CN100470590C

CN100470590C - Camera calibration method and calibration device used

Info

Publication number: CN100470590C
Application number: CNB2007100514857A
Authority: CN
Inventors: 郑顺义; 张剑清; 施俊
Original assignee: Wuhan University WHU
Current assignee: Wuhan University WHU
Priority date: 2007-02-05
Filing date: 2007-02-05
Publication date: 2009-03-18
Anticipated expiration: 2027-02-05
Also published as: CN101013505A

Abstract

The invention relates to a calibration device for camera calibration, which is composed of two plane grid plates perpendicular to each other, on the plane grid board there are plane grids and six or more mark points evenly distributed, each mark Points have unique codes. The present invention also provides a method for calibrating a camera, comprising the following steps: (1) collecting the image of the above-mentioned calibration device; (2) carrying out one-to-one correspondence between the image point coordinates of the obtained marker points and the object space coordinates; (3) projecting the plane The grid point obtains the initial value of the pixel coordinate of the grid point; (4) utilizes straight line extraction to intersect to obtain the precise value of the pixel coordinate of the grid point; (5) utilizes three-dimensional direct linear transformation to solve the initial value of the calibration parameter; (6 ) is solved iteratively by beam adjustment to obtain the internal and external orientation elements of the camera. In the present invention, after the calibration device shoots an image, the subsequent calibration process is automatically completed by a computer. Automatic and fast are the advantages of the present invention.

Description

Camera calibration method and calibration device used

技术领域 technical field

本发明属相机标定技术领域，特别是涉及相机标定方法及所用标定装置。The invention belongs to the technical field of camera calibration, and in particular relates to a camera calibration method and a used calibration device.

背景技术 Background technique

求相机内部参数的过程称为标定。利用中心投影的影像恢复三维形状，一般进行相机标定是一个必须的步骤。相机标定的方法有多种。有基于平面标定场进行标定的方法(Z.Zhang：Flexible Camera Calibration by Viewing a Plane from Unknown Orientations.Proc of 7^thInt.Conference on Computer Vision，Kerkyra，Greece.pp.666-673，Sept.1999.)，这种方法需要拍摄至少两张不同角度的影像，因此需要移动平面标定场或相机，难以实现自动化；有基于三维控制场的标定，三维控制场难以维护，而且携带不方便；还有不需要任何标定场的自标定方法，自标定方法计算不稳定，在实际应用中采用的不多。另外，上述方法为了实现像点坐标与物方点坐标的对应，一般都需要人工指定几个点的对应。The process of finding the internal parameters of the camera is called calibration. To restore the 3D shape using the centrally projected image, camera calibration is generally a necessary step. There are several methods of camera calibration. There is a calibration method based on a plane calibration field (Z. Zhang: Flexible Camera Calibration by Viewing a Plane from Unknown Orientations. Proc of 7 ^th Int. Conference on Computer Vision, Kerkyra, Greece.pp.666-673, Sept.1999. ), this method needs to take at least two images from different angles, so it needs to move the plane calibration field or camera, which is difficult to realize automation; there are calibrations based on the 3D control field, which are difficult to maintain and inconvenient to carry; The self-calibration method that requires any calibration field is unstable in calculation and is rarely used in practical applications. In addition, in order to realize the correspondence between image point coordinates and object space point coordinates in the above method, it is generally necessary to manually specify the correspondence of several points.

发明内容 Contents of the invention

本发明针对上述问题，提出了一种简便的相机标定方法及所用标定装置，该方法简便且可以实现像点坐标与物方点坐标的自动对应，最终实现相机的自动标定。Aiming at the above problems, the present invention proposes a simple camera calibration method and the calibration device used. The method is simple and can realize automatic correspondence between image point coordinates and object space point coordinates, and finally realize automatic camera calibration.

本发明提供的技术方案是：一种用于相机标定的标定装置，由两个互相垂直的平面格网板组成，平面格网板上有平面格网和均匀分布的六个或六个以上标志点，每个标志点具有唯一的编码。The technical solution provided by the invention is: a calibration device for camera calibration, which is composed of two mutually perpendicular plane grid plates, on which there are plane grids and six or more uniformly distributed marks Points, each marker point has a unique code.

