIT2007 (6th Information Science Forum), 2007, p. 541-542

  However, in the above-described conventional technology, the relationship of the coordinate system is not considered between the calibration patterns, and the accuracy of camera calibration may not be sufficient. Therefore, in order to improve the accuracy of camera calibration, it is strongly desired to realize a method for estimating camera model parameters with higher accuracy.

  It is an object of the present invention to provide a camera model parameter estimation apparatus and a program for estimating a camera model parameter with high accuracy.

  In view of the above-described problems, a camera model parameter estimation apparatus according to the present invention is a camera model parameter estimation apparatus that estimates camera model parameters of a shooting camera using shot images obtained by shooting a plurality of calibration patterns with a plurality of shooting cameras A feature point extraction unit, an initial value generation camera calibration unit, a first external parameter setting unit, a second external parameter calculation unit, a calibration pattern relational expression setting unit, a predicted image coordinate calculation unit, And a camera model parameter optimization unit.

According to this configuration, the camera model parameter estimation device extracts the feature point of the calibration pattern from the captured image for each captured image by the feature point extraction unit, and outputs the observed image coordinates that are the coordinates of the extracted feature point. .
In the camera model parameter estimation device, the initial value generation camera calibration unit calculates the initial value of the internal parameter for each photographing camera by camera calibration.

In the camera model parameter estimation device, the first external parameter setting unit sets an initial value of a first external parameter for converting the pan / tilt coordinate system to the camera coordinate system for each photographing camera.
The pan / tilt coordinate system is a three-dimensional coordinate system in a pan / tilt head on which a photographing camera panned / tilted from the photographing origin is mounted.
The camera coordinate system is a three-dimensional coordinate system at the optical center of the photographing camera panned / tilted from the photographing origin.

The camera model parameter estimation device uses the second external parameter calculation unit to convert, for each photographing camera, a second external parameter for converting a reference calibration pattern coordinate system in a preset one of the calibration patterns into a pan head coordinate system. The initial value of is calculated.
The reference calibration pattern coordinate system is a three-dimensional coordinate system centered on an arbitrary point of the reference calibration pattern.
The pan / tilt head coordinate system is a three-dimensional coordinate system in a pan / tilt head that is not panned / tilted from the photographing origin and has a photographing camera facing the photographing origin.

In the camera model parameter estimation apparatus, an initial value of a calibration pattern relational expression representing a relation of a coordinate system between calibration patterns is set in advance by a calibration pattern relational expression setting unit.
By setting this calibration pattern relational expression in advance, the positional relationship of the calibration pattern can be shared by a plurality of photographing cameras, and stronger constraint conditions can be added to the estimation of the camera model parameters.

In the camera model parameter estimation apparatus, calibration pattern information is preset by the predicted image coordinate calculation unit, and the predicted image coordinates are calculated from the coordinates of the feature points of the calibration pattern information.
The calibration pattern information is information representing the coordinates of feature points included in the calibration pattern.
The predicted image coordinates are obtained by predicting the coordinates of feature points included in an image photographed by the photographing camera using camera model parameters.

The camera model parameter estimation device optimizes an evaluation formula including a camera model parameter and a calibration pattern relational expression so that a distance between an observed image coordinate and a predicted image coordinate is minimized by a camera model parameter optimization unit. Thus, the camera model parameters are estimated.
The camera model parameter is a model that includes an internal parameter of the photographing camera, a first external parameter, and a second external parameter of the photographing camera, and represents the state of the camera system.

According to the present invention, the following excellent effects can be obtained.
The camera model parameter estimation apparatus according to the present invention can estimate a highly accurate camera model parameter in order to share the positional relationship of the calibration pattern among a plurality of shooting cameras and to add a stronger constraint condition to the estimation of the camera model parameter. it can. Thereby, the camera model parameter estimation apparatus according to the present invention can further improve the accuracy of camera calibration.

In 1st Embodiment of this invention, it is explanatory drawing explaining a calibration pattern coordinate system, a pan / tilt coordinate system, a camera coordinate system, and a pan head coordinate system. In 1st Embodiment of this invention, it is explanatory drawing explaining arrangement | positioning of a camera system and a calibration pattern. In 1st Embodiment of this invention, it is explanatory drawing explaining a calibration pattern. In 1st Embodiment of this invention, it is explanatory drawing explaining imaging | photography of the calibration pattern by a camera system. (A)-(e) is explanatory drawing of the picked-up image image | photographed with the camera system. In 1st Embodiment of this invention, it is explanatory drawing explaining conversion of each coordinate system. In 1st Embodiment of this invention, it is explanatory drawing explaining omission of a relational expression. It is a block diagram which shows the structure of the camera calibration apparatus which concerns on 1st Embodiment of this invention. It is a block diagram which shows the structure of the camera model parameter estimation part of FIG. It is a flowchart which shows operation | movement of the camera calibration apparatus of FIG. 10 is a flowchart showing the operation of the initial value generation unit in FIG. 9. In 2nd Embodiment of this invention, it is explanatory drawing explaining each coordinate system before and behind transfer. In 2nd Embodiment of this invention, it is explanatory drawing explaining a calibration pattern coordinate system, a pan / tilt coordinate system, a camera coordinate system, and a pan head coordinate system. It is a block diagram which shows the structure of the camera calibration apparatus which concerns on 2nd Embodiment of this invention. It is a block diagram which shows the structure of the camera model parameter estimation part of FIG. It is a flowchart which shows operation | movement of the camera calibration apparatus of FIG. It is a flowchart which shows operation | movement of the initial value production | generation part of FIG.

(First embodiment)
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings as appropriate. In each embodiment, the same means and the same process are denoted by the same reference numerals, and description thereof is omitted.
First, after describing the camera calibration method according to the first embodiment of the present invention, the specific configuration of the camera calibration apparatus (camera model parameter estimation apparatus) according to the first embodiment of the present invention will be described.

