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What is OpenCV calibration?

    The calibration allows you to remove the distortion inherent in the camera and determine the relationship between the camera’s natural units (pixels) and the real world units (for example millimeters). There are two primary types of distortion that OpenCV accounts for; radial and tangential.

How to distort an image in OpenCV?

    OpenCV doesn't provide distort function for image, but you can implement one by yourself. All you need are: Intrinsic params (camera matrix and distortion coefficients) and size of the distorted image. Denoted as cam_mtx, dis_cef, and image_size. Intrinsic params (camera matrix) and size of the undistorted image.

Which distortion models are used in global camera calibration?

    For example, direct distortion models are used in global camera calibration [29], [32], [17], [30]. Yet, in most plumb-line methods [3], [9], [1], [2], [25], [23], [22], [6] or some pattern-free methods [26], [31], [10], [19], [28], [7], [21], [4], [16], the very same radial correction models are used without any fuss to inverse the distortion.

How is distortion calibrated in LensFun?

    In Lensfun, the distortion is calibrated with some prede?ned models (see Table II), based on the matching points between two images taken by the same camera on the same focal length.4The ?nal calibrated distortion models in Lensfun are represented in the normalized image domain [ 1:0;+1:0] [ 1:0;+1:0]5.

Camera calibration

Hala DJEGHIM

January 5, 2022

1 Introduction

A camera is a device that converts the 3D world into a 2D image. The equationx = PXcan represent a camera, where x is the 2D image point, P the camera matrix and X the 3D world point. Calibrating a camera helps identifying the geometric characteristics of the image creation process. The camera is often categorized on the basis of a set of intrinsic parameters such as skew of the

axis, focal length, and main point in these applications, and its orientation is expressed by extrinsic

parameters such as rotation and translation. Linear or nonlinear algorithms are used to estimate intrinsic and extrinsic parameters utilizing known points in real-time and their projections in the picture plane.

2 Camera calibration

Camera calibration is a technique that estimates the characteristics of a camera, which are needed to

establish a relationship between 3D point and its 2D projection. In order to calibrate our camera, we took 35 images of a chessboard in diffferent positions.

Figure 1: Images example

In order to Calibrate the camera, the ifirst step will be to read in calibration Images of a chess board. It's recommended to use at least 20 images to get a reliable calibration.

2.1 Chessboard

Our world coordinates are ifixed by this the chessboard pattern in the image, our 3D points are the corners of the squares in the chessboard. We choose the chessboard patterns because they are distinct and easy to detect, the corners squares have sharp gradients in two directions and are located at the intersection of the chessboard lines. OpenCV gives us an easy way to detect chessboard corners with a function calledifindChessboard- Corners(), that returns the corners found in a grayscale image. So, we will convert the image to

greyscale and then pass that to the ifindChessboardCorners() function. This function takes in a grayscle

image along with the dimensions of the chess board corners. The last step, use calibrateCamera func- tion and read the parameters. We feed our map and all the points we detected from the images. 2 1

Figure 2: Chessboard corners

2.2 Intrinsic parameters

Intrinsic parameters are the parameters that allows the mapping between pixel coordinates and camera

coordinates in the image frame, like the focal length, optical center and distortion coeiÌifiÌicients. After

calibrating the camera with the opencv function, we had the camera matrix shown in 3 as a result,

knowing that from a camera matrix we can extract the focal length ( fx,fy) and optical centers ( cx,cy)

3 2

Figure 3: Camera matrix

ParameterValue

Optical center(1894.90, 1520.18)

Focal length in pixels(3143.94, 3135.301)

Distortion coes(0.14097, -0.00982, 0.00278, -0.0106, -1.0406)

Table 1: Intrinsic parameters.

2.2.1 Focal length

We calculated the focal length of our camera in meters, thanks to the opencv function calibrationMa- trixValues(), we found it equal to 15.0127 mm

2.3 Extrinsic parameters

They describes the orientation and location of the camera. This refers to the rotation and translation

of the camera with respect to some world coordinate system. The rotation and translation which translates a coordinates of a 3D point to a coordinate system. Their results was given as an output from the calibration function that returns the rotation and translation vectors.

3 Radial distortion

Radial distortion is caused by unequal light bending. The rays bend more at the lens's borders than

they do at the lens's center It causes straight lines to appear curved. To observe this problem, we tried

to draw straight line on our chessboard lines, here is the result 4

Figure 4: Radial distortion

3.1 Undistort the image

Using the camera clibration results, we control the percentage of undesired pixels in the undistorted

image by ifine-tuning the camera matrix (getOptimalNewCameraMatrix() function in opencv), then we used the revised camera matrix to remove distortion from the image. We obtained the result shown in 5 , where the rest of the image is distorted, but the chessboard is aligned. 3

Figure 5: Radial distortion

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