WO2019105044A1

WO2019105044A1 - Method and system for lens distortion correction and feature extraction

Info

Publication number: WO2019105044A1
Application number: PCT/CN2018/096004
Authority: WO
Inventors: 王峰; 肖飞; 汪进; 黄祖德; 邱文添; 李诗语; 曹彬
Original assignee: 东莞市普灵思智能电子有限公司
Priority date: 2017-11-28
Filing date: 2018-07-17
Publication date: 2019-06-06
Also published as: CN109842756A

Abstract

Disclosed are a method and system for lens distortion correction and feature extraction. Said method mainly comprises the following six steps: acquiring lens picture information; preprocessing a picture; extracting picture contour points and performing lens distortion correction; extracting graphic characteristics keypoints; performing inverse perspective transformation on the keypoints; and computing an equation for the keypoints in the physical world. The system mainly comprises hardware modules which provide an operating platform for the method of the present application, i.e. an image input module, a picture pre-processing module, an image contour point extraction module, a contour point distortion correction module, a graphic characteristic keypoint extraction module, a keypoint inverse perspective transformation module, and a module for obtaining an equation for graphic characteristics in the physical world. Compared with the conventional method and system, the method and system of the present application can reduce the amount of CPU computation by more than 6 times, significantly reducing hardware cost while improving the computational efficiency, being able to quickly obtain ground-related physical characteristic information, realizing high-precision indoor positioning, being particularly applicable to an embedded system having less computational resources.

Description

Method and system for correcting lens distortion and feature extraction

Technical field

The invention belongs to the field of computer vision detection, and in particular relates to a method and a system for correcting lens distortion and feature extraction with high computational efficiency and effective reduction of CPU running time.

Background technique

Computer vision inspection has broad application prospects in the fields of robots, unmanned vehicles and drones. The amount of data to be processed is large and the real-time requirements are high. Lens distortion calibration and feature extraction have a wide range of applications in the field of computer vision detection, especially indoor positioning systems. In the high-precision indoor positioning system, radio ranging is popular, for example, using ultra-wideband positioning or WiFi to receive signal strength positioning, and then using the triangulation principle to determine the absolute position of the camera. Radio positioning requires early grasp of environmental information, which has high positioning accuracy but high cost and maintenance. Other positioning methods such as odometer positioning method, inertial sensor positioning method, etc., after the initial pose of a given robot or drone, the displacement amount is accumulated by using a sensor such as a robot or a drone. Robots or drones can obtain higher positioning accuracy within a short distance of movement, but deviations in position and attitude angles due to vertical or horizontal sliding of robots or drones, and odometers or inertial sensors, etc. It is easy to produce error accumulation itself. If the error is not corrected in time, it will directly lead to lower positioning accuracy of the robot or drone. Therefore, it is not suitable for long-term use, which is not conducive to the popularity of robots or other devices.

In view of the inherent defects of positioning methods such as radios, odometers, and inertial sensors, the use of optical sensors for positioning has gradually become the mainstream in the field of computer vision detection. The visual sensor mainly relies on the processing and recognition of the collected images, thereby sensing the surrounding environment and realizing its own positioning. At present, the visual sensors are mainly divided into three types: panoramic vision sensor, binocular vision sensor and monocular vision sensor. Among them, the panoramic sensor has a large observation range, but due to its difficult processing, high price, easy image distortion, and complicated image processing, it is difficult to obtain a panoramic sensor. The binocular vision sensor is mainly used in the case where the depth of the scene is high, and the image processing capability of the computer is also high, so it cannot be widely used. The monocular vision sensor is low in price and is suitable for applications where the image processing is not demanding in a general daily life environment, and can meet a wide range of application requirements. In addition, the camera can be mounted on the bottom of the robot and captured and decoded based on the ground-based QR code to calculate the position of the robot.

Distortion correction and feature extraction are especially important during visual sensor positioning. The traditional distortion correction and feature extraction system is shown in Figure 1. It generally consists of the following key modules: camera calibration module, distortion correction module, inverse perspective mapping (IPM) module, inverse perspective transformation output image processing module, RANSAC (Random Sample Consensus) extraction feature Graphic key module.