[Camera calibration method]
As shown in FIG. 1, the camera system (photographing camera) C _i is a system including a camera body CB _i , a pan head CP _i, and a sensor CS _i (FIG. 8). In the present embodiment, the camera system C _i, it is assumed that a multi-view camera for photographing the multi-view image.

The camera body CB _i is a general video camera that captures images.
Camera platform CP _i is configured to mount the camera body CB _i, the camera body CB _i is the base for moving to pan and tilt.
Sensor CS _i is one in which the camera system C _{i (universal} head CP _i) is measured and the tilt value that represents the pan value representing the angle obtained by panning, the angle of the camera system C _{i (universal} head CP _i) is tilted .

Here, in order to define the camera model considering a physical configuration of the camera system C _i, consider the conversion of a simple coordinate system. When converting from one coordinate system sigma _A different coordinate system sigma _B, the coordinate transformation, the rotation angle alpha, beta, and gamma, the translation vector t _x, t _y, as t _z, expressed in total six parameters be able to. That is, the coordinate conversion can be expressed by Expression (1). At this time, θ _ext in Expression (1) is called an external parameter. Note that the subscript 'T' represents transposition.

This equation (1) can be expressed by equations (2) to (6) using the rotation matrix ^B R _A and the translation vector ^B t.
In the matrix, when subscripts are added to both the lower right and upper left, the lower right subscript represents the coordinate system before conversion, and the upper left subscript represents the coordinate system after conversion.
In the translation vector, the subscript at the upper left represents the coordinate system.

Further, Equation (2) to (6), using the matrix ^B M _A representing a rigid transformation can be expressed by Equation (7).

Here, in one camera system C _i and one calibration pattern P _j , a coordinate system as shown in FIG. 1 is defined and a camera model is considered.
The coordinate system of the calibration pattern P _j, the calibration pattern coordinate system sigma _Pj. The calibration pattern coordinate system sigma _Pj is that the 3-dimensional coordinate system with the origin of an arbitrary point of the calibration pattern P _j.

In the camera platform CP _i , one point where the orthogonal pan axis and tilt axis intersect is defined as the camera platform center Q. A three-dimensional coordinate system when the camera system C _i is _directed to the photographing origin at the pan head center Q (that is, when the pan value and tilt value are 0) is defined as a pan head coordinate system _ΣCPi .

In the pan head center Q, the camera system C _i is the pan-tilt coordinate system sigma _PTi 3-dimensional coordinate system after the pan and tilt. A three-dimensional coordinate system after the camera system C _i pans and tilts at the optical center S of the camera body CB _i is a camera coordinate system Σ _Ci .

Here, the conversion from the calibration pattern coordinate system sigma _Pj to the camera platform coordinate system _{sigma CPi,} when the parameter denoted ^CP theta _{ext, i,} and becomes a ^CPi M _Pj With matrix notation (second external parameters).
The conversion from the pan-tilt coordinate system sigma _PTi to the camera coordinate system _{sigma Ci,} when the parameter notation ^C theta _{ext, i,} and becomes a ^Ci M _PTi With matrix notation (first external parameter).
In this case, the external parameter θ _{ext, i} to be obtained can be expressed by Expression (8).

The _{transformation} from the pan head coordinate system _ΣCPi to the pan / tilt coordinate system _ΣPTi is expressed as ^PTi M _CPi (third external parameter). This matrix ^PTi M _CPi can be expressed by Equation (9). The rotation matrix ^PTi R _{CPi in} Expression (9) represents a rotation matrix from the pan head coordinate system _ΣCPi to the pan / tilt coordinate system _ΣPTi . In equation (9), since the pan head coordinate system Σ _CPi and the pan / tilt coordinate system Σ _PTi both have the pan head center Q as the origin, the translation vector ^PTi t becomes zero.

The rotation matrix ^PTi R _CPi can be obtained by Expression (10). In this formula (10), φ is the tilt angle and ρ is the pan angle. Therefore, the rotation matrix ^PTi R _CPi can be obtained by substituting the pan value and tilt value measured by the sensor CS _i into the equation (10).

Thus, the relationship of the coordinate system in the camera system C _i can be expressed by Equation (11). In other words, equation (11), the matrix ^Ci M _{^PTi, PTi} M _CPi, which represents the ^CPi M _Pj, the relationship between the matrix ^Ci M _Pj.
Incidentally, the matrix ^Ci M _Pj is to convert the calibration pattern coordinate system sigma _Pj in the camera coordinate system _{sigma Ci} (fourth external parameter).

Further, the internal parameter θ _{int, i} of the camera system C _i can be expressed by Expression (12). In this equation (12), the focal length f _i , the aspect ratio α _i , the image center c _{u, i} , c _{v, i} , and the lens distortion coefficients k _{1, i} , k _{2, i} , k _{3, i} , k _{4, i} is represented.

The lens distortion coefficients k1 _{, i to} k4 _{, i} can be expressed by Expression (13). In this equation (13), image coordinates [u _{n, i} , v _{n, i} ] ^T when imaged with an ideal lens without distortion, image coordinates when imaged with a lens with distortion aberration [ u _{d, i} , v _{d, i} ] ^T , and distance r _i from the image center. Here, r _i ² = un _{, i} ² + v _{n, i} ² .

In the present invention, as shown in FIG. 2, a plurality of camera systems C _i and a plurality of calibration patterns P _j are arranged to estimate camera model parameters. Here, n camera systems C _i (i = 1,..., N) and m calibration patterns (j = 1,..., M) (where m and n are natural numbers exceeding 1). ).

For example, the calibration pattern P _j is a checkerboard pattern as shown in FIG. Further, all the calibration patterns P _j are arranged so as to be visible from all the camera systems C _i . Each camera system C _i photographs a certain calibration pattern P _j while changing the posture. Further, as shown in FIG. 4, each camera system C _i performs shooting while changing the posture with respect to another calibration pattern P _j .

