CN1896682A

CN1896682A - X-shaped angular-point sub-pixel extraction

Info

Publication number: CN1896682A
Application number: CNA200510082766XA
Authority: CN
Inventors: 张广军; 陈大志; 王颖
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2005-07-12
Filing date: 2005-07-12
Publication date: 2007-01-17

Abstract

The invention belongs to the calibration technology of a three-dimensional visual detection system, and relates to the improvement of an X-shaped corner point sub-pixel extraction method. The extraction step of the present invention is: determine the pixel position of the X-shaped corner point according to the Hessian matrix; then use the second-order Taylor expansion to describe the gray value in the area around the point, and its saddle point is the sub-pixel position of the X-shaped corner point. The extraction process of the invention is simple and fast. Even in the case of image distortion and large noise, it still has high extraction accuracy.

Description

A method for sub-pixel extraction of X-shaped corner points

技术领域technical field

本发明属于三维视觉检测系统标定技术，涉及对X型角点亚像素提取方法的改进。The invention belongs to the calibration technology of a three-dimensional visual detection system, and relates to the improvement of an X-shaped corner point sub-pixel extraction method.

背景技术Background technique

标定点的提取是三维视觉检测系统标定过程中的重要环节，通常为了保证系统标定结果的精度及稳定性，要求标定点的提取精度要在亚像素级。X型角点(见图1)由于其易于识别、提取方法简单及提取精度高在视觉检测系统的标定中应用十分广泛，传统的亚像素提取方法主要有：The extraction of calibration points is an important link in the calibration process of the 3D visual inspection system. Usually, in order to ensure the accuracy and stability of the system calibration results, the extraction accuracy of the calibration points is required to be at the sub-pixel level. X-shaped corner points (see Figure 1) are widely used in the calibration of visual inspection systems due to their easy identification, simple extraction method and high extraction accuracy. The traditional sub-pixel extraction methods mainly include:

(1)Harris角点提取。(1) Harris corner extraction.

Harris算子是一种比较常用的特征点提取算子，主要是根据特征点附近区域内图像灰度变化的相关度来判定特征点的形状。基于Harris的X型角点亚像素提取通常先根据Harris算子判定角点的像素位置，然后利用插值算法计算该点附近区域内亚像素位置点的灰度值，并根据这些点拟合局部图像的灰度分布曲面，再计算该曲面的鞍点即为X型角点的亚像素位置。该方法的优点是提取精度高，缺点是计算复杂，提取过程繁琐。The Harris operator is a commonly used feature point extraction operator, which mainly determines the shape of the feature point according to the correlation degree of the image gray level change in the area near the feature point. Harris-based X-type corner point sub-pixel extraction usually first determines the pixel position of the corner point according to the Harris operator, and then uses an interpolation algorithm to calculate the gray value of the sub-pixel position point in the area around the point, and fits the local image based on these points The gray distribution surface of the surface, and then calculate the saddle point of the surface, which is the sub-pixel position of the X-shaped corner point. The advantage of this method is that the extraction accuracy is high, and the disadvantage is that the calculation is complicated and the extraction process is cumbersome.

(2)边缘拟合求交点。(2) Edge fitting to find the intersection point.

该方法主要是利用Sobel等边缘算子提取角点附近区域内黑白块的边缘点，并利用直线拟合计算两边缘的直线方程，则两直线的交点即为X型角点的亚像素位置。该方法的优点是提取过程简单，缺点是当图像存在畸变或较大噪声时，提取精度不高。This method mainly uses edge operators such as Sobel to extract the edge points of black and white blocks in the area near the corner points, and uses straight line fitting to calculate the straight line equation of the two edges, then the intersection of the two straight lines is the sub-pixel position of the X-shaped corner point. The advantage of this method is that the extraction process is simple, but the disadvantage is that the extraction accuracy is not high when there is distortion or large noise in the image.

发明内容Contents of the invention

本发明的目的是：针对现有方法的不足，提出一种提取过程简单、精度高的X型角点的亚像素提取方法。The object of the present invention is to propose a sub-pixel extraction method of X-shaped corner points with simple extraction process and high precision for the deficiencies of the existing methods.