Camera calibration is the most advanced step, and subsequent processing steps are inseparable from the camera parameters. The calibration method uses the widely used Zhang Zhengyou calibration method. This method requires the camera to take pictures of the calibration plate from different angles, and then provide these pictures to the calibration toolbox, which can give the camera's internal reference matrix and distortion coefficient. The calibration toolbox is a set of calibration procedures. Due to the extensive use of Zhang Zhengyou's calibration method, these program groups can be downloaded online. Matlab and opencv have corresponding calibration toolboxes.

First, the lens captures the image first, and then pre-processes the image, including adjusting the brightness and contrast of the image, so that the subsequent image processing steps are better. The next step is distortion correction. Since the image after distortion correction only removes the distortion and preserves the original perspective effect of the image, the inverse perspective transformation is performed to obtain the image without the perspective effect. At this time, the image outputted by the reverse perspective is processed. , including the color map into a grayscale image, noise reduction processing on the image, and then edge detection. Then the RANSAC algorithm is used to extract the feature graph and obtain the key points of the graph. Finally, the coordinates of the key points in the physical space are calculated to calculate the equation of the feature graph in the physical world, which is convenient for calculating the positional relationship between the lens and the feature graph in the physical world. . Among them, distortion correction and inverse perspective transformation are very time-consuming. Taking HDTV images as an example, 1920×1080 pictures need to process 2 million points of data, resulting in low efficiency of correction and inverse perspective transformation, which cannot be satisfied. Real-time requirements.

It turns out that using traditional distortion correction and feature extraction systems for image correction and matching in the Linux environment of Raspberry Pi 3 consumes a lot of CPU resources and time, making it impossible for robots or drones to locate in real time.

Summary of the invention

The invention aims to solve the technical problem that the distortion correction and feature extraction method and the system in the prior art have large data processing capacity and high CPU usage, which makes the robot or the drone unable to perform real-time positioning, and provides a new high computational efficiency. Method and system for lens distortion correction and feature extraction.

The key to the invention lies in: by means of advanced calculation methods, the lens distortion of the image is quickly corrected and the feature points are extracted, and then converted to the physical space, and then the analytical form of the feature points is obtained to realize real-time matching and positioning.

In order to solve the above technical problems, the present invention adopts the following technical solutions:

A method for lens distortion correction and feature extraction includes the following steps:

S101. Acquire lens image information.

S102: Image pre-processing, the image pre-processing includes changing a color map into a gray image, adjusting picture brightness and contrast, and edge detection, thereby displaying an outline of the image;

S103, extracting image contour points and performing lens distortion correction, extracting contour points displayed by the image processed by S102, and then correcting the contour points by using a correction formula, and resting the contour points to an undistorted plane;

S104, extracting key points of the graphic feature, fitting the feature image by using the RANSAC algorithm, and extracting key points capable of characterizing the feature graphic;

S105, the key point inverse perspective transformation, the key points processed by S104 are subjected to inverse perspective transformation, and the key points in the real physical world coordinates are obtained;

S106: Calculate the physical world equation of the key point, and calculate the equation of the characteristic graphic in the physical world coordinate system by using the key points obtained by S105 in the real physical world coordinates.

The invention also provides a system for lens distortion correction and feature extraction adapted to the above method, which comprises the following modules:

Input image module for collecting picture information;

The image preprocessing module is configured to change the color map into a gray image, adjust the brightness and contrast of the picture, perform noise reduction processing on the picture, and then perform edge detection to display the outline of the image;

Extracting an image contour point module for extracting contour points displayed after processing by the image preprocessing module;

a contour point distortion correction module, configured to restore the contour points extracted by the extracted image contour point module to an undistorted plane;

Extracting a graphical feature key point module for extracting key points capable of characterizing the feature graphic;

The key point inverse perspective transformation module is used for performing inverse perspective transformation on the key points extracted in the key feature module of the extracted graphic feature, and obtaining the key points in the real physical world coordinates;

The feature graph physical world equation module is obtained, and the key points obtained by the key point inverse perspective transformation module are used in the real physical world coordinates to calculate the equation of the feature graph in the physical world coordinate system.

Beneficial effects:

Compared with the traditional distortion correction and feature extraction method, the present invention extracts the contour points of the image before the distortion correction, and then performs distortion correction on the contour points, which can greatly reduce the data amount of the distortion correction processing and greatly improve the calculation efficiency. The key points of the feature graphic are extracted before the inverse perspective transformation, thereby reducing the amount of data of the inverse perspective transformation and further improving the calculation efficiency. Therefore, the present invention can significantly reduce the amount of CPU calculation under high fidelity requirements, significantly reduce the hardware cost while improving the calculation efficiency, and can quickly obtain ground-related physical feature information and achieve high-precision positioning in the room.