上述标志点由中心圆及圆环组成，圆环由若干等分弧段组成，每个弧段用黑色或者白色标识，且通过黑色和白色的排列构成每个标志点的唯一的编码。The above-mentioned mark points are composed of a central circle and a ring. The ring is composed of several equally divided arc segments. Each arc segment is marked with black or white, and the unique code of each mark point is formed by the arrangement of black and white.

本发明还提供了利用上述的标定装置标定相机的方法，包括以下步骤：The present invention also provides a method for calibrating a camera using the above calibration device, comprising the following steps:

(1)采集上述标定装置的影像(1) Collect the image of the above calibration device

用待标定相机拍摄标定装置的影像，然后通过计算机对影像进行逐行扫描，得到影像上的六个或六个以上标志点的像点坐标；Take the image of the calibration device with the camera to be calibrated, and then scan the image line by line through the computer to obtain the image point coordinates of six or more marker points on the image;

(2)将步骤(1)得到的标志点的像点坐标与物方坐标进行一一对应(2) Carry out one-to-one correspondence between the image point coordinates of the marker points obtained in step (1) and the object space coordinates

根据步骤(1)得到的标志点的编码以及预先设定的编码与物方坐标的对应关系，确定各标志点对应的物方坐标；According to the coding of the marking points obtained in step (1) and the correspondence between the preset coding and the object coordinates, determine the corresponding object coordinates of each marking point;

(3)投影平面格网点得到平面格网点的像点坐标的初值(3) Project the plane grid points to get the initial value of the image point coordinates of the plane grid points

根据步骤(2)得到的标志点的像点坐标与物方坐标的一一对应关系，建立平面透视变换，计算出影像上其他格网点的像点坐标的初值，并投影在影像上；According to the one-to-one correspondence between the image point coordinates of the marker points obtained in step (2) and the object space coordinates, a plane perspective transformation is established, and the initial values of the image point coordinates of other grid points on the image are calculated, and projected on the image;

(4)利用直线提取求交，获取格网点的像点坐标的精确值；(4) Utilize straight line extraction to intersect, obtain the precise value of the image point coordinate of grid point;

(5)利用三维直接线性变换求解标定参数的初值；(5) Using three-dimensional direct linear transformation to solve the initial value of the calibration parameter;

(6)用光束法平差进行迭代求解，获得相机的内外方位元素。(6) Iteratively solve by beam adjustment to obtain the internal and external orientation elements of the camera.

按照本发明，在上述步骤(1)中用待标定相机拍摄标定场的影像后，通过计算机对影像进行逐行扫描，找出影像上黑色弧段以确定这些黑色弧段所属的标志点；逆时针或顺时针方向绕标志点的中心对标志点的圆环进行360度的扫描，碰到黑色弧段就将该弧段的编码设为1，否则设为0；扫描结束后，任选一个0和1的分界点开始顺序列出，得到二进制码；通过对二进制码循环排序并将这些二进制码转为十进制，取其中的最大值作为该标志点的编码；再进行步骤(2)的操作。According to the present invention, after the image of the calibration field is taken with the camera to be calibrated in the above step (1), the image is scanned line by line by a computer to find out the black arc segments on the image to determine the marker points to which these black arc segments belong; Scan the circle of the marker point clockwise or clockwise around the center of the marker point for 360 degrees. When encountering a black arc segment, set the code of the arc segment to 1, otherwise set it to 0; after scanning, choose one The demarcation points of 0 and 1 are listed in order to obtain binary codes; by cyclically sorting the binary codes and converting these binary codes into decimal, the maximum value is taken as the code of the mark point; and then the operation of step (2) is performed .

