JP2005308641A - Camera calibration apparatus and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a camera calibration apparatus having a simple structure and a method which do not require points of measurements of which the three-dimensional positions are known, the correspondence between the points of measurement, or synchronization between cameras when images are acquired. <P>SOLUTION: A plurality of items of position data in the locus of movement of an object moving within a range of measurement common for a plurality of stereoscopic cameras 4 and 5 are measured in coordinate systems centered at the stereoscopic cameras 4 and 5. Since the coordinate systems of the stereoscopic cameras 4 and 5 are arranged differently, the plurality of items of position data, measured in this way by the stereoscopic cameras 4 and 5, are numerically different from each other, but their shapes of distribution are identical. For converting the state of distribution of the position data into a numerical form, principal component analysis is performed on the position data to constitute a coordinate system common for the stereoscopic cameras and estimate the relative arrangement of the coordinate systems of the stereoscopic cameras 4 and 5 via the common coordinate system. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a camera calibration apparatus and method for obtaining various characteristics and parameters of a camera used for image acquisition.

  Camera calibration includes an operation of estimating optical distortion caused by a lens, an operation of estimating camera-specific parameters such as a focal length and an image center, and an operation of estimating parameters representing the position and orientation of the camera.

  Conventionally, a calibration object with a known three-dimensional shape is used in estimating parameters representing the position and orientation of a camera, that is, a translation vector and a rotation matrix (for example, see Non-Patent Documents 1 and 2).

FIG. 1 is a diagram for explaining an estimation principle of a translation vector and a rotation matrix in a conventional camera calibration apparatus. In FIG. 1, four measurement points o, p ₁ , p ₂ , and p ₃ of the calibration object 1 whose three-dimensional positions are known are provided within a common visual field of a plurality of stereo cameras. It is assumed that the _three vectors constituted by the point o and the point p ₁ , the point o and the point p _2, and the point o and the point p ₃ are orthogonal to each other. In FIG. 1 and FIG. 2 to be described later, i represents a natural number of 1 or more, and j represents a natural number larger than i.

と表す。これらの点は、

とする３次元座標値を有するものとする。 The four measurement points o, p ₁ , p ₂ , and p ₃ measured at the coordinate system at the center of each stereo camera and measured by the i-th stereo camera 2. Dot

It expresses. These points

And having a three-dimensional coordinate value.

と点

及び点

と点

が３次元空間内の同一の点であるという情報が必要となる。これらの情報を基にして、これら４点から構成される三つのベクトルを

と表すものとする。 In this case, it is necessary to take correspondence between points measured by each camera. That is, with the conventional method,

And point

And points

And point

Is required to be the same point in the three-dimensional space. Based on these information, three vectors composed of these four points are

It shall be expressed as

と

はそれぞれ、第ｉ番目のステレオカメラ２の座標系Σ_Ｓｉから共有座標系Σ_Ｗへの回転行列及び並進ベクトルを表すものとする。これらの回転行列及び並進ベクトルは、上記４点の情報を用いて次のように表すことができる。

here

When

Respectively shall be the i-th coordinate system sigma _Si of the stereo camera 2 represents the rotation matrix and the translation vector to the shared coordinate system sigma _W. These rotation matrices and translation vectors can be expressed as follows using the information of the above four points.

と

はそれぞれ次のように表すことができる。

このようにして、２個のステレオカメラ２，３の座標系間の相対位置を表す回転行列及び並進ベクトルを求めることができるようになる。
高橋裕信等 「ロボットビジョンのためのカメラキャリブレーション」、日本ロボット学会誌 Vol. 10, No. 2, pp.177~pp. 184, 1992 R. Tsai. A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses, IEEE Journal of Robotics and Automation, Vol. 3, No. 4, pp.323-344, 1987 Using these relationships, the i-th rotation matrix from the coordinate system sigma _Si of the stereo camera 2 to the j-th of the stereo camera 3 in the coordinate system sigma _Sj

When

Can be expressed as follows.

In this way, a rotation matrix and a translation vector representing the relative positions between the coordinate systems of the two stereo cameras 2 and 3 can be obtained.
Hironobu Takahashi et al. “Camera Calibration for Robot Vision”, Journal of the Robotics Society of Japan Vol. 10, No. 2, pp.177-pp. 184, 1992 R. Tsai.A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses, IEEE Journal of Robotics and Automation, Vol. 3, No. 4, pp.323-344, 1987

  However, when the translation vector and the rotation matrix are estimated in the conventional camera calibration apparatus, it is necessary to provide a measurement point whose three-dimensional position is known and a correspondence between these measurement points in order to construct a common coordinate system. In order to estimate the relative arrangement between a plurality of cameras, it is necessary to synchronize when acquiring images between the cameras.

