Extraction and regularization of building roof boundaries from LiDAR data using the alpha-shape algorithm and CD-Spline

This Doctoral dissertation deals with the automatic extraction and regularization of building roof boundaries from LiDAR (Light Detection and Ranging) data, obtained by airborne LASER (Light Amplification by Stimulated Emission