Accordingly, as shown in FIG. 5 (a) ~ (e) , in the captured image by the camera system C _i is taken, the position and orientation of the calibration patterns P _j are different. That is, in the camera system _{C i,} the external parameter ^CP theta _ext representing the relationship between the camera platform coordinate system _{sigma CPi} and calibration pattern coordinate system Σ _Pj, i (j) is equal in number to the number m of the calibration pattern _{P j.} Therefore, camera model parameters of the camera system C _i is as Equation (14).

A calibration pattern relational expression η _j representing a coordinate system relationship between the calibration patterns P _j includes rotation angles ^P α _j , ^P β _j , ^P γ _j and translation vectors ^P t _{x, j} , ^P t _{y, j} , ^{Using P} _{tz, j} , it can be expressed by equation (15).

From all of the calibration pattern P _j, pre-set one of the calibration pattern as a reference calibration pattern P _w. Here, it is assumed that w th calibration pattern is the reference calibration pattern _{P w (1 ≦ w ≦ m} ). In this reference calibration pattern P _w, reference calibration the 3-dimensional coordinate system with the origin of the arbitrary point pattern coordinate system (world coordinate system) and sigma _Pw. At this time, the relational expression η _j exists for the number m of the calibration patterns P _j , and one of them represents the relationship between the reference calibration patterns P _w . Therefore, it is not necessary to determine the relationship between the reference calibration pattern P _w.

There camera system _{C i} and the calibration patterns _{P 1, ..., P w,} ..., the relationship between _{P m,} is shown in FIG. When optimizing, reducing the number of variables improves the accuracy of the camera model parameters. Further, since the calibration parameter relational expression is defined for the external parameter ^CP θ _{ext, i} (j), it is not necessary to obtain all of them, and only one needs to be obtained.

Therefore, when limited to the relationship between the camera platform coordinate system sigma _CPi and the reference calibration pattern P _w, camera model parameters of formula (14) can be simplified as equation (16). ^CP theta _ext included in this equation _(16), i (w) is the conversion of the reference calibration pattern coordinate system sigma _Pw to the camera platform coordinate system _{sigma CPi} is obtained by the parameter representation. The reason why the relational expression can be simplified will be described later.

Therefore, the parameter μ to be evaluated by the optimization can be expressed by Expression (17). This equation (17) includes internal parameters θ _int and external parameters ^C θ _ext , ^CP θ _ext (w) in all camera systems C ₁ ,..., C _n and all calibration pattern relational expressions in equation (15). η _j is included.

The posture when the camera system C _i changes the pan angle and the tilt angle and photographs the calibration pattern P _j is k _ij = 1,..., P _ij (where p _ij is a natural number exceeding 1). In addition, the number of the feature points of the calibration pattern P _j is set to l _j = 1,..., Q _j (where q _j is a natural number exceeding 1). The coordinates of the feature point l _j extracted from the captured image are called observation image coordinates.

Since the coordinate of the feature point l _j of the calibration pattern P _j is known, using a calibration pattern information set in advance, the camera system C _i is the coordinate of the feature point l _j upon shooting calibration pattern P _j at position k _ij Predict. The predicted coordinates of the feature point l _j are called predicted image coordinates, and the calculation method will be described later.
Incidentally, the calibration and the pattern information, for each calibration pattern P _j, is information representing the coordinate and the number of feature points included in the calibration patterns P _j.

The parameters μ in Expression (17) are all obtained by obtaining the distance between the observed image coordinates and the predicted image coordinates and minimizing the sum of squares of the obtained distances. That is, the parameter μ is obtained by optimizing the expression (18) as the evaluation expression. Thereafter, camera calibration is performed using the camera model parameter θ _i included in the parameter μ and the pan value and the tilt value measured by the sensor CS _i .
In Equation (18), “arg min” represents minimization, “||” represents a norm, u ^ _ijkijj represents predicted image coordinates, and _uijkijlj represents observed image coordinates.

<Reason for simplifying relational expression, calculation method of predicted image coordinates>
With reference to FIG. 7, the reason why the equation (14) can be simplified as the equation (16) and the method of calculating the predicted image coordinates will be described.
For calibration pattern P _j other than the reference calibration pattern P _w, it converts the 3-dimensional coordinate system of all the feature points in the reference calibration pattern coordinate system sigma _Pw. In this case, the three-dimensional coordinate x of the feature point of the calibration pattern _Pj can be expressed by Expression (19).

Here, “˜” represents the homogeneous coordinate system of the three-dimensional coordinate x, and the coordinate system of the vector representing the three-dimensional coordinate is represented by a subscript at the upper left of the vector. That is, the three-dimensional vector in the calibration pattern coordinate system _ΣPj is ^Pj x. An expression for converting the three-dimensional vector ^Pj x from the calibration pattern coordinate system _ΣPj to the reference calibration pattern coordinate system _ΣPw can be expressed by Expression (20).

Thus, to align the coordinate system of the feature points included in the calibration patterns P _j on the reference calibration pattern coordinate system sigma _Pw, equation (14) can be simplified as equation (16). Then, using equation (21), to convert the feature point in the reference calibration pattern coordinate system sigma _Pw in the camera coordinate system sigma _Ci. Thereafter, by projecting the feature points in the camera coordinate system sigma _Ci to images, it is possible to obtain the predicted image coordinates.

Specifically, the predicted image coordinates are obtained as follows. Here, the coordinates (X, Y, Z) of the feature point l _j of the calibration pattern P _j can be expressed by the camera coordinates (x, y, z) of the camera system C _i , as in Expression (22). . Also, normalized image coordinates u _{n, i} , v _{n, i} are obtained from x, y in equation (22), as in equation (23).

Then, the above-mentioned using equation (13), the normalized image coordinates u _{n, i, v} n, to the lens distortion is reflected in _i, the image coordinates u _d when taken with the lens with _{distortion, i} , V _{d, i} are obtained. Thereafter, the predicted image coordinates u _i and v _i can be obtained by projecting the image coordinates u _{d, i} , v _{d, i} as shown in Expression (24).