本发明的技术方案是：一种X型角点亚像素提取方法，其特征在于，提取步骤如下：The technical solution of the present invention is: a method for extracting X-shaped corner sub-pixels, characterized in that the extraction steps are as follows:

1、根据Hessian矩阵判定X型角点的像素位置；Hessian矩阵的表达式如式1所示：1. Determine the pixel position of the X-shaped corner point according to the Hessian matrix; the expression of the Hessian matrix is shown in formula 1:

$H h = = [\begin{matrix} {f f}_{xx xx} & {f f}_{xy xy} \\ {f f}_{xy xy} & {f f}_{yy yy} \end{matrix}] - - - - - - ((11))$

其中，f_xx、f_xy、f_yy分别为图像灰度相对于x、y的二阶偏导数，可以通过图像灰度与相应微分形式的高斯算子卷积得到，对于X型角点，Hessian矩阵的两个特征值一个为正，另一个为负，则判定其像素位置的算子s表示为：Among them, f _xx , f _xy , and f _yy are the second-order partial derivatives of the image grayscale with respect to x and y, respectively, which can be obtained by convolving the image grayscale with the Gaussian operator in the corresponding differential form. For X-shaped corner points, Hessian One of the two eigenvalues of the matrix is positive and the other is negative, then the operator s to determine its pixel position is expressed as:

$S S = = {λ λ}_{11} \cdot &Center Dot; {λ λ}_{22} = = {f f}_{xx xx} {f f}_{xy xy} - - {f f}_{xy xy}^{22} - - - - - - ((22))$

其中，λ₁、λ₂为Hessian矩阵的特征值；Among them, λ ₁ and λ ₂ are the eigenvalues of the Hessian matrix;

2、确定X型角点的亚像素位置；2. Determine the sub-pixel position of the X-shaped corner;

在判定角点的像素位置后，利用一个二阶泰勒展开式描述该点附近区域内任意一点的灰度值，其表达式为：After determining the pixel position of the corner point, a second-order Taylor expansion is used to describe the gray value of any point in the area near the point, and the expression is:

$r r (({x x}_{00} + + s the s,, {y the y}_{00} + + t t)) = = {r r}_{00} + + [\begin{matrix} s the s & t t \end{matrix}] [\begin{matrix} {r r}_{x x} \\ {r r}_{y the y} \end{matrix}] + + \frac{11}{22} [\begin{matrix} s the s & t t \end{matrix}] [\begin{matrix} {r r}_{xx xx} & {r r}_{xy xy} \\ {r r}_{xy xy} & {r r}_{xy xy} \end{matrix}] [\begin{matrix} s the s \\ t t \end{matrix}] - - - - - - ((33))$

其中，(x₀，y₀)是角点的像素位置，r₀为该点的灰度，r_x、r_y、r_xx、r_xy、r_yy分别为该点灰度相对于x、y的一二阶偏导数，s，t为角点相对于(x₀，y₀)的亚像素位置，经过低通滤波后角点附近区域图像灰度的分布曲面为一平滑鞍面，其鞍点即X型角点的亚像素位置，根据鞍点的性质，在式(3)的基础上得到确定鞍点位置的线性方程组：Among them, (x ₀ , y ₀ ) is the pixel position of the corner point, r ₀ is the gray level of the point, r _x , _ry , r _xx , r _xy , ry _yy are the gray level of the point relative to x, y The first and second order partial derivatives of , s, t are the sub-pixel position of the corner point relative to (x ₀ , y ₀ ). After low-pass filtering, the distribution surface of the image gray level near the corner point is a smooth saddle surface, and the saddle point That is, the sub-pixel position of the X-shaped corner point. According to the nature of the saddle point, the linear equation system for determining the position of the saddle point is obtained on the basis of formula (3):

$\{\begin{matrix} {r r}_{xx xx} s the s + + {r r}_{xy xy} t t + + {r r}_{x x} = = 00 \\ {r r}_{xy xy} s the s + + {r r}_{yy yy} t t + + {r r}_{y the y} = = 00 \end{matrix} - - - - - - ((44))$

