A Comparative Study on Camera-Radar Calibration Methods

综述文

Abstract

compare three types of the calibration methods presented in previous studies on fusing camera and radar in terms of calibration accuracy.
Experimental results show that one type of the methods is not appropriated to the camera-radar calibration, and the methods belonging to the other types provide quite similar accuracy.

I. INTRODUCTION

ADAS:advanced driver assistance systems

The camera-radar calibration presented in the literature can be divided into three categories.

1. first category based on affine transformation, obtained by the least squares using pseudo inverse.
2. second category based on projective transformation. the transformation can be regard as a two dimensional homography from radar plane to image plane, and it is obtained using the least squares using singular value decomposition.
3. third category based on the transformation that maps a point in a three dimensional
   space to a point on image plane of camera. Those methods are similar to the extrinsic calibration for camera pose estimation.

II. CALIBRATION METHODS

1. Pseudo inverse (PI)
   six unknown variables
   an optimization problem can be formulated to minimize the projection error on the image plane as follows.

2. Direct linear transformation (DLT)
   corresponds to the two dimensional homography estimation between radar plane and image plane.
   the solution computed by DLT depends on the coordinate system, and a normalization, which is called as the pre-conditioning, is recommended to be conducted together with DLT.

transformation H can be more refined by additionally performing a nonlinear optimization method such as Levenberg-Marquardt (LM) algorithm [15] using H as its initial point.
One of the popular objective functions used in the nonlinear optimization is the symmetric transfer error as follows.

3. Extrinsic calibration (EC)
   different from previous 2 methods. similar as camera and lidar calibration.
   In the literature, the extrinsic calibration is performed by solving a nonlinear optimization problem with the following objective function:formula here
   The LM algorithm is one of the popular algorithms to solve this optimization problem when N ≥ 6.

III. EXPERIMENTS

a radar sensor (Continental ARS408-21) and a camera sensor(FLIR Chameleon3 with the lens of Theia SL183M)
sensors are installed behind the frontal grill and behind the windshield of our automotive platform (Hyundai IONIQ Electric)
resolution of the image was fixed to 1280 × 720 pixels.

Since the absolute sizes of the corner reflectors are not large enough, they are invisible if they are placed at a distance from the camera.

not easy to manually decide the image coordinates of the corner reflectors with the distances above
about 40 meters.

twelve sets were divided into training data and test data:

calibration error for given N pairs of {p i } and {q i }

In summary, PI was not suitable for the camera-radar calibration, and the differences of the other calibration meth-
ods were insignificant quantitatively and qualitatively. In a situation that the calibration speed is critical together with
its accuracy, NDLT may be a better choice than the other methods because DLT is based on the optimization problem
having a closed form solution whereas LM is an iterative algorithm. Lastly, the accurate calibration can be obtained
from about 20 radar-image data pairs.

IV. CONCLUSION

1. described the camera-radar calibration methods;
2. compared them in terms of the calibration error.

PI was not appropriate to the camera-radar calibration and DLT based methods provided slightly better than EC in most cases we considered.
Also, the pre-conditioning normalization is slightly more effective than the nonlinear refinement under
the assumption that target objects have almost same height.

Words

Nonetheless 尽管如此
resolution 决议
water drop 水滴
affine 仿射
pseudo 伪,冒充的
arbitrary 随意的
pre-conditioning 预处理
isotropic |ˌīsəˈträpik| 各向同性
symmetric |səˈmetrik| 对称的
grill 烤架
windshield 挡风玻璃
reflectors 反射器