Local warping is often used in applications of computer vision for stabilization, image resizing, panorama creation, and image editing. In current research, the improvement of the stabilized scene after global and local warping is achieved using stable key points’ trajectories and the correspondences of line segments and arcs. Local warping may cause distortion artifacts that are highly noticeable, especially in structural elements of a scene with lines, arcs, and planes. In the case of the complex scene with multi-level motion, it is reasonable to classify the key points into multi-level sets in order to find the correspondences in the restricted surrounding of the current motion level. First, the proposed method detects the line segments and rarely the arcs in a key frame and groups them in the motion levels. Second, the stable key points’ trajectories are classified into the motion levels. Third, the end points of segments are matched in the current stabilized frame relative to the nearest key frame. The line segments are simply replaced, while the arcs require a special tuning in a view of interpolation or arc samples. The experiments demonstrate the sufficient improvement of visibility in scenes warped locally.