DRAWINGS

1 is a block flow diagram of a conventional distortion correction and feature extraction system;

2 is a block flow diagram of a lens distortion correction and feature extraction system of the present invention;

3 is a flow chart of a lens distortion correction and feature extraction method according to the present invention;

Figure 4 is a diagram showing the relationship between the camera and the physical world coordinate system of the present invention.

Detailed ways

The present invention will be described in detail in conjunction with the specific embodiments.

As shown in FIG. 2, the lens distortion correction and feature extraction system of the present invention comprises the following modules: an input image module, a picture preprocessing module, an extracted image contour point module, a contour point distortion correction module, an extraction feature key module, and a key point. The inverse perspective transformation module obtains the feature graphic physical world equation module.

Correspondingly, the method for lens distortion correction and feature extraction of the present invention comprises the following six steps, that is, S101 acquires lens picture information, S102 picture pre-processing, S103 extracts picture contour points and performs lens distortion correction, S104 extracts graphic feature key points, S105 key point inverse perspective transformation, S106 calculation key point physical world equation, as shown in Figure 3. Specific steps are as follows:

S101: Perform step S101 by using an input image module. Use the camera to capture images and measure and record the camera's height and attitude angle for subsequent module processing.

S102: Perform step S102 by using a picture preprocessing module. This includes turning the color map into a gray image, adjusting the brightness and contrast of the image, denoising the image, and then performing edge detection to display the outline of the image. The color map becomes a grayscale image, which can greatly reduce the amount of data processed, and the image information such as details and texture of the image is not reduced compared with the original image. The subsequent processing steps also utilize the information of the image details, and need not be utilized. The color information of the image, so turning into a grayscale image is a good choice. After converting to a grayscale image, the image is denoised. The noise reduction process suppresses the noise of the target image while preserving the features of the graphic detail as much as possible, which can increase the effectiveness and reliability of the subsequent processing. After completing the two steps of the preamble, edge detection can be performed to display detailed information such as the outline of the image. Preferably, the cut picture step is performed after the edge detection step to remove the disturbed contour portion. Thereby further reducing the amount of data processing for subsequent operations.

S103: Perform step S103 by using the extracted image contour point module and the contour point distortion correction module. The contour points displayed after processing the image preprocessing module are extracted; then, using the calibrated camera internal reference matrix and the distortion coefficient, the contour points are corrected radially and tangentially by the correction formula to restore the undistorted plane.

Among them, extracting the image contour point is to save the coordinates of the displayed contour point on the binary image after the edge detection. In order to reduce the amount of data, equidistant points can be taken on the column, and equidistant points of the same value or different values can be used on the line, or both. For example, when collecting points, the equidistant sampling value of the column is 5, and the equidistant sampling value of the row is 3, that is, every 5 columns, one point is taken until the end of the line, and then every 5 columns can be continued across 3 lines. point. After such a sampling process, the amount of data can be reduced by an order of magnitude. Of course, it is necessary to select a reasonable sampling value according to the size of the picture, otherwise the contour information of the image will be seriously lost, and the later feature graphics cannot be reconstructed in the physical world. Contour point distortion correction is to correct the coordinates of the contour points saved on the distortion plane to the coordinate points on the undistorted plane. On undistorted planes, these corrected contour points show the true physical shape of the image contained in the image.

The imaging model of the camera established in the contour point distortion correction module is as follows:

Let (X, Y, Z) be a three-dimensional world coordinate point, and the two-dimensional coordinates projected on the image are (u, v), and the projection relationship is as follows:

Where R and T represent the rotation matrix and the translation vector in the camera external reference, respectively, and (x, y, z) is the coordinate transformed from the three-dimensional world coordinate point to the camera coordinate system.

x'=x/z

y'=y/z

r ² =x' ² +y' ²

θ=atan(r)

θ'=θ(1+k ₁ θ ² +k ₂ θ ⁴ +k ₃ θ ⁶ +k ₄ θ ⁶ )

x′′=(θ′/r)x

y′′=(θ′/r)y

u=f _u *x"+c _u

v=f _v *y"+c _v

among them:

f _u : the lateral focal length of the camera, which is obtained by the camera calibration;

f _v : the longitudinal focal length of the camera, which is obtained by the camera calibration;

c _u : the lateral coordinate of the image center point corresponding to the optical axis of the camera, which is obtained by the camera calibration;

c _v : the longitudinal coordinate of the image center point corresponding to the optical axis of the camera, which is obtained by the camera calibration;

K1, k2, k3, k4 are the distortion coefficients of the camera, which are obtained by camera calibration.

