It is one of the central issues in augmented reality and computer vision to track a planar object moving relatively to a camera in an accurate and robust manner. In previous studies, it was pointed out that there are several factors making the tracking difficult, such as illumination change and motion blur, and effective solutions were proposed for them. In this paper, we point out that degradation in effective image resolution can also deteriorate tracking performance, which typically occurs when the plane being tracked has an oblique pose with respect to the viewing direction, or when it moves to a distant location from the camera. The deterioration tends to become significantly large for extreme configurations, e.g., when the planar object has nearly a right angle with the viewing direction. Such configurations can frequently occur in AR applications targeted at ordinary users. To cope with this problem, we model the sampling and reconstruction process of images, and present a tracking algorithm that incorporates the model to correctly handle these configurations. We show through several experiments that the proposed method shows better performance than conventional methods.