[Configuration of camera calibration device]
The configuration of the camera calibration apparatus 1 will be described with reference to FIG.
The camera calibration apparatus 1 estimates the camera model parameters of the camera system C _i using the captured images obtained by capturing each of the plurality of calibration patterns P _{j with} the plurality of camera systems C _i (C ₁ ,..., C _n ). To do.
As shown in FIG. 8, the camera calibration apparatus 1 includes a synchronization signal generation unit 10, an information recording unit 20, a camera model parameter estimation unit 30, and a camera calibration unit 40.

The camera system C _i acquires an image by the camera body CB _i according to the synchronization signal input from the synchronization signal generation unit 10, and acquires a sensor value (pan value and tilt value) by the sensor CS _i . Then, the camera system C _i outputs the acquired video and sensor values to the camera model parameter estimation unit 30. Further, the camera system C _i outputs the acquired sensor value to the camera calibration unit 40.

The synchronization signal generation unit 10 outputs a synchronization signal to the camera system C _i (camera body CB _i , pan head CP _i and sensor CS _i ) in order to synchronize the video and the sensor value. In the present embodiment, the synchronization signal generator 10, since the camera body CB _i acquires the multi-view image, and outputs the same synchronization signal to all of the camera system C _i. With this synchronization signal, the camera body CB _{i and the} sensor CS _i can acquire the image and the sensor value at the same timing.

  The information recording unit 20 is a recording device such as a memory or a hard disk that records various types of information. The information recording unit 20 records in advance calibration pattern information necessary for camera model parameter estimation. The information recording unit 20 records the camera model parameter information input from the camera model parameter estimation unit 30.

Camera model parameter estimation unit 30 refers to the calibration pattern information recorded in the information recording unit 20, and estimates the camera model parameters of the camera system C _i. Then, the camera model parameter estimation unit 30 outputs the estimated camera model parameters to the information recording unit 20 as camera model parameter information.
Details of the camera model parameter estimation unit 30 will be described later.

Camera calibration unit 40 performs camera calibration of the camera system C _i, and outputs the camera parameters of the camera system C _i. In this case, the camera calibration unit 40 uses a camera model parameter information recorded in the information recording section 20, and a sensor value input from the camera system C _i, performs camera calibration.

[Configuration of camera model parameter estimation unit]
With reference to FIG. 9, the structure of the camera model parameter estimation part 30 is demonstrated (refer FIG. 8 suitably).
As shown in FIG. 9, the camera model parameter estimation unit 30 includes a video input unit 302, a sensor value input unit 304, a frame synchronization unit 306, a captured image / sensor value recording unit 310, an information selection unit 320, and a feature. A point extraction unit 330, an initial value generation unit 340, and an optimization unit 350 are provided.

Image input unit 302, the image input from the camera system C _i, and converts the still image for each frame (captured image). That is, the video input unit 302 outputs each frame image included in the video to the frame synchronization unit 306 as a captured image.

The sensor value input unit 304 converts the sensor value into text data so that the camera model parameter estimation unit 30 can handle the sensor value (measurement signal of the sensor CS _i ) input from the camera system C _i. is there. Then, the sensor value input unit 304 outputs the sensor value converted to text data to the frame synchronization unit 306.

  The frame synchronization unit 306 synchronizes the captured image input from the video input unit 302 and the sensor value input from the sensor value input unit 304. For example, the frame synchronization unit 306 associates a captured image having the same time code with a sensor value. Then, the frame synchronization unit 306 outputs the synchronized captured image and sensor value to the captured image / sensor value recording unit 310.

  The photographed image / sensor value recording unit 310 is a recording device such as a memory or a hard disk that records the photographed image and sensor value input from the frame synchronization unit 306.

  The information selection unit 320 selects a combination of a captured image and a sensor value to be used for camera model parameter estimation from among the combination of the captured image and the sensor value stored in the captured image / sensor value recording unit 310. For example, the information selection unit 320 automatically selects a combination of a captured image and a sensor value for each fixed frame. The information selection unit 320 may manually select a combination of the captured image and the sensor value. Thereafter, the information selection unit 320 outputs the captured image included in the selected combination to the feature point extraction unit 330, and outputs the sensor value included in the selected combination to the initial value generation unit 340 and the optimization unit 350. .

The feature point extraction unit 330 extracts feature points from the captured image input from the information selection unit 320. For example, the feature point extraction unit 330 performs feature point extraction processing such as a corner detection method on the captured image, and extracts the feature points of the calibration pattern P _j included in the captured image. Then, the feature point extraction unit 330 outputs the extracted feature point coordinates (observation image coordinates) to the initial value generation unit 340 as the feature point information.

  The initial value generation unit 340 generates initial values necessary for optimization, and includes an initial value generation camera calibration unit 341, a first external parameter setting unit 343, and a second external parameter calculation unit 345. And a third external parameter calculation unit 347 and a calibration pattern relational expression setting unit 349.

The initial value generation camera calibration unit 341 calculates the initial value of the internal parameter θ _{int, i} of Expression (16) and the fourth external parameter ^Ci _{MP Pj} by camera calibration. Here, the initial value generation camera calibration unit 341 performs camera calibration using the feature point information input from the feature point extraction unit 330 and the calibration pattern information recorded in the information recording unit 20.

For example, the camera calibration unit 341 for generating an initial value can use the technique described in Reference Document 1 below as camera calibration.
Reference 1: Z.Zhang.A flexible new technique for camera calibration.IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (11), 1330-1334.

The first external parameter setting unit 343 sets an initial value of the first external parameter ^Ci M _PTi . For example, in the first external parameter setting unit 343, the initial value of the first external parameter ^Ci M _PTi is manually set by actual measurement or empirical rule.

Second external parameter calculator 345 is for calculating the initial value of the second external parameters ^CPi M _Pj. The second external parameter calculation unit 345 calculates the initial value of the second external parameter ^CPi M _Pj ( ^CP θ _ext (j) in the case of vector notation) using Equation (11) set in advance as a conversion equation. .