本发明方法只需要对标定装置拍摄一张影像，其余过程(标志点的提取与识别、参数解算等)全部由计算机自动完成。本发明标定装置由互相垂直的两个平面组成，造价低廉，构造容易，克服了平面板没有深度信息的缺点，同时比三维控制场易于维护。标定装置上布置了一定数量的具有唯一编码的标志点，能够方便，快速的自动识别，提供足够的识别精度，使像点中心的精度达到子像素，能够避免大部分影像噪声的干扰，可以实现像点坐标与物方点坐标的自动对应，减少人工干预。The method of the present invention only needs to take an image of the calibration device, and the rest of the process (extraction and recognition of marker points, parameter calculation, etc.) are all automatically completed by the computer. The calibration device of the present invention is composed of two planes perpendicular to each other, has low cost and easy structure, overcomes the shortcoming of no depth information on the plane plate, and is easier to maintain than the three-dimensional control field. A certain number of marking points with unique codes are arranged on the calibration device, which can be conveniently and quickly automatically identified and provide sufficient recognition accuracy, so that the accuracy of the center of the image point can reach sub-pixels, which can avoid the interference of most image noise and can realize The automatic correspondence between image point coordinates and object space point coordinates reduces manual intervention.

附图说明 Description of drawings

图1为本发明方法流程框图；Fig. 1 is a flow chart of the method of the present invention;

图2为本发明标定装置示意图；Fig. 2 is a schematic diagram of the calibration device of the present invention;

图3为图2中的标注有二进制编码的标志点示意图。FIG. 3 is a schematic diagram of marker points marked with binary codes in FIG. 2 .

具体实施方式 Detailed ways

一、标定装置1. Calibration device

参见图2，本发明涉及两个互相垂直的平面组成的标定装置，并在两个平面上打上均匀的格网(格网由相互垂直的两组平行直线组成，直线的交点为格网点)。为了能够使像点坐标与物方点坐标一一对应，对每个格网点进行了编号：以O点为中心从下往上，从里到外用个位与十位表示列号，百位与千位表示行号，左边平面万位为1，右边平面万位为0。例如，11211表示左平面第12行11列，706表示右平面第7行第6列。接着在平面格网上摆放了一定数量的带有编码的标志点(下面简称标志点)，目的在于进行标志点的自动识别以及和物方点坐标的自动对应，标志点的形状和分布如图2所示。Referring to Fig. 2, the present invention relates to the calibration device that two mutually perpendicular planes form, and mark uniform grid on two planes (grid is made up of two groups of parallel straight lines perpendicular to each other, and the intersection point of straight line is grid point). In order to enable one-to-one correspondence between the coordinates of the image point and the coordinates of the object space point, each grid point is numbered: from the bottom to the top with the O point as the center, from the inside to the outside, the column number is represented by the ones and tens, and the hundreds and The thousands place represents the line number, the ten thousand place on the left plane is 1, and the ten thousand place on the right plane is 0. For example, 11211 represents the 12th row and 11th column of the left plane, and 706 represents the 7th row and 6th column of the right plane. Then a certain number of coded marker points (hereinafter referred to as marker points) are placed on the plane grid, the purpose is to automatically identify the marker points and automatically correspond to the coordinates of the object space points. The shape and distribution of the marker points are shown in the figure 2.