  SUMMARY OF THE INVENTION An object of the present invention is to provide a camera calibration apparatus and method having a simple configuration that does not need to provide measurement points with known three-dimensional positions, correspondence between these measurement points, and synchronization when acquiring images between cameras. Is to provide.

The camera calibration device according to the present invention comprises:
A camera calibration device for a plurality of stereo cameras arranged to have a common measurement range,
Means for measuring a plurality of position data in a movement trajectory of an object moving in the common measurement range in a coordinate system of the center of the stereo camera;
The position data is subjected to principal component analysis to form a common coordinate system for the stereo cameras, and a means for estimating a relative arrangement between the coordinate systems of the stereo cameras via the common coordinate system is provided. It is characterized by that.

The camera calibration method according to the present invention includes:
A method for calibrating a plurality of stereo cameras arranged to have a common measurement range,
Measuring a plurality of position data in a movement trajectory of an object moving in the common measurement range in a coordinate system of the center of the stereo camera; and
Analyzing the position data to form a coordinate system common to the stereo cameras, and estimating a relative arrangement between the coordinate systems of the stereo cameras via the common coordinate system. It is characterized by that.

  According to the present invention, when performing camera calibration of a plurality of stereo cameras arranged so as to have a common measurement range, a plurality of position data in the movement trajectory of an object moving in the common measurement range is converted into a stereo camera. Measure each in the center coordinate system.

  The position data for each stereo camera thus measured is numerically different because the arrangement of the coordinate system of the stereo camera is different from each other, but the distribution shape is the same. Therefore, in order to quantify the distribution of position data, the position data is principally analyzed to form a common coordinate system for the stereo cameras, and between the stereo camera coordinate systems via the common coordinate system. By estimating the relative placement, translation vectors and rotation matrices can be estimated.

  As a result, it is no longer necessary to provide measurement points whose three-dimensional positions are known, correspondence between these measurement points, and synchronization when acquiring images between cameras, and camera calibration can be performed with a simple configuration. Become.

Embodiments of a camera calibration apparatus and method according to the present invention will be described in detail with reference to the drawings.
FIG. 2 is a diagram for explaining the principle of translation vector and rotation matrix estimation in the camera calibration apparatus according to the present invention. The present invention estimates the relative positional relationship between stereo cameras by calibration based on principal component analysis of a plurality of stereo cameras.

  As described above, if a coordinate system fixed in the environment within the common field of view of a plurality of stereo cameras is created, the relative positional relationship between the stereo cameras can be estimated. Therefore, the point to be measured is moved within the common visual field, and the three-dimensional position of the moving point is measured in the coordinate system of each stereo camera. By using a stereo camera, the three-dimensional position of the measurement point can be acquired.

と表すことにし、

とする３次元座標値を有するものとする。この際、ステレオカメラの各々で計測された点同士の対応をとる必要がない。すなわち、点

と

とは、３次元空間内の同一の点であるという条件を満足する必要がない。 It is assumed that N _i pieces of data of the three-dimensional positions of the measured points have been acquired for the i-th stereo camera 4. Where these N _i points are

And

And having a three-dimensional coordinate value. At this time, it is not necessary to take correspondence between points measured by each stereo camera. That is, the point

When

Does not have to satisfy the condition that they are the same point in the three-dimensional space.

とする。固有ベクトルの性質から、これら三つの固有ベクトルは互いに直交している。また、共分散行列を求めるときに、既に求められている平均値ベクトルを

とする。ここで、以下のような関係が成立する。

The N _i number of 3-dimensional coordinate data in the coordinate system of each of the stereo camera principal component analysis. That is, the covariance matrix C ⁱ of N _i three-dimensional coordinate data is calculated, and the covariance matrix is subjected to eigenvalue decomposition. The eigenvector obtained as a result of eigenvalue decomposition is

And Due to the nature of the eigenvectors, these three eigenvectors are orthogonal to each other. In addition, when calculating the covariance matrix, the average value vector already determined is

And Here, the following relationship is established.

  The position in the three-dimensional space indicated by the average value vector related to the coordinate system of each stereo camera and the direction in the three-dimensional space represented by the three eigenvectors are actually all the same. ing. This corresponds to observing one coordinate system (referred to as a “shared coordinate system”) from the coordinate system of each stereo camera, and between the coordinate systems of the stereo camera via this shared coordinate system. Can be estimated.