Specifically, the second external parameter calculation unit 345 includes the fourth external parameter ^Ci M _Pj calculated by the initial value generation camera calibration unit 341 and the first external parameter ^Ci M set by the first external parameter setting unit 343. _{By substituting} the initial value of _PTi and the matrix ^PTi M _CPi calculated by the third external parameter calculation unit 347, which will be described later, into the equation (11), the initial value of the second external parameter ^CPi M _Pj is calculated backward.

The third external parameter calculation unit 347 calculates the third external parameter ^PTi M _CPi from the sensor value input from the information selection unit 320. Here, the third external parameter calculation unit 347 ^obtains the rotation matrix ^PTi R _CPi by substituting the sensor value into Expression (10), and calculates the third external parameter ^PTi M _CPi using Expression (9).

The calibration pattern relational expression setting unit 349 sets an initial value of the calibration pattern relational expression η _j . Here, in the calibration pattern relationship setting unit 349, since the position of the reference calibration pattern P _w it is known, using the sensor value when there camera system C _i is facing the calibration patterns P _j, the calibration pattern P _j To set the initial value of equation (15) representing the relationship of the coordinate system.

For example, the calibration pattern relation setting unit 349 as an initial value of the calibration pattern relationship eta _j, the relationship ^Pw M _P1 of the calibration pattern ^{_{P 1, P W, · Pw}} M P1 = Pw M Ci' · Ci' M Ci Set as ^Ci M _P1 . Here, ^Pw M ^Ci _′ and ^Ci M _P1 are obtained from the fourth external parameter ^Ci M _Pj . _Ci ^′ M _Ci is obtained from the rotation matrix indicated by the sensor value by approximating the translation vector with 0.

In this way, the initial value generation unit 340 includes the internal parameter θ _{int, i} of the equation (16) of each camera system C _i , the first external parameter ^C θ _{ext, i} ( ^Ci M _PTi ), and the second external parameter An initial value with the parameter ^CP θ _{ext, i} ( ^CPi M _Pj ) is obtained. Further, the initial value generation unit 340 obtains an initial value of a calibration pattern relational expression η _j that represents the relationship of the coordinate system between the calibration patterns P _j as shown in Expression (15). As a result, the initial value generation unit 340 can generate the initial value of the parameter μ in Expression (17). Thereafter, the initial value generation unit 340 outputs the generated initial value and the feature point information to the optimization unit 350.

  The optimization unit 350 performs optimization using the feature point information and the initial value input from the initial value generation unit 340 and the sensor value input from the information selection unit 320. The optimization unit 350 includes a predicted image coordinate calculation unit 351 and a camera model parameter optimization unit 353.

  The predicted image coordinate calculation unit 351 refers to the calibration pattern information stored in the information recording unit 20, and calculates the predicted image coordinates from the coordinates of the feature points of the calibration pattern information. Specifically, the predicted image coordinate calculation unit 351 calculates the predicted image coordinates using Expression (13) and Expression (22) to Expression (24).

The camera model parameter optimization unit 353 uses the feature point information (observation image coordinates) and the initial value (formula 17) input from the initial value generation unit 340 and the predicted image coordinates calculated by the predicted image coordinate calculation unit 351. Thus, optimization (for example, reprojection error minimization) is performed. Specifically, the camera model parameter optimization unit 353 optimizes the equation (18) so that the distance between the observed image coordinates and the predicted image coordinates is minimized, so that the camera model parameter θ in the equation (16) is obtained. _i is estimated. Then, the camera model parameter optimization unit 353 outputs the estimated camera model parameter θ _i to the information recording unit 20 as camera model parameter information.

[Operation of camera calibration device]
The operation of the camera calibration apparatus 1 in FIG. 8 will be described with reference to FIG. 10 (see FIGS. 8 and 9 as appropriate).
Each camera system C _i and each calibration pattern P _j are arranged at predetermined positions. In the camera calibration device 1, calibration pattern information is recorded in advance in the information recording unit 20 (step S0).
Note that the process of step S0 is illustrated by a broken line because it is a preparatory work for camera calibration.

Camera calibration device 1, the synchronization signal generator 10 generates a synchronization signal, and inputs the generated synchronization signal to the camera system C _i.
The camera calibration apparatus 1 acquires a video from the camera system C _i by the video input unit 302 and converts it into a still image (photographed image) for each frame.
Camera calibration device 1, the sensor value input unit 304, acquires a sensor value from the camera system C _i, is converted into text data (step S1).

The camera calibration apparatus 1 uses the frame synchronization unit 306 to synchronize the captured image acquired in step S1 with the sensor value (step S2).
The camera calibration apparatus 1 records the combination of the captured image and the sensor value synchronized in step S2 in the captured image / sensor value recording unit 310 by the frame synchronization unit 306 (step S3).

  In the camera calibration device 1, the information selection unit 320 selects a combination of a captured image and a sensor value to be used for camera model parameter estimation from among the combination of the captured image and the sensor value recorded in Step S3 (Step S4). .

In the camera calibration device 1, the feature point extraction unit 330 extracts feature points from the captured image selected in step S4 (step S5).
The camera calibration device 1 generates an initial value by the initial value generation unit 340 (step S6). Details of the process of step S6 will be described later.

The camera calibration apparatus 1 calculates the predicted image coordinates by the predicted image coordinate calculation unit 351.
The camera calibration apparatus 1 optimizes the camera model parameter optimization unit 353 using the initial value generated in step S6, the feature point information, the predicted image coordinates, and the calibration pattern information, and sets the camera model parameter. Estimate (step S7).
The camera calibration device 1 performs camera calibration by using the camera model parameter estimated in step S7 and the sensor value by the camera calibration unit 40 (step S8).

<Generation of initial values>
With reference to FIG. 11, the process of step S6 of FIG. 10 will be described (see FIG. 9 as appropriate).
The camera calibration device 1 performs camera calibration by the initial value generation camera calibration unit 341, and calculates the initial value of the internal parameter θ _{int, i} and the fourth external parameter ^Ci _MPj (step S61).