则X型角点的亚像素位置即(x₀+s，y₀+t)，其中，Then the sub-pixel position of the X-shaped corner point is (x ₀ +s, y ₀ +t), where,

$s the s = = \frac{{r r}_{y the y} {r r}_{xy xy} - - {r r}_{x x} {r r}_{xy xy}}{{r r}_{xx xx} {r r}_{xy xy} - - {r r}_{}^{xy xy}},,$ $t t = = \frac{{r r}_{x x} {r r}_{xy xy} - - {r r}_{y the y} {r r}_{xx xx}}{{r r}_{xx xx} {r r}_{yy yy} - - {r r}_{}^{xy xy}} . . - - - - - - ((55))$

本发明的优点是：The advantages of the present invention are:

(1)相对于传统的基于Harris的角点提取算法，本发明不需要插值和曲面拟合，提取过程简单，速度快。(1) Compared with the traditional corner point extraction algorithm based on Harris, the present invention does not need interpolation and surface fitting, and the extraction process is simple and fast.

(2)相对于边缘拟合求交点的方法，本发明只是利用角点临近区域内的图像灰度，因此，即使是在图像存在畸变及较大噪声的情况下，仍具有较高的提取精度。(2) Compared with the method of edge fitting to find the intersection point, the present invention only utilizes the image grayscale in the adjacent area of the corner point, so even in the case of image distortion and large noise, it still has high extraction accuracy .

附图说明Description of drawings

图1是具有X型角点的靶标示意图。Figure 1 is a schematic diagram of a target with X-shaped corners.

图2是X型角点附近区域的S值分布示意图。Fig. 2 is a schematic diagram of the S value distribution in the area near the X-shaped corner.

图3是X型角点附近区域的灰度分布示意图。Fig. 3 is a schematic diagram of the gray level distribution of the area near the X-shaped corner point.

图4是一个由计算机生成的虚拟平面靶标。Figure 4 is a computer-generated virtual planar target.

图5是图4的靶标经虚拟摄像机成像之后的靶标图像。FIG. 5 is a target image of the target in FIG. 4 after being imaged by a virtual camera.

具体实施方式Detailed ways

下面对本发明做进一步详细说明。本发明根据Hassian矩阵的特征值判定X型角点的像素位置，然后利用一个二阶泰勒展开式描述该角点附近区域图像灰度的分布曲面，则该曲面的鞍点即所求角点的亚像素位置。具体提取步骤如下：The present invention will be described in further detail below. The present invention determines the pixel position of the X-shaped corner point according to the eigenvalue of the Hassian matrix, and then uses a second-order Taylor expansion to describe the distribution surface of the image gray level in the vicinity of the corner point, and then the saddle point of the curved surface is the sub-point of the corner point. pixel location. The specific extraction steps are as follows:

(1)根据Hessian矩阵判定X型角点的像素位置(1) Determine the pixel position of the X-shaped corner point according to the Hessian matrix

Hessian矩阵的表达式如式1所示：The expression of the Hessian matrix is shown in formula 1:

其中，f_xx、f_xt、f_yy分别为图像灰度相对于x、y的二阶偏导数，可以通过图像灰度与相应微分形式的高斯算子卷积得到。对于X型角点，Hessian矩阵的两个特征值一个为正，另一个为负，则判定其像素位置的算子表示为：Among them, f _xx , f _xt , and f _yy are the second-order partial derivatives of the image grayscale with respect to x and y, respectively, which can be obtained by convolving the image grayscale with the Gaussian operator in the corresponding differential form. For an X-shaped corner point, one of the two eigenvalues of the Hessian matrix is positive and the other is negative, then the operator for determining its pixel position is expressed as:

其中，λ₁、λ₂为Hessian矩阵的特征值。图2为理想情况下角点附近区域的S值分布，其负极值点即角点所在位置。Among them, λ ₁ and λ ₂ are the eigenvalues of the Hessian matrix. Figure 2 shows the distribution of S values in the area near the corner under ideal conditions, and its negative extreme point is the location of the corner.

