High dynamic range (HDR) displays that incorporate two optically-coupled image planes have recently been developed. The existence of such displays requires HDR image splitting algorithms that send appropriate signals to each plane to faithfully reproduce the appearance of the HDR input. In this paper we introduce a new appearance-based HDR image splitting algorithm that incorporates the iCAM06 image appearance model to do image enhancement. We compare its performance to the widely used luminance square root algorithm and report the results of image quality experiments that compare the two algorithms with respect to contrast, color, sharpness, naturalness, and overall quality. We find that the overall quality, color, and naturalness of the images produced by the new algorithm is superior to those produced by the square root method. The new algorithm provides a principled and effective approach for presenting HDR images on dual imager HDR displays.