Building extraction is one of the main research topics of the photogrammetry community. This paper presents automatic algorithms for building boundary extractions from aerial LiDAR data. First, segmenting height information generated from LiDAR data, the outer boundaries of aboveground objects are expressed as closed chains of oriented edge pixels. Then, building boundaries are distinguished from nonbuilding ones by evaluating their shapes. The candidate building boundaries are reconstructed as rectangles or regular polygons by applying new algorithms, following the hypothesis verification paradigm. These algorithms include constrained searching in Hough space, enhanced Hough transformation, and the sequential linking technique. The experimental results show that the proposed algorithms successfully extract building boundaries at rates of 97%, 85%, and 92% for three LiDAR datasets with varying scene complexities.