There are currently several automatic building extraction methods introduced in the literature, but none of them are capable to completely extract portions of a building that are below a pre-defined building minimum height threshold. This paper proposes a systematic method which analyzes the height differences between the extracted adjacent planes above and below the height threshold as well as the planes' connectivity, thereby, extracting all portions belonging to buildings more completely. In general, the height difference between the edges of the adjacent planes above and below the height threshold that belong to the same building is more uniform. In addition, the extracted planes below the height threshold that belong to a building and their adjacent ground planes also have a clear height difference. The proposed method incorporates such information to achieve better performance in building extraction. We have compared our proposed method to a current state-of-the-art building extraction method qualitatively and quantitatively. Our experimental results show that our proposed method successfully recovers portions of a building below the height threshold, thereby achieving relatively higher average completeness (an improvement of 1.14%) and quality (an improvement of 0.93%).