二、标志点2. Marking points

1.具体设计。实现标志点的设计方案是：标志点的中心是一个圆，在圆点的周围有一圈具有一定宽度，并且被n等份的圆环(建议取n＝4～12)，每个弧段用黑或者白来表示，为了能够对圆环进行编号，黑色弧段用1表示，白色弧段用0表示。在两个平面上布置了一定数量(大于等于6个)的标志点，每个标志点都有一个唯一确定的编码，编码的规则如下介绍。图3显示了一个标志点的结构，在标志点的中心是一个圆，我们可以很方便的求取圆的中心作为该标志点的中心坐标。在圆的周围有一圈被8等份的圆环，每个弧段用黑或者白来表示，为了能够对圆环进行编号，黑色弧段用1表示，白色弧段用用0表示。然后逆时针读取这些编码，很显然根据开始位置的不同，有8种不同的可能：10101011，01010111，10101110，01011101，10111010，01110101，11101010，11010101。在这8个二进制数中，11101010(11101010₂＝234₁₀)是最大值，我们就将234作为该标志点的唯一编号。需要注意的是，并不是所有的正整数都对应着这样的一个编码环，我们只是用所有编码里最大的一个来标识这个标志点。另外一个需要注意的是，这里确定的标志点的编码并不是前面所述的格网点的编号，对于每个标志点对应的格网点的编号需要预先设定好，比如编码为234的标志点对应的格网点编号为11202(参见图2)。1. Specific design. The design scheme to realize the mark point is: the center of the mark point is a circle, and there is a ring with a certain width around the point, which is divided into n equal parts (it is recommended to take n=4~12), and each arc segment is used Black or white to represent, in order to be able to number the ring, the black arc segment is represented by 1, and the white arc segment is represented by 0. A certain number (greater than or equal to 6) of marker points are arranged on two planes, and each marker point has a unique code, and the code rules are introduced as follows. Figure 3 shows the structure of a marker point. The center of the marker point is a circle, and we can easily obtain the center of the circle as the center coordinate of the marker point. There is a ring of 8 equal parts around the circle, and each arc segment is represented by black or white. In order to be able to number the ring, the black arc segment is represented by 1, and the white arc segment is represented by 0. Then read these codes counterclockwise. Obviously, depending on the starting position, there are 8 different possibilities: 10101011, 01010111, 10101110, 01011101, 10111010, 01110101, 11101010, 11010101. Among these 8 binary numbers, 11101010 (11101010 ₂ =234 ₁₀ ) is the maximum value, so we use 234 as the unique number of this marker point. It should be noted that not all positive integers correspond to such a code ring, we just use the largest one among all codes to mark this mark point. Another thing to note is that the code of the marker point determined here is not the number of the grid point mentioned above. The number of the grid point corresponding to each marker point needs to be set in advance. For example, the marker point coded as 234 corresponds to The grid point number is 11202 (see Figure 2).

2.识别。根据影像的特点，利用梯度的变化对影像进行逐行扫描，可以方便快速的得到关于标志点的几块候选黑色区域。由于标志点与格网一起都会被扫描出来，所以在标志识别之前，最好按照如下的顺序对该区域进行判断，排除格网对标志点识别的干扰：2. Identification. According to the characteristics of the image, using the gradient change to scan the image line by line, it is convenient and fast to obtain several candidate black areas of the marker points. Since the marker points and the grid will be scanned together, before the marker recognition, it is best to judge the area in the following order to eliminate the interference of the grid on the marker point recognition:

(1)象素的个数：如果象素的个数太少，排除该区域。(1) Number of pixels: If the number of pixels is too small, exclude this area.

(2)宽度：对圆心和圆环的宽度设定一个最小阈值，排除小于该宽度的区域。(2) Width: Set a minimum threshold for the width of the center of the circle and the ring, and exclude areas smaller than the width.

(3)距离：对圆心到圆环的距离设定一个最大阈值，排除大于该距离的区域。(3) Distance: Set a maximum threshold for the distance from the center of the circle to the ring, and exclude areas greater than this distance.

在只剩下标志点区域的情况下，对标志点的几个区域根据到其他区域距离最短的原则确定该标志点的中心区域，并取该区域的重心为标志点的中心。接着，将中心一周划分为360个刻度，并从中心引出一条射线，从某个方向开始逆时针绕中心进行360度的扫描，碰到标志区域就将该刻度设为1，否则设为0。扫描结束后，对360个刻度联成一个圆环并从一个0，1的分界点开始进行统计，以1/8圆为一个单位大小，如果在一个单位长度内，刻度均为1，则认为这个弧段为1，否则就为0。这样，就将整个圆环转换为一个8位的二进制码。通过对二进制码循环排序并将这些二进制的编码转为十进制作为该编码对应的编码值，根据读取的起始位置不同，有不同的编码值，取所有编码值的最大值作为该标志点的编码，显而易见，每个标志点对应的编码值是唯一的。根据该标志点编码以及预先设定的编码与格网点编号的对应关系，可以确定该标志点对应的物方点的编号。这样，就完成了像点坐标与物方点坐标的一一对应。In the case of only the mark point area, determine the center area of the mark point for several areas of the mark point according to the principle of the shortest distance to other areas, and take the center of gravity of the area as the center of the mark point. Then, divide the center circle into 360 scales, and draw a ray from the center, start from a certain direction to scan 360 degrees counterclockwise around the center, set the scale to 1 when it touches the marked area, otherwise set it to 0. After scanning, 360 scales are connected into a ring and counted from a 0, 1 dividing point, with 1/8 circle as a unit size, if the scales are all 1 within a unit length, it is considered 1 for this segment, 0 otherwise. In this way, the entire ring is converted into an 8-bit binary code. By cyclically sorting the binary codes and converting these binary codes into decimals as the code values corresponding to the codes, there are different code values depending on the starting position of the reading, and the maximum value of all code values is taken as the code value of the mark point Encoding, obviously, the encoding value corresponding to each marker point is unique. According to the marker point code and the preset correspondence between the code and the grid point number, the number of the object space point corresponding to the marker point can be determined. In this way, the one-to-one correspondence between the image point coordinates and the object space point coordinates is completed.