The above is a transformation formula for transforming the three-dimensional world coordinate points (X, Y, Z) to image coordinates (u, v). The point correction is the inverse process described above, and the formula is still applicable.

S104: Execute S104 by using the extracted graphic feature key module. The feature pattern is first fitted with RANSAC, and the key points that can characterize the feature pattern are extracted.

The RANSAC extracts feature key points on the undistorted plane. The first thing to do is to find the feature graphic and then extract the key points of the feature graphic. Depending on the feature graphic, a reasonable number of representative key points can be selected as needed without having to send all the key points to subsequent steps for processing. It is advisable to select representative key points to ensure that the original graphics can be restored. For example, a graph with a function analytic pattern, such as a line or a circle, it is not necessary to send the contour points on the entire line or the circle to the subsequent steps for processing, because 2 points can determine a straight line, 3 points It is possible to determine a circle, so that two contour points can be selected at the contour point of the line, and the contour points on the circle are selected and sent to the subsequent steps for processing, and the reconstruction of the graphics in the physical world can be completed.

S105: Perform step S105 by using a keypoint inverse perspective transformation module. The key point inverse perspective transformation is to transform the coordinates of the key points of the extracted feature graphics to the real physical world coordinates. This physical world coordinate is represented in the camera coordinate system, so this step requires the height and attitude angle information of the camera. Because the key point coordinates of the extracted feature graphic are the coordinates in the undistorted plane, which is converted from the distortion plane, but the distortion is eliminated, the perspective effect of the camera shooting is not eliminated. Therefore, the key point inverse perspective transformation is to transform the points on the undistorted plane into the real physical space. At this time, there is no perspective effect, and the positional relationship between the transformed points truly reflects the positional relationship in the physical world.

The formula for inverse perspective transformation is as follows:

T is the transformation matrix, where:

h: camera height, which can be obtained by measurement;

s ₁ : the sine value sinα of the camera depression angle α;

s ₂ : sinusoidal value sinβ of camera yaw angle β;

c ₁ : cosine value cosα of the camera depression angle α;

c ₂ : cosine value cosβ of camera yaw angle β;

Assume that the coordinates of the key points are (u, v), then:

Where (x, y) is the coordinate of the physical world corresponding to (u, v).

S106: Execute S106 by using the obtained feature graphic physical world equation module. Based on the coordinates of the obtained key points in the camera coordinate system, the equations of the feature patterns described by these key points can be recalculated. Therefore, it is convenient to calculate the positional relationship between the camera and the feature graphic, and complete high-precision positioning.

Compared to conventional distortion correction and feature extraction methods and systems, the operational efficiency of the present invention is increased by several orders of magnitude because it optimizes precisely the time-consuming distortion correction and inverse perspective transformation steps of conventional methods.

Taking the 1920×1080 picture as an example, the traditional method needs to process 2 million points of data in both distortion correction and inverse perspective transformation. The new method has to deal with a thousand points. Because for such a size of the picture, the extractable contour points are about a thousand points, so only need to process the thousands of data, the amount of processed data is three orders of magnitude smaller than 2 million, so the correct operation efficiency is greatly improve. Feature graphics can be represented by a few representative key points: for example, a line or line segment can be represented by two points; a circle can be represented by three points on a circle. For the extracted feature graphics, the previously extracted contour points also contain redundant data quantities. We only need to send the representative key points that can represent the feature graphics to the inverse perspective for processing, so the inverse perspective transforms the processing data of this step. The amount can be greatly reduced on the basis of the original thousands of data points, and the operational efficiency is improved. After this step of RANSAC extracting the key points of the feature graphics, the amount of data can be greatly reduced, and processing these key points is three orders of magnitude less than the thousands of points before running RANSAC. In the experiment, when using the Linux environment running in the Raspberry Pi 3, processing 30 frames per second is 6 times higher than the previous processing of 5 frames per second by the conventional method. If the size of the image is larger, the advantage is more obvious. Therefore, the method of the present invention can provide good real-time performance.

