## 2 Image Undistortion
Generally, iterative solvers are used. Image undistortion requires an accurate camera calibration in order to estimate the intrinsic camera parameters. Subsequently, lens distortion can be removed by applying the reverse distortion model, eliminating image artifacts due to lens aberrations. Many different methods are available to perform camera calibration [17]. The most common are based on calibration patterns printed on flat plates [18], particularly using the procedure proposed in [19]. This method requires different observations of the pattern with different orientations. Control points on the pattern with well-known correspondences to world coordinates and extracted. The set of correspondences between the image and world coordinates are used to first estimate linear projection models for each orientation. Subsequently, intrinsic camera parameters are calculated considering all orientations. Finally, a non-linear optimization method is used to finely tune the camera parameters, including distortion. Calibration plates are readily available for most camera configurations. However, cameras that are installed on aerial vehicles usually have long focal lengths that limit the applicability of printed calibration patterns due to the required size of the pattern. In this work, an alternative approach is proposed: camera calibration that is based on natural landmarks. The landmarks are situated on a flat surface on the scene, and they are observed while the aerial vehicle moves around them while the camera rotates. Multiple images are acquired from the same natural landmarks with different orientations as a result. Therefore, they can be assimilated to images acquired from a calibration pattern on a flat plate, and the procedure proposed in [19] can be used to calibrate the camera and estimate the distortion parameters. Moreover, the same procedure can be used for visible and infrared cameras, depending on the selected natural landmarks. Landmarks must be distinguishable in visible images, but also in infrared images, i.e, they are required to emit different infrared radiation than the surroundings in the scene. This can be achieved when using materials of different emissivity [20]. The proposed approach in this work as natural landmarks are the corner of windows. Windows are placed on flat walls, i.e., all control points (corners) lie on the same plane. Moreover, glass and window frames have very different emissivity than walls. Thus, they can be easily distinguished in the infrared spectrum. The proposed approach has a major advantage when compared with other methods: no complex calibration apparatus is needed. Moreover, there is no need to establish artificial landmarks. The result is a straightforward method that provides a reliable estimation of the camera parameters, both for visible or for infrared cameras. These parameters can then be used to undistort the acquired images. Figure 2 shows the results of image undistortion for visible images. Different images are acquired from the facade of a building with windows. For each image, natural landmarks on the corner of some windows are labeled. The positions of the windows on the facade are well-known. Thus, correspondences between image and world coordinates can be established, which is the required information for camera calibration. The estimated camera parameters can then be used to undistort  
the images, as can be seen in Figure 2c,d. The resulting images do not present the undesirable artifacts that are caused by lens distortion: straight lines in the scene do remain straight in the images, as can be seen in the figure. The same approach can be used with infrared images. Figure 3 shows the equivalent images in the infrared spectrum. The same procedure is followed: corners in the images are associated with the positions in the scene and the camera is calibrated. The images are undistorted using the estimation of lens distortion.