3.获取坐标。根据得到的这些标志点的像点坐标及相应的物方坐标值，建立平面透视变换，计算出影像上其他格网点的像点坐标的初值，并投影在影像上。经平面透视变换计算出来的像点坐标并不十分的准确，为了获得格网点的精确坐标，采用直线提取求交的方法(如直线模板匹配法)，求出格网初值点附近相交的2段直线的精确位置，并将它们的交点作为格网点的精确坐标。3. Get the coordinates. According to the image point coordinates of these marker points and the corresponding object space coordinate values obtained, a plane perspective transformation is established, and the initial values of the image point coordinates of other grid points on the image are calculated, and projected on the image. The image point coordinates calculated by the plane perspective transformation are not very accurate. In order to obtain the precise coordinates of the grid points, the method of extracting and intersecting straight lines (such as the straight line template matching method) is used to find the 2 points that intersect near the initial value points of the grid. The precise position of the segment lines, and their intersections as the precise coordinates of the grid points.

三标定方法：Three calibration methods:

1 理论基础1 Theoretical basis

直接线性变换(directlineartransformation DLT)是建立像点坐标和物点坐标直接线性关系的算法，处理时不需要摄像机内外方位元素的初值。因此利用三维直接线性变换来求取摄影机的初值，3D DLT模型可表示为：Direct linear transformation (direct linear transformation DLT) is an algorithm that establishes a direct linear relationship between image point coordinates and object point coordinates, and does not require the initial value of the camera's internal and external orientation elements during processing. Therefore, using three-dimensional direct linear transformation to obtain the initial value of the camera, the 3D DLT model can be expressed as:

$x x = = \frac{{L L}_{11} X x + + {L L}_{22} Y Y + + {L L}_{33} Z Z + + {L L}_{44}}{{L L}_{99} X x + + {L L}_{1010} Y Y + + {L L}_{1111} Z Z + + 11}$

$y = \frac{L_{5} X + L_{6} Y + L_{7} Z + L_{8}}{L_{9} X + L_{10} Y + L_{11} Z + 1}$ (1) $the y = \frac{L_{5} x + L_{6} Y + L_{7} Z + L_{8}}{L_{9} x + L_{10} Y + L_{11} Z + 1}$ (1)

式(1)中，L₁，L₂，L₃，L₄，L₅，L₆，L₇，L₈，L₉，L₁₀，L₁₁为三维直接线性变换的11个变换参数；X，Y，Z是三维控制场中格网点的空间坐标；x，y是相应的像坐标。为了求解这11个参数，至少需要已知6个像点及其对应的物方点的空间坐标。当像点个数大于6个时，可用最小二乘来求解这个超定方程组。In formula (1), L ₁ , L ₂ , L ₃ , L ₄ , L ₅ , L ₆ , L ₇ , L ₈ , L ₉ , L ₁₀ , and L ₁₁ are the 11 transformation parameters of three-dimensional direct linear transformation; X , Y, Z are the space coordinates of grid points in the three-dimensional control field; x, y are the corresponding image coordinates. In order to solve these 11 parameters, at least 6 image points and the spatial coordinates of their corresponding object space points need to be known. When the number of image points is greater than 6, the least squares can be used to solve the overdetermined equations.

