Eye-based interaction is one of the solutions for achieving intuitive interfaces on surfaces such as a large display, and thus, various eye-tracking methods have been studied. Cross-ratio based gaze estimation, which determines the point-of-gaze on a screen, has been studied actively as a novel eye-tracking method because the method does not require a hardware calibration defining the relationship between a camera and monitor. We expect that the cross-ratio method will be a breakthrough for eye-based interaction under various circumstances such as tabletop devices and digital whiteboards. In eye-tracking, near-infrared light is often emitted, and at least four LEDs are located on display corners for detecting the screen plane in the cross-ratio based method. However, long-time radiation of near-infrared light can make a user fatigued. Therefore, in this study, we attempted to extract the screen area correctly without near-infrared radiation emission. A polarizing filter is included in the display, and thus, visibility of the screen can be controlled by the light__ polarization direction of the external polarized light filter. We propose gaze estimation based on the cross-ratio method using a developed polarization camera system, which can capture two polarized images of different angles simultaneously. Further, we confirmed that the point-of-gaze could be estimated using the screen reflection detected by computing the differences between two images without near-infrared emission.