The camera calibration apparatus 1 _sets the initial value of the first external parameter ^Ci M _PTi by the first external parameter setting unit 343 (step S62).
The camera calibration apparatus 1 calculates the third external parameter ^PTi M _CPi from the sensor value selected in step S4 by the third external parameter calculation unit 347 (step S63).

In the camera calibration apparatus 1, the second external parameter calculation unit 345 calculates the fourth external parameter ^Ci M _Pj calculated in step S61, the initial value of the first external parameter ^Ci M _PTi set in step S62, and the calculation in step S63. The initial value of the second external parameter ^CPi M _Pj is calculated by substituting the third external parameter ^PTi M _CP into the equation (11) (step S64).

Camera calibration device 1, the calibration pattern relation setting unit 349 sets an initial value of the formula (15) representing the relationship between the coordinate system calibration pattern P _j (step S65).

As described above, the camera calibration device 1 according to the first embodiment of the present invention sets the calibration pattern P _j with the plurality of camera systems C _i by setting the expression (15) representing the relationship of the coordinate system with the calibration pattern P _j. The positional relationship of P _j can be shared, and stronger constraint conditions can be added to the estimation of camera model parameters. As a result, the camera calibration apparatus 1 can estimate camera model parameters with high accuracy and perform camera calibration with high speed, high accuracy, and high stability. As a result, the camera calibration apparatus 1 can perform various image processing on the multi-viewpoint video in real time, and is expected to be applied to various uses.

(Second Embodiment)
Hereinafter, the second embodiment of the present invention will be described while referring to differences from the first embodiment.
The camera calibration device 1 according to the first embodiment described above needs to shoot a plurality of calibration patterns P _j in various postures using a plurality of camera systems C _i and solve an optimization problem with a large number of parameters. is there. Therefore, the camera calibration device 1, after the setting of the camera system C _i, it takes time and effort before the end of the estimation of the camera model parameters. Of course, at the shooting site, the time that can be spent on setting up the system is limited, and it is preferable that the time and effort be less.
Incidentally, herein referred to as relocated placing the camera system C _i to another location. For example, moving the camera system C _i by 10 cm also corresponds to the transfer of the camera system C _i .

Here, the camera model parameter includes a plurality of external parameters (first external parameter ^C θ _{ext, i} and second external parameter ^CP θ _{ext, i} ) and one internal parameter θ _int per camera system C _{i. , I.}

Among these parameters, the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} do not depend on the world coordinate system (that is, the arrangement of the camera system C _i ). For this reason, the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} can be used as they are even if the camera system C _i is moved to another location.

On the other hand, the second external parameters ^CP theta _{ext, i} is (also fourth external parameters) because it depends on the world coordinate system, when the relocation of the camera system C _i, it is necessary to ask again. Since the second external parameter ^CP θ _{ext, i} is composed of 6 parameters per camera system C _i, it can be obtained by solving a relatively simple optimization problem.

[Installed camera calibration]
First, after describing the camera calibration method in the second embodiment of the present invention, a specific configuration of the camera calibration apparatus 1B according to the second embodiment of the present invention will be described.
As a premise of the second embodiment, it is necessary to estimate camera model parameters by the method of the first embodiment as shown in FIG. Hereinafter, the method of the first embodiment is referred to as “initial camera calibration”.
Thereafter, the camera model parameters of the transferred camera system C _i are estimated using the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} obtained by the initial camera calibration. Hereinafter, the method described in the second embodiment is referred to as “installed camera calibration”.

In FIG. 12, for two camera systems C ₁ and C ₂ , three calibration patterns P _w , P ₁ , and P ₂ are used for initial camera calibration, and two calibration patterns P are used for installation camera calibration. _{w 1} and P ₁ are used.
Further, in the camera set up calibration of FIG. 12, the conversion from the known values become pan-tilt coordinate system sigma _PTi to the camera coordinate system sigma _Ci (the first external parameter) illustrated by dashed arrows. Further, parameters obtained by optimization are illustrated by solid arrows.

Hereinafter, the installation camera calibration will be described in detail.
Here, consider a case where there are n camera systems C _i (i = 1,..., N) and m calibration patterns P _j (j = 1,..., M). General external parameters are composed of a total of six parameters, three parameters for the rotation angle and three parameters for the translation vector. That is, the external parameter θ _ext is expressed by the equation (1).

As shown in FIG. 13, when considering for a single camera system _{C i,} representing the second external parameters for converting from the calibration pattern coordinate system sigma _Pj to the camera platform coordinate system _{Σ CPi} ^CP _{θ ext,} as i (j) . That is, the parameter to be estimated in the camera system C _i is expressed by Expression (25). Here, in the installed camera calibration, unlike the initial camera calibration, the internal parameter θ _{int, i} and the first external parameter ^C θ _{ext, i} are handled as known fixed values, and thus are not included in the equation (25).

In FIG. 13, the conversion from the known values pan-tilt coordinate system sigma _PTi to the camera coordinate system _{sigma Ci} (first external parameter), the camera platform coordinate system _{sigma CPi} to pan-tilt coordinate system sigma _PTi The conversion (third external parameter) is indicated by a broken-line arrow.

Similarly to the external parameters, the calibration pattern relational expression η _j is composed of three parameters for the rotation angle and three parameters for the translation vector. After relocation of the camera system C _i, the calibration pattern P _j new reference calibration pattern one from among (world coordinates) is set as P _w. Here, consider a case where the w-th calibration pattern P _j is set as the reference calibration pattern P _w (1 ≦ w ≦ m). In this case, the reference calibration pattern _{P w} and equation eta _j of another calibration pattern _{P j} is expressed by Equation (15).

For the camera system C _i , the second external parameter ^CP θ _{ext, i} (w) to be estimated has only to be obtained from the relationship with the new reference calibration pattern P _w, and is expressed by the equation (26). As described above, the parameter μ to be evaluated by the optimization is expressed by Expression (27).