摄影时相机的内方位元素x₀.y₀.f和外方位元素

ω，κ，X_s，Y_s，Z_s都已经包含在L₁至L₁₁的系数中，经反算可以得出：Camera's inner orientation element x ₀ .y ₀ .f and outer orientation element during photography

ω, κ, X _s , Y _s , and Z _s are all included in the coefficients from L ₁ to L ₁₁ , and can be obtained by inverse calculation:

内方位元素：Inner Orientation Elements:

x₀＝(L₁L₉+L₂L₁₀+L₃L₁₁)L′x ₀ =(L ₁ L ₉ +L ₂ L ₁₀ +L ₃ L ₁₁ )L'

y₀＝(L₅L₉+L₆L₁₀+L₇L₁₁)L′y ₀ =(L ₅ L ₉ +L ₆ L ₁₀ +L ₇ L ₁₁ )L'

${f f}_{x x} = = - - {x x}_{00}^{22} + + (({L L}_{11}^{22} + + {L L}_{22}^{22} + + {L L}_{33}^{22})) L L' ' - - - - - - ((22))$

${f f}_{y the y} = = - - {y the y}_{00}^{22} + + (({L L}_{55}^{22} + + {L L}_{66}^{22} + + {L L}_{77}^{22})) L L' '$

f＝(f_x+f_y)/2f＝(f _x +f _y )/2

其中 ${L'}^{2} = 1 / (L_{9}^{2} + L_{10}^{2} + L_{11}^{2});$ in ${L'}^{2} = 1 / (L_{9}^{2} + L_{10}^{2} + L_{11}^{2});$

外方位元素；outer orientation element;

$\begin{matrix} {L L}_{11} {X x}_{s the s} + + {L L}_{22} {Y Y}_{s the s} + + {L L}_{33} {Z Z}_{s the s} = = - - {L L}_{44} \\ {L L}_{55} {X x}_{s the s} + + {L L}_{66} {Y Y}_{s the s} + + {L L}_{77} {Z Z}_{s the s} = = - - {L L}_{88} \\ {L L}_{99} {X x}_{s the s} + + {L L}_{1010} {Y Y}_{s the s} + + {L L}_{1111} {Z Z}_{s the s} = = - - 11 \end{matrix}\} - - - - - - ((33))$

a₃＝L₉L′a ₃ =L ₉ L'

b₃＝L₁₀L′b ₃ =L ₁₀ L'

(4)(4)

c₃＝L₁₁L′c ₃ =L ₁₁ L'

a₂＝(L₅+L₉y₀)L′/f_x a ₂ =(L ₅ +L ₉ y ₀ )L'/f _x

解得像片的各L系数后，即可根据上述各关系式解求相应像片的9个独立的参数。并把它作为光束法平差的初值。After solving the L coefficients of the photo, the nine independent parameters of the corresponding photo can be solved according to the above-mentioned relational expressions. And use it as the initial value of bundle adjustment.

解算出相机的内外方位元素初值后，接着可用摄影测量中常用的光束法平差进行相机的标定。对非专业相机，镜头的畸变一般比较大，考虑径向畸变和偏心畸变的影响，采用如下的改正模型：After calculating the initial value of the camera's internal and external orientation elements, the camera can then be calibrated using bundle adjustment commonly used in photogrammetry. For non-professional cameras, the distortion of the lens is generally relatively large. Considering the influence of radial distortion and eccentric distortion, the following correction model is adopted:

Δx＝(x-x₀)(k₁r²+k₂r⁴)+p₁(r²+2(x-x₀)²)+2p₂(x-x₀)(y-y₀)Δx＝(xx ₀ )(k ₁ r ² +k ₂ r ⁴ )+p ₁ (r ² +2(xx ₀ ) ² )+2p ₂ (xx ₀ )(yy ₀ )

(6) (6)

Δy＝(y-y₀)(k₁r²+k₂r⁴)+p₁(r²+2(y-y₀)²)+2p₂(x-x₀)(y-y₀)Δy=(yy ₀ )(k ₁ r ² +k ₂ r ⁴ )+p ₁ (r ² +2(yy ₀ ) ² )+2p ₂ (xx ₀ )(yy ₀ )

