An appearance-based display system has been developed to reproduce the accurate gloss appearance of real object. For the reproduction of the gloss appearance, BTF (Bi-directional 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. The proposed method separates the reflected light to the specular, the cast shadow and the invariant diffuse elements. By applying the LPCA (Local Principal Component Analysis) to the specular and the cast shadow images, the proposed method performs accurate reproduction by fewer principal components in comparison with the conventional method. As the result of demonstration on the appearance-based display, BTF rendering with proposed method was two times faster than the conventional method.