(2)确定X型角点的亚像素位置(2) Determine the sub-pixel position of the X-shaped corner point

在判定角点的像素位置后，可以利用一个二阶泰勒展开式描述该点附近区域内任意一点的灰度值，其表达式为：After determining the pixel position of the corner point, a second-order Taylor expansion can be used to describe the gray value of any point in the area near the point, and the expression is:

其中，(x₀，y₀)是角点的像素位置，r₀为该点的灰度，r_x、r_y、r_xx、r_xy、r_yy分别为该点灰度相对于x、y的一二阶偏导数，(s，t)为角点相对于(x₀，y₀)的亚像素位置。Among them, (x ₀ , y ₀ ) is the pixel position of the corner point, r ₀ is the gray level of the point, r _x , _ry , r _xx , r _xy , ry _yy are the gray level of the point relative to x, y The first and second order partial derivatives of , (s, t) is the sub-pixel position of the corner point relative to (x ₀ , y ₀ ).

图3是经过低通滤波后角点附近区域图像灰度的分布曲面，该曲面为一平滑鞍面，其鞍点即X型角点的亚像素位置。根据鞍点的性质，在式3的基础上可得确定鞍点位置的线性方程组：Fig. 3 is a distribution surface of the gray level of the image near the corner after low-pass filtering. The surface is a smooth saddle surface, and the saddle point is the sub-pixel position of the X-shaped corner. According to the nature of the saddle point, the linear equations for determining the position of the saddle point can be obtained on the basis of formula 3:

$s the s = = \frac{{r r}_{y the y} {r r}_{xy xy} - - {r r}_{x x} {r r}_{xy xy}}{{r r}_{xx xx} {r r}_{xy xy} - - {r r}_{xy xy}^{22}},,$ $t t = = \frac{{r r}_{x x} {r r}_{xy xy} - - {r r}_{y the y} {r r}_{xx xx}}{{r r}_{xx xx} {r r}_{yy yy} - - {r r}_{xy xy}^{22}} . . - - - - - - ((55))$

实施例Example

以下是一组仿真实例。图4是一个由计算机生成的虚拟平面靶标，靶标上共有144个X型角点，每两点间距16mm。虚拟摄像机的图像分辨率设为512×512；内部参数设定为：α＝1000，β＝1000，γ＝0，u₀＝256，v₀＝256；外部参数设定为：r₁＝[0.951 -0.174 0.255]^T，r₂＝[0.168 0.9850.045]^T，t＝[0 0 500]^T。图5是经虚拟摄像机成像之后的靶标图像。具体提取过程如下：The following is a set of simulation examples. Fig. 4 is a virtual plane target generated by computer, there are 144 X-shaped corner points on the target, and the distance between every two points is 16mm. The image resolution of the virtual camera is set to 512×512; the internal parameters are set as: α=1000, β=1000, γ=0, u ₀ =256, v ₀ =256; the external parameters are set as: r ₁ =[ 0.951 -0.174 0.255] ^T , r ₂ =[0.168 0.9850.045] ^T , t = [0 0 500] ^T . Fig. 5 is the target image after being imaged by the virtual camera. The specific extraction process is as follows:

(1)针对图像中的每一个像点，利用微分形式的高斯卷积核计算该点灰度相对于x，y的各阶偏导数r_x，r_y，r_xx，r_xy，r_yy；(1) For each image point in the image, use the Gaussian convolution kernel in differential form to calculate the partial derivatives r _x , r _y , r _xx , r _xy , r _yy of the point gray relative to x, y;

(2)计算各像点所对应的Hessian矩阵及其特征值，并根据式2判断该点是否为X型角点的像素位置；(2) Calculate the corresponding Hessian matrix and eigenvalue thereof of each image point, and judge whether this point is the pixel position of the X-shaped corner point according to formula 2;

(3)对符合式2的像素点，根据式5计算X型角点的亚像素位置。(3) For the pixels conforming to Formula 2, calculate the sub-pixel position of the X-shaped corner point according to Formula 5.