其中，r²＝(x-x₀)²+(y-y₀)²；k₁，k₂称为径向畸变差，p₁，p₂是偏心畸变差将该畸变带入共线条件方程[7，8]：Among them, r ² =(xx ₀ ) ² +(yy ₀ ) ² ; k ₁ and k ₂ are called the radial distortion difference, p ₁ and p ₂ are the eccentric distortion difference and bring the distortion into the collinear conditional equation [7, 8]:

$x x - - {x x}_{00} - - Δx Δx = = - - {f f}_{x x} \frac{{a a}_{11} ((X x - - {X x}_{s the s})) + + {b b}_{11} ((Y Y - - {Y Y}_{s the s})) + + {c c}_{11} ((Z Z - - {Z Z}_{s the s}))}{{a a}_{33} ((X x - - {X x}_{s the s})) + + {b b}_{33} ((Y Y - - {Y Y}_{s the s})) + + {c c}_{33} ((Z Z - - {Z Z}_{s the s}))}$

$y - y_{0} - Δy = - f_{x} \frac{a_{2} (X - X_{s}) + b_{2} (Y - Y_{s}) + c_{2} (Z - Z_{s})}{a_{3} (X - X_{s}) + b_{3} (Y - Y_{s}) + c_{3} (Z - Z_{s})}$ (7) $the y - {the y}_{0} - Δy = - f_{x} \frac{a_{2} (x - x_{the s}) + b_{2} (Y - Y_{the s}) + c_{2} (Z - Z_{the s})}{a_{3} (x - x_{the s}) + b_{3} (Y - Y_{the s}) + c_{3} (Z - Z_{the s})}$ (7)

对上式用泰勒公式线性化得到误差方程式：Linearize the above formula with Taylor's formula to get the error equation:

$+ + \frac{δx δx}{δ δ {Z Z}_{s the s}} Δ Δ {Z Z}_{s the s} + + \frac{δx δx}{δ δ {k k}_{11}} Δ Δ {k k}_{11} + + \frac{δx δx}{δ δ {k k}_{22}} Δ Δ {k k}_{22} + + \frac{δx δx}{δ δ {p p}_{11}} Δ Δ {p p}_{11} + + \frac{δx δx}{δ δ {p p}_{22}} Δ Δ {p p}_{22} + + \frac{δx δx}{δX δX} ΔX ΔX + + \frac{δx δx}{δY δY} ΔY ΔY + + \frac{δx δx}{δZ δZ} ΔZ ΔZ - - {l l}_{x x}$

各系数Coefficients

$+ + \frac{δy δy}{δ δ {Z Z}_{s the s}} Δ Δ {Z Z}_{s the s} + + \frac{δy δy}{δ δ {k k}_{11}} Δ Δ {k k}_{11} + + \frac{δy δy}{δ δ {k k}_{22}} Δ Δ {k k}_{22} + + \frac{δy δy}{δ δ {p p}_{11}} Δ Δ {p p}_{11} + + \frac{δy δy}{δ δ {p p}_{22}} Δ Δ {p p}_{22} + + \frac{δy δy}{δX δX} ΔX ΔX + + \frac{δy δy}{δY δY} ΔY ΔY + + \frac{δy δy}{δZ δZ} ΔZ ΔZ - - {l l}_{y the y}$

值及常数值通过对共线方程求偏导得到。Values and constants are obtained by taking partial derivatives of collinear equations.

2 实现过程(参见图1)2 Implementation process (see Figure 1)

(1)本发明标定装置是2块互相垂直的平板组成，在每个平面上布置了平面格网，除此之外，还有一些均匀分布的标志点。(1) The calibration device of the present invention is composed of two mutually perpendicular flat plates, and a plane grid is arranged on each plane. Besides, there are some evenly distributed marking points.

(2)采集影像前，调整好标定装置与相机的距离，使成像清晰，并且相机的像幅能够包括所有的标志点，采集一张影像输入计算机。(2) Before collecting the image, adjust the distance between the calibration device and the camera to make the image clear, and the image frame of the camera can include all the marker points, and collect an image and input it into the computer.