It is assumed that the pan / tilt is changed by the camera system C _i and the calibration pattern P _j is photographed with a certain posture k _ij . At this time, the parameters μ in Expression (27) are all obtained by obtaining the distance between the observed image coordinates and the predicted image coordinates and minimizing the sum of squares of the obtained distances. That is, the parameter μ is obtained by optimizing the expression (28) as the evaluation expression.

[Configuration of camera calibration device]
The configuration of the camera calibration apparatus 1B will be described with reference to FIG.
The camera calibration apparatus 1B estimates the camera model parameters of the relocated camera system C _i using the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} obtained in the initial camera calibration.
As illustrated in FIG. 14, the camera calibration apparatus 1B includes a synchronization signal generation unit 10, an information recording unit 20B, a camera model parameter estimation unit 30B, and a camera calibration unit 40.

The information recording unit 20B records the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} obtained by the initial camera calibration. The first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} are referred to by the camera model parameter estimation unit 30B when the installed camera is calibrated.
The other points, the information recording unit 20B, are the same as those in the first embodiment, and thus further description thereof is omitted.

The camera model parameter estimation unit 30B refers to the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} recorded in the information recording unit 20, and estimates the camera model parameter of the relocated camera system C _i It is. Then, the camera model parameter estimation unit 30B outputs the estimated camera model parameters to the information recording unit 20B as camera model parameter information.

[Configuration of camera model parameter estimation unit]
The configuration of the camera model parameter estimation unit 30B will be described with reference to FIG. 15 (see FIG. 14 as appropriate).
As shown in FIG. 15, the camera model parameter estimation unit 30B includes a video input unit 302, a sensor value input unit 304, a frame synchronization unit 306, a captured image / sensor value recording unit 310, an information selection unit 320, and a feature. A point extraction unit 330, an initial value generation unit 340B, and an optimization unit 350B are provided.

The initial value generation unit 340B includes an initial value generation camera calibration unit 341B, a first external parameter setting unit 343, a second external parameter calculation unit 345B, a third external parameter calculation unit 347, and a calibration pattern relational expression setting unit. 349.
The initial value generation unit 340B is illustrated with a broken line because it does not have to include the first external parameter setting unit 343 when the installed camera is calibrated.

The initial value generation camera calibration unit 341B is the camera calibration, and calculates a fourth external parameter ^Ci M _Pj. That is, since the initial value generation camera calibration unit 341B is the same as that of the first embodiment except that the initial value of the internal parameter θ _{int, i} is not calculated, further description thereof is omitted.

Second external parameter calculator 345B includes a fourth external parameters ^Ci M _Pj and the first external parameters recorded on the information recording section 20 ^Ci M _PTi and the third external parameters ^PTi initial value generation camera calibration unit 341B has calculated and M _CPi by substituting the equation (11) is for calculating back the initial value of the second external parameters ^CPi M _Pj.
Note that the second external parameter calculation unit 345B performs the same processing as in the first embodiment, and thus further description thereof is omitted.

In this way, the initial value generation unit 340B obtains the initial value of the second external parameter ^CP θ _{ext, i} (w) of Expression (26) for the moved camera system C _i . Further, the initial value generation unit 340B obtains an initial value of a calibration pattern relational expression η _j that represents the relationship of the coordinate system between the calibration patterns P _j as shown in Expression (15). As a result, the initial value generation unit 340B can generate the initial value of the parameter μ in Expression (27). Thereafter, the initial value generation unit 340B outputs the generated initial value and feature point information to the optimization unit 350B.

The optimization unit 350B includes a predicted image coordinate calculation unit 351 and a camera model parameter optimization unit 353B.
The camera model parameter optimizing unit 353B optimizes the equation (28) so that the distance between the observed image coordinates and the predicted image coordinates is minimized, so that the camera model parameter θ _i (second external) of the equation (26) is obtained. Parameter). Then, the camera model parameter optimization unit 353B records the estimated camera model parameter θ _i , the first external parameter ^Ci M _PTi and the internal parameter θ _{int, i} obtained by the initial camera calibration as camera model parameter information. To the unit 20B.

[Operation of camera calibration device]
The operation of the camera calibration device 1B of FIG. 14 will be described with reference to FIG. 16 (see FIGS. 14 and 15 as appropriate).
Here, it is assumed that the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} obtained by the initial camera calibration are recorded in the information recording unit 20B.

  The camera calibration device 1 generates an initial value by the initial value generation unit 340B (step S6B). Details of the process of step S6B will be described later.

The camera calibration apparatus 1 calculates the predicted image coordinates by the predicted image coordinate calculation unit 351.
The camera calibration apparatus 1 estimates the camera model parameter θ _i (second external parameter) of the equation (26) by optimizing the above equation (28) by the camera model parameter optimization unit 353B (step S7B). ).

<Generation of initial values>
With reference to FIG. 17, the process of step S6B of FIG. 16 will be described (see FIG. 15 as appropriate).
Camera calibration device 1, by the initial value generation camera calibration unit 341B, performs camera calibration, to calculate a fourth external parameter ^Ci M _Pj (step S61B).

The camera calibration apparatus 1 calculates the fourth external parameter ^Ci M _Pj calculated in step S61B, the first external parameter ^Ci M _PTi recorded in the information recording unit 20B, and the second external parameter calculation unit 345B in step S63. The initial value of the second external parameter ^CPi M _Pj is calculated by substituting the third external parameter ^PTi M _CP into the equation (11) (step S64B).

As described above, the camera calibration apparatus 1B according to the second embodiment of the present invention requires fewer parameters to be estimated than the initial camera calibration, so that the number of calibration patterns P _j to be used and the camera system C _i are different. The number of postures when photographing the calibration pattern _Pj can be reduced. Furthermore, since the camera calibration apparatus 1B can reduce the time for the optimization process, the time and labor at the photographing site can be greatly reduced, and the operability is improved.

  As mentioned above, although each embodiment of this invention was explained in full detail, this invention is not limited to above-described embodiment, The design change etc. of the range which does not deviate from the summary of this invention are also included.