Example 1

The application scenario of this embodiment is an indoor area capable of extracting ground features for indoor positioning. Firstly, the camera is used to obtain the feature information of the indoor floor tile edge line. The X-axis and Y-axis directions are established with reference to FIG. 4, and the position of the camera center point is directly changed to the relative position information of the line in the captured picture.

S101: Acquire a lens image. Capture images for subsequent module processing.

S102: Image preprocessing. Converting the captured lens image from a color map to a grayscale image; edge detection, displaying the outline of the image; cutting the image to remove the contour portion of the interference.

Converting a picture from a color map to a grayscale image can reduce the amount of computation of subsequent data to be processed, speed up operational efficiency, and make grayscale images easier to process.

Edge detection can be used to display outline information of an image. Significant changes in image properties often reflect important events and changes in the image. Edge detection can identify points in the image where the brightness changes significantly, and these points can be used to form the edge features of the image. Edge detection of the image can greatly reduce the amount of data of the original image, and eliminate information that can be considered irrelevant, retaining important structural properties of the image, thereby facilitating subsequent extraction of feature information of the image. In the embodiment of the present invention, the Canny operator can be used to perform edge detection on the image.

Cut the picture, because the camera is fixedly mounted on a car, it may capture the fixed contour of some parts of the car itself. This is not useful information. You can shoot every frame of the picture and the original picture with the outline of the car. Perform image difference and remove the interference information of the fixed contour in the car, which can enhance the robustness of the fitted feature points.

S103: Extract a picture outline point and correct it. The contours displayed by the image processed by the S102 module are extracted, and the contour points of the camera are corrected by radial and tangential correction using the calibration camera internal reference matrix and the distortion coefficient, so as to be restored to the undistorted plane.

Through the S102 process, the contour point related information of the ground figure is obtained, plus the calibrated camera internal reference matrix and the distortion coefficient, and the obtained contour points are efficiently corrected. Such point correction is more efficient than the entire picture correction, greatly reducing CPU runtime. This method runs under the Linux environment of Raspberry Pi 3, which can greatly reduce the hardware cost.

The obtained contour points may be related parameters used to describe the characteristics of the ground image. The formed feature graphic may be an analytical geometry that can be described using parameters, and the specific shape of the feature graphic may be a straight line, a circle, a diamond, or the like. In the embodiment of the present invention, the specific shape of the feature graphic is not limited. Taking the indoor floor tile as an example, when the robot is traveling in the room, the feature pattern fitted in the image taken from the camera may be the edge line of the indoor tile.

In the embodiment of the present invention, the feature pattern may be fitted from the corrected feature points by using a Hough Transform, or the feature pattern may be fitted from the image by using the RANSAC algorithm.

S104: RANSAC extracts a key point. The feature pattern is first fitted with RANSAC, and the key points that can characterize the feature pattern are extracted.

The system first fits the contour point to the straight line, because the line of the floor is a straight line, the fitting straight line uses a random sampling consistency algorithm to fit the straight line, and selects two key points in the contour point of the found floor straight line. Yes, because the line only needs 2 points to be characterized. Thereby, the amount of subsequent operation data can be further reduced.

S105: Key point inverse perspective transformation. Perform the inverse perspective transformation on the key points obtained in step S104 to obtain the physical coordinates of these key points in the real world.

According to the needs of the experiment, such as extracting straight lines in the algorithm, the program sets up to two lines of square floor at the same time, so four key points can be obtained, which are the starting point of a straight line extracted by RANSAC (u _s1 , v _s1 ), and the end point is (u _e1 , v _e1 ), extract another line starting point (u _s2 , v _s2 ), and the end point is (u _e2 , v _e2 ). The matrix generated by extracting the start and end points of each line is:

The generated matrix M is imported into the transformation matrix of the inverse perspective transformation image and converted to the ground, and a matrix composed of corresponding physical world coordinate points is obtained. The matrix form is as follows:

Where T is the inverse perspective transformation matrix, the generated points (x _s1 , y _s1 ), (x _e1 , y _e1 ), (x _s2 , y _s2 ), (x _e2 , y _e2 ) are key points in the image transformed to The coordinates of the physical world. The coordinates of this physical world are based on the camera's optical axis point.