(3)由计算机自动提取标志点并解码。(3) Automatically extract and decode marker points by computer.

(4)投影格网点，并进行格网点精确对准(参见具体实施方式二、3)。(4) Projecting the grid points and performing precise alignment of the grid points (see specific implementation methods 2 and 3).

(5)三维DLT变换求标定初值，然后用光束法平差进行迭代求解，获得相机的内外方位元素，即实现了相机的标定。(5) Three-dimensional DLT transformation is used to calculate the initial calibration value, and then iteratively solves it by beam adjustment to obtain the internal and external orientation elements of the camera, which realizes the calibration of the camera.

显然，本领域的技术人员可以对本发明进行适当的调整和变形而不脱离本发明的精神和范围。这样，倘若这些调整和变形属于本发明要求及其等同技术的范畴，则本发明也意图包含这些调整和变形在内。Obviously, those skilled in the art can make appropriate adjustments and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these adjustments and modifications belong to the requirements of the present invention and the scope of equivalent technologies, the present invention also intends to include these adjustments and modifications.

Claims

1. caliberating device that is used for camera calibration, it is characterized in that: be made up of two mutually perpendicular planar grid plates, planar grid and equally distributed six or six above monumented points are arranged on the planar grid plate, each monumented point has unique encoding.

2. caliberating device according to claim 1, it is characterized in that: monumented point is made up of center circle and annulus, annulus is made up of some five equilibrium segmental arcs, and each segmental arc identifies with black or white, and constitutes the unique encoding of each monumented point by the arrangement of black and white.

3. the method for utilizing the described caliberating device of claim 1 to demarcate camera is characterized in that may further comprise the steps:

(1) image of the described caliberating device of collection claim 1

With the image of camera shooting caliberating device to be calibrated, by computing machine image is lined by line scan then, obtain the picpointed coordinate of six or six above monumented points on the image;

(2) picpointed coordinate of the monumented point that step (1) is obtained carries out corresponding one by one with object coordinates

The coding of the monumented point that obtains according to step (1) and the corresponding relation of predefined coding and object coordinates are determined the object coordinates of each monumented point correspondence;

(3) the projection plane grid points obtains the initial value of the picpointed coordinate of planar grid point

The picpointed coordinate of the monumented point that obtains according to step (2) and the one-to-one relationship of object coordinates are set up the plane perspective conversion, calculate the initial value of the picpointed coordinate of other grid points on the image, and are projected on the image;

(4) utilize straight line to extract and ask friendship, obtain the exact value of the picpointed coordinate of grid points;

(5) utilize three-dimensional direct linear transformation to find the solution the initial value of calibrating parameters;

(6) carry out iterative with bundle adjustment, obtain the s internal and external orientation of camera.

4. the method for utilizing the described caliberating device of claim 2 to demarcate camera is characterized in that may further comprise the steps:

(1) image of the described caliberating device of collection claim 2

Take the image of caliberating device with camera to be calibrated, by computing machine image is lined by line scan then, find out black segmental arc on the image to determine the monumented point under these black segmental arcs; Counterclockwise or clockwise direction is carried out the scannings of 360 degree around the center of monumented point to the annulus of monumented point, runs into the black segmental arc and just the coding of this segmental arc is made as 1, otherwise be made as 0; Behind the end of scan, optional one 0 and 1 separation begin order to be listed, and obtains binary code; By transferring the decimal system to, get wherein maximal value as the coding of this monumented point to the binary code cyclic ordering and with these binary codes;

(2) picpointed coordinate of the monumented point that step (1) is obtained carries out corresponding one by one with the object space point coordinate

The coding of the monumented point that obtains according to step (1) and the corresponding relation of predefined coding and object space point coordinate are determined the object space point coordinate of each monumented point correspondence;

The picpointed coordinate of the monumented point that obtains according to step (2) and the one-to-one relationship of object space point coordinate are set up the plane perspective conversion, calculate the initial value of the picpointed coordinate of other grid points on the image, and are projected on the image;