目的 以非平行于目标的姿态成像时，线阵相机采集的图像的几何变换规律与面阵相机不同，这导致面阵图像的几何变换模型及其直接配准方法无法实现线阵图像的配准；同时，亮度恒常假设无法满足大视场镜头引起的图像亮度衰减问题。因此，提出了一种几何联合分段亮度的线阵图像直接配准方法。方法 根据线阵图像的几何变换模型和分段增益-偏置亮度模型，将线阵图像的配准问题表示为一个非线性最小二乘问题。采用高斯-牛顿法对配准问题中的几何变换参数和亮度变换参数联合进行优化；此外，针对以单位变换为初始值时配准图像存在较大几何误差致使优化不收敛，设计了一种初始值快速搜索策略。结果 实验数据包含本文采集的线阵图像数据集和真实列车线阵图像。配准结果表明，采用本文提出的方法配准后的标注点坐标均方根误差均小于1个像素，优于采用面阵图像几何变换模型的直接配准方法。算法对亮度变化具有更强的鲁棒性，提高了线阵图像配准的成功率。结论 本文所提出的几何联合分段亮度线阵图像配准方法可以精确、鲁棒的对齐非平行姿态线阵相机所采集的图像。

Objective Image registration is a fundamental problem in computer vision and image processing, which aims to eliminate the geometric difference of the object in the image collected by the different cameras at different times and poses. Imaging registration has been widely used in several visual applications, such as image tracking, image fusion, image analysis and anomaly detection. The main image registration methods can be classified into two kinds: feature-based registration methods and direct registration methods. The former calculates the parameters in the geometric transformation model by extracting and matching the features, such as corners or edges, while the latter directly uses the image intensities to infer the parameters. Obviously, it is the key to image alignment to choose a reasonable geometric transformation model. The principle of the line-scan camera and the area-scan camera are identity and both of them conform to the principle of pin-hole imaging, but the imaging model of the line-scan camera is different from that of the area-scan camera due to the characteristics of its sensor. With the same change of the camera pose, the locations of the same three-dimensional world points mapped to the two kinds of images are different. In other words, the geometric transformation law of the object in the images caused by the pose change of the two kinds of cameras is different. When the image plane of the line-scan camera is non-parallel to the object plane, the geometric transformation models commonly used for area-scan image registration, such as the rigid transformation model, affine transformation model, projection transformation model and so on, cannot conform to the geometric transformation law of line-scan images. The direction registration method based on the geometric transformation model of the area-scan image cannot realize the geometric alignment of the line-scan image. Besides, most of the existing direct image registration method to solve the image alignment problem is based on the brightness constancy assumption and only the geometric transformation is considered. In real-world applications, the variation of the brightness is unavoidable and the brightness constancy assumption cannot meet the problem of brightness attenuation when capturing images with a large-angle lens. Therefore, the line-scan image registration problem which estimates the geometric and photometric transformations between two images is considered, and a direct registration method of the line-scan image based on geometric and piecewise photometric is proposed in this paper. Method Firstly, the optimization objective function of line-scan image registration is constructed by using the sum of squares difference of image intensities. According to the geometric transformation model of line-scan images and the piecewise gain-bias photometric transformation model, the registration problem of the line-scan image is expressed as a nonlinear least square problem. Second, the Gauss-Newton method is used to optimize the geometric and photometric transformation parameters in the registration problem. The non-linear optimization objective function is linearized by performing a first-order Taylor expansion. The Jacobian of the warp and photometric is derived based on the geometric transformation model of the line-scan image and the gain-bias model. At last, to obtain the optimal geometric and photometric transformation parameters, the incremental of warp and photometric are repeatedly computed until it is below a threshold according to the normal equation. Since the identity warp as the initial value cannot be guaranteed near the optimal solution, the iteration does not converge in the registration process. This problem is solved by designing an initial value fast matching method which provides an initial solution closer to the optimal solution. The process of the initial value fast matching method is as follows: fixed-size areas are selected in the four corners of the template image respectively, and then matched in the target image in the corresponding position. The minimum and maximum coordinates of the optimal matching position in the horizontal and vertical directions are selected. Then the scale factor and translation factor in the horizontal and vertical directions are solved, and the result is taken as the initial value for the iteration. The initial value provided by the initial value fast matching method reduces the geometric difference between the template image and the target image, and the success rate of the registration method is improved. Result In order to verify the proposed line-scan image registration method, a line-scan image acquisition system was built to obtain line-scan images of the planar object under different imaging poses and illumination variations. The experimental data also include EMU train line-scan images, which were collected by the line-scan camera in the natural environment. Images collected by the line-scan image acquisition system and EMU train line-scan images are annotated respectively, and the RMSE of the annotated point coordinates is used as the evaluation index of the geometric error. On the line-scan image dataset collected in this paper, the performance of the initial value fast matching method is verified. The geometric error between the template image and the warped target image based on the initial value provided by the fast template block matching method is smaller than that based on the identity warp. It indicates that the initial value provided by the initial value fast matching method is closer to the optimal solution of the geometric transformation. Through the registration experiments on the collected dataset and EMU train line-scan image, the results show that the RMSE of the annotated point coordinates are less than 1 pixel, and the registration accuracy is excellent. Conclusion Our algorithm is more robust to lighting changes and improves the success rate of line-scan image registration. The joint geometric and piecewise photometric line-scan image registration method proposed in this paper can accurately align the images collected in practical application scenes, which also is a foundation for train anomaly detection based on line-scan images. Therefore, the direct registration method proposed in this paper can accurately and robustly align the line-scan images collected under non-parallel poses.