The algorithm can also fit other geometric figures and calculate the corresponding geometric image equations to further calculate the corresponding physical information.

S106: Calculate a physical world equation of a key point. Using the real world physical coordinates of the key points obtained in S105, the equations of the feature graph in the physical world coordinate system are calculated.

Using the physical world coordinates of the obtained key points, the geometric equation represented by the key points can be obtained, and the geometric image converted from the geometric image in the picture to the physical world coordinates is completed, and the physical world coordinates are utilized. The straight line equation below makes it easy to find the distance from the camera to the edge of the floor, thus achieving high-precision positioning in the room.

It is apparent that the above-described embodiments are merely illustrative of the examples, and are not intended to limit the embodiments. Other variations or modifications of the various forms may be made by those skilled in the art in light of the above description. There is no need and no way to exhaust all of the implementations. As long as the common-sense modification made on the basis of the embodiment of the present invention is within the protection scope of the present invention.

Claims

A method for lens distortion correction and feature extraction includes the following steps:

S101. Acquire lens image information.

S102: Image pre-processing, the image pre-processing comprises: changing a color map into a gray image, adjusting a picture brightness and contrast, performing noise reduction processing on the picture, and performing edge detection, thereby displaying an outline of the image;

S103, extracting image contour points and performing lens distortion correction, extracting contour points displayed by the image processed by S102, and then correcting the contour points by using a correction formula, and resting the contour points to an undistorted plane;

S104, extracting key points of the graphic feature, using the feature fitting algorithm to fit the feature image, and extracting key points capable of characterizing the feature graphic;

S105, the key point inverse perspective transformation, the key points processed by S104 are subjected to inverse perspective transformation, and the key points in the real physical world coordinates are obtained;

S106: Calculate the physical world equation of the key point, and calculate the equation of the characteristic graphic in the physical world coordinate system by using the key points obtained by S105 in the real physical world coordinates.
The method according to claim 1, wherein the step S102 further comprises a picture cropping process, that is, removing the contour portion of the interference.
The method according to claim 1, wherein in S103, only the extracted contour points are corrected when the distortion is corrected, instead of correcting the entire image, and when the contour points are extracted, the equidistance is respectively adopted on the columns and the rows. Take points to pick up points.
The method according to claim 1, wherein in S103, said lens distortion correction comprises radial and tangential correction, and the correction coefficient is obtained by prior lens calibration.
The method according to claim 4, wherein the pre-shooting calibration comprises collecting a calibration plate image, and then inputting a calibration program toolbox, and calculating a camera internal reference matrix and a distortion coefficient by the calibration program toolbox.
The method according to claim 1, wherein in S104, for the feature graphic having the function analytic expression, the selected contour point is a representative key point capable of determining the shape of the characteristic graphic shape.
A system for lens distortion correction and feature extraction, comprising the following modules:

Input image module for collecting picture information;

The image preprocessing module is configured to change the color map into a gray image, adjust the brightness and contrast of the picture, perform noise reduction processing on the picture, and then perform edge detection to display the outline of the image;

Extracting an image contour point module for extracting contour points displayed after processing by the image preprocessing module;

a contour point distortion correction module, configured to restore the contour points extracted by the extracted image contour point module to an undistorted plane;

Extracting a graphical feature key point module for extracting key points capable of characterizing the feature graphic;

The key point inverse perspective transformation module is used for performing inverse perspective transformation on the key points extracted in the key feature module of the extracted graphic feature, and obtaining the key points in the real physical world coordinates;

The feature graph physical world equation module is obtained, which is used to calculate the equation of the feature graph in the physical world coordinate system by using the key points obtained by the key point inverse perspective transformation module in the real physical world coordinates.
The system according to claim 7, wherein said contour point distortion correction module comprises a camera calibration module, said camera calibration module is mainly for collecting a calibration plate picture, and then inputting a calibration program toolbox, by a calibration program toolbox. Calculate the internal reference matrix and distortion coefficient of the camera.
The system according to claim 8, wherein said contour point lens distortion correction module employs radial and tangential correction, and the correction coefficient is obtained by calculating a camera internal reference matrix and a distortion coefficient by said calibration program toolbox.