表1是传统的Harris角点提取方法与新方法提取结果的对比，本发明的提取精度要略优于传统方法。Table 1 is a comparison of the extraction results of the traditional Harris corner point extraction method and the new method, and the extraction accuracy of the present invention is slightly better than that of the traditional method.

表1两种方法的提取精度对比噪声水平提取精度传统方法本方法 0 0.0088 0.0086 0.04 0.0331 0.0327 0.08 0.0644 0.0638 0.12 0.0958 0.0949 0.16 0.1279 0.1268 0.20 0.1598 0.1585 Table 1 Comparison of extraction accuracy of the two methods noise level Extraction accuracy traditional method This method 0 0.0088 0.0086 0.04 0.0331 0.0327 0.08 0.0644 0.0638 0.12 0.0958 0.0949 0.16 0.1279 0.1268 0.20 0.1598 0.1585

表2是两种方法对144个角点提取时间的对比，可知新方法的提取速度要明显快于传统方法。Table 2 is a comparison of the extraction time of the two methods for 144 corner points. It can be seen that the extraction speed of the new method is significantly faster than that of the traditional method.

表2两种方法的提取速度对比提取时间(秒/144个角点) 传统方法新方法 3.17 1.15 Table 2 Comparison of extraction speeds of the two methods Extraction time (seconds/144 corner points) traditional method new method 3.17 1.15

Claims

1, a kind of X type angular-point sub-pixel extracting method is characterized in that extraction step is as follows:

1.1, judge the location of pixels of X type angle point according to the Hessian matrix; The expression formula of Hessian matrix is as shown in Equation 1:

H = [\begin{matrix} f_{xx} & f_{xy} \\ f_{xy} & f_{yy} \end{matrix}] - - - (1)

Wherein, f _Xx, f _Xy, f _YyBe respectively the second-order partial differential coefficient of gradation of image with respect to x, y, can obtain by the Gauss operator convolution of gradation of image and corresponding differential form, for X type angle point, one of two eigenwert of Hessian matrix are for just, another judges then that for negative the operator s of its location of pixels is expressed as:

S = λ_{1} \cdot λ_{2} = f_{xx} f_{xy} - f_{xy}^{2} - - - (2)

Wherein, λ ₁, λ ₂Eigenwert for the Hessian matrix;

1.2, determine the sub-pixel location of X type angle point;

Behind the location of pixels of judging angle point, utilize a second order Taylor expansion to describe the interior gray-scale value of any arbitrarily of this near zone, its expression formula is:

r (x_{0} + s, y_{0} + t) = r_{0} + [\begin{matrix} s & t \end{matrix}] [\begin{matrix} r_{x} \\ r_{y} \end{matrix}] + \frac{1}{2} [\begin{matrix} s & t \end{matrix}] [\begin{matrix} r_{xx} & r_{xy} \\ r_{xy} & r_{yy} \end{matrix}] [\begin{matrix} s \\ t \end{matrix}] - - - (3)

Wherein, (x ₀, y ₀) be the location of pixels of angle point, r ₀Be the gray scale of this point, r _x, r _y, r _Xx, r _Xy, r _YyBe respectively the second-order partial differential coefficient of this gray scale with respect to x, y, s, t are that angle point is with respect to (x ₀, y ₀) sub-pixel location, distribution surface through angle point near zone gradation of image after the low-pass filtering is a level and smooth saddle face, its saddle point is the sub-pixel location of X type angle point, according to the character of saddle point, obtains determining the system of linear equations of saddle point position on the basis of formula (3):

\{\begin{matrix} r_{xx} s + r_{xy} t + r_{x} = 0 \\ r_{xy} s + r_{yy} t + r_{y} = 0 \end{matrix} - - - (4)

Then the sub-pixel location of X type angle point is (x ₀+ s, y ₀+ t), wherein,

s = \frac{r_{y} r_{xy} - r_{x} r_{yy}}{r_{xx} r_{yy} - r_{xy}^{2}}, t = \frac{r_{x} r_{xy} - r_{y} r_{xx}}{r_{xx} r_{yy} - r_{xy}^{2}} . - - - (5)