In the embodiments described above, as a calibration pattern P _j available in the present invention has been illustrated checkerboard pattern of FIG. 3, but is not limited thereto. For example, the calibration pattern P _j available in the present invention, the dot pattern can be mentioned.

Further, if the arrangement and number of feature points are known, different types of calibration patterns _Pj may be mixed. For example, the calibration pattern P _j, checkerboard pattern and a dot pattern may be mixed. Further, the calibration pattern P _j may be the same type of checkerboard pattern, or the number of feature points and the interval may be different.

Further, as long as each calibration pattern P _j is visible from all the camera systems C _i , its position and orientation are not limited. As shown in FIG. 2, the calibration patterns _Pj may be arranged in the same direction on a horizontal straight line. Further, it is preferable that each calibration pattern P _j is arranged at various positions and orientations within a range that can be seen from all the camera systems C _i because it can correspond to various postures of the camera system C _i .

In the embodiments described above, it has been described that the camera system C _i is a multi-view camera is not limited thereto. For example, the present invention can also be applied to the same film studios and a plurality of camera systems located within the imaging area, C _i.

Here, when the camera system C _i is not a multi-view camera, the synchronization signal generation unit 10 may not output the same synchronization signal to different camera systems C _i . However, the synchronization signal generation unit 10 needs to output the same synchronization signal to the camera body CB _i , the camera platform CP _i, and the sensor CS _i included in one camera system C _i .

In the second embodiment described above, the first external parameter ^C θ _{ext, i} and the internal parameter θ _{int, i} obtained by the initial camera calibration have been described. However, the present invention is not limited to this. For example, the present invention may use only the first external parameter ^C θ _{ext, i} obtained by the initial camera calibration, and obtain the internal parameter θ _{int, i} during the installation camera calibration.

  In each of the embodiments described above, the camera calibration devices 1 and 1B have been described as independent hardware, but the present invention is not limited to this. For example, the camera calibration devices 1 and 1B can be realized by a camera calibration program that causes hardware resources such as a CPU, a memory, and a hard disk included in a computer to operate in cooperation with each other as described above. This program may be distributed through a communication line, or may be distributed by writing in a recording medium such as a CD-ROM or a flash memory.

1, 1B Camera calibration apparatus 10 Synchronization signal generation unit 20, 20B Information recording unit 30, 30B Camera model parameter estimation unit 40 Camera calibration unit 302 Video input unit 304 Sensor value input unit 306 Frame synchronization unit 310 Image / sensor value recording unit 320 Information selection unit 330 Feature point extraction unit 340, 340B Initial value generation unit 341, 341B Initial value generation camera calibration unit 343 First external parameter setting unit 345, 345B Second external parameter calculation unit 347 Third external parameter calculation unit 349 Calibration pattern relation setting unit 350,350B optimization unit 351 predicted image coordinate calculation unit 353,353B camera model parameter optimization unit _{C i} camera system (imaging camera)

Claims (5)

A camera model parameter estimation device for estimating camera model parameters of the photographing camera using photographed images obtained by photographing a plurality of calibration patterns with a plurality of photographing cameras,
A feature point extraction unit that extracts feature points of the calibration pattern from the photographed image for each photographed image and outputs observation image coordinates that are coordinates of the extracted feature points;
By camera calibration, an initial value generation camera calibration unit that calculates an initial value of an internal parameter for each photographing camera;
A pan / tilt coordinate system in a pan / tilt mounted with the photographing camera panned / tilted from the photographing origin is converted into a camera coordinate system at the optical center of the photographing camera panned / tilted from the photographing origin for each photographing camera. A first external parameter setting unit for setting an initial value of the first external parameter;
For each of the photographing cameras, a reference calibration pattern coordinate system in one of the calibration patterns set in advance is converted into a pan head coordinate system in a pan head on which the photographing camera facing the photographing origin is mounted. A second external parameter calculation unit for calculating an initial value of the two external parameters;
A calibration pattern relational expression setting unit that presets an initial value of a calibration pattern relational expression that represents a coordinate system relationship between the calibration patterns;
Calibration pattern information representing the coordinates of feature points included in the calibration pattern is preset, and feature points included in an image captured by the imaging camera facing the calibration pattern from the coordinates of the feature points of the calibration pattern information A predicted image coordinate calculation unit that calculates predicted image coordinates obtained by predicting the coordinates of
The camera model parameter and the calibration pattern relational expression including the internal parameter, the first external parameter, and the second external parameter are included so that the distance between the observed image coordinate and the predicted image coordinate is minimized. A camera model parameter optimizing unit for estimating the camera model parameter by optimizing the evaluation formula;
A camera model parameter estimation device comprising: A third external parameter calculator for calculating a third external parameter for converting the pan head coordinate system to the pan / tilt coordinate system from the pan value and tilt value of the photographing camera facing the calibration pattern;
The initial value generation camera calibration unit further calculates a fourth external parameter for converting the calibration pattern coordinate system in the calibration pattern into the camera coordinate system by the camera calibration,
The second external parameter calculation unit includes:
A conversion equation that associates the first external parameter, the second external parameter, and the third external parameter with respect to the fourth external parameter is preset,
The initial value of the second external parameter is calculated by substituting the initial value of the first external parameter, the third external parameter, and the fourth external parameter into the conversion formula. The camera model parameter estimation apparatus described in 1.   3. The camera model according to claim 1, wherein the feature point extraction unit receives the photographed image from a multi-viewpoint camera that photographs the same subject from different viewpoints as the photographing camera. Parameter estimation device. The second external parameter calculation unit calculates an initial value of the second external parameter for the moved shooting camera,
The camera model parameter optimizing unit optimizes an evaluation formula including the camera model parameter and the calibration pattern relational expression, which are composed of second external parameters of the moved photographing camera, so that the camera of the moved photographing camera The camera model parameter estimation apparatus according to any one of claims 1 to 3, wherein the model parameter is estimated.   The camera model parameter estimation program for functioning a computer as a camera model parameter estimation apparatus as described in any one of Claims 1-4.

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