と

はそれぞれ、第ｉ番目のステレオカメラ４の座標系Σ_Ｓｉから共有座標系Σ_Ｅへの回転行列及び並進ベクトルを表すものとする。これら回転行列及び並進ベクトルは、上記固有ベクトル及び平均値ベクトルを用いて以下のように表すことができる。

here,

When

Respectively shall be the coordinate system sigma _Si of the i-th of the stereo camera 4 represents the rotation matrix and the translation vector to the shared coordinate system sigma _E. These rotation matrix and translation vector can be expressed as follows using the above eigenvectors and average vector.

と並進ベクトル

はそれぞれ、以下のように表すことができる。

このようにして、二つのステレオカメラ４，５の座標系間の相対的配置を表す回転行列及び並進ベクトルを求めることができる。 Using these relationships, the rotation matrix from the coordinate system sigma _Si of the i-th of the stereo camera 4 to the coordinate system sigma _Sj of the j-th of the stereo camera 5

And translation vector

Each can be expressed as:

In this way, a rotation matrix and a translation vector representing the relative arrangement between the coordinate systems of the two stereo cameras 4 and 5 can be obtained.

  Next, for each stereo camera, the movement locus of the colored measurement points that are arbitrarily moved within the common field of view of the two stereo cameras (hereinafter referred to as “stereo camera a” and “stereo camera b”). Explain the results of the recorded experiment. FIG. 3 is a diagram showing a movement locus in the stereo camera a, and FIG. 4 is a diagram showing a movement locus in the stereo camera b. In this experiment, 100 movement trajectory data were acquired with the stereo camera a, and 76 movement trajectory data were acquired with the stereo camera b. From these movement trajectory data, a rotation matrix and a translation vector representing a relative arrangement between the stereo camera a and the stereo camera b are obtained by the calculation method described with reference to FIG.

表１に示すように、変換された移動軌跡データとステレオカメラａで計測された移動軌跡データとがほぼ一致していることがわかる。 FIG. 5 shows a relative arrangement of the stereo cameras a and b estimated by the obtained rotation matrix and translation vector. Further, in order to evaluate the obtained rotation matrix and translation vector, the measurement points are measured using the stereo camera a and the stereo camera b at the four places 1 to 4 in the common visual field, and measured by the stereo camera b. The obtained movement locus data is converted into movement locus data relating to the coordinate system of the stereo camera a, and it is confirmed whether or not the converted movement locus data matches the movement locus data measured by the stereo camera a. The measurement point was measured 100 times, and the average value was taken as the three-dimensional position of the measurement point. Table 1 shows the measurement position of the stereo camera a and the measurement position of the stereo camera b after coordinate conversion.

As shown in Table 1, it can be seen that the converted movement trajectory data and the movement trajectory data measured by the stereo camera a substantially coincide.

  According to the present embodiment, since it is not necessary to provide measurement points whose three-dimensional positions are known, correspondence between these measurement points, and synchronization when acquiring images between cameras, camera calibration can be performed with a simple configuration. It can be carried out.

The present invention is not limited to the above-described embodiment, and many changes and modifications can be made.
For example, in the above embodiment, the case where measurement is performed using an orthogonal coordinate system as a three-dimensional coordinate system has been described, but the present invention can also be applied to the case where measurement is performed using a polar coordinate system.

  The present invention can be applied to fields such as a non-contact three-dimensional position measurement device, a biological behavior measurement device, and a human interface device used in various information systems.

It is a figure for demonstrating the estimation principle of the translation vector and rotation matrix in the conventional camera calibration apparatus. It is a figure for demonstrating the estimation principle of the translation vector and rotation matrix in the camera calibration apparatus by this invention. It is a figure which shows the movement locus | trajectory in the stereo camera a. It is a figure which shows the movement locus | trajectory in the stereo camera b. The relative arrangement | positioning of the stereo camera a and the stereo camera b estimated by the calculated | required rotation matrix and translation vector is shown.

Explanation of symbols

1 Calibration object 2, 3, 4, 5 Stereo camera

Claims (2)

A camera calibration device for a plurality of stereo cameras arranged to have a common measurement range,
Means for measuring a plurality of position data in a movement trajectory of an object moving in the common measurement range in a coordinate system of the center of the stereo camera;
The position data is subjected to principal component analysis to form a common coordinate system for the stereo cameras, and a means for estimating a relative arrangement between the coordinate systems of the stereo cameras via the common coordinate system is provided. A camera calibration device characterized by that. A method for calibrating a plurality of stereo cameras arranged to have a common measurement range,
Measuring a plurality of position data in a movement trajectory of an object moving in the common measurement range in a coordinate system of the center of the stereo camera; and
Analyzing the position data to form a coordinate system common to the stereo cameras, and estimating a relative arrangement between the coordinate systems of the stereo cameras via the common coordinate system. A camera calibration method characterized by the above.

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