An appearance-based display system has been developed to reproduce the accurate gloss appearance of real object. For the reproduction of the gloss appearance of rough surface, BTF (Bidirectional Texture Function) rendering is thought to be used in this system. However, efficient compression and reproduction methods are required for real-time rendering. In this paper, we propose an efficient approach of BTF compression based on dichromatic reflection model. This proposed method separates the reflected light to the specular, the cast shadow and the invariant diffuse elements. The efficient compression for the BTF rendering is performed by applying the LPCA (Local Principal Component Analysis) to the specular and the cast shadow images, since their appearance depends on the direction of the viewing or illumination. This method performs accurate reproduction by fewer principal components in comparison with the conventional method. The final projection image in an arbitrary direction of the viewing and illumination is synthesized from the specular reflection image, the cast shadow image and the invariant diffuse reflection image. Finally, the proposed method is implemented on the appearance-based display, and demonstrated high-speed BTF rendering which is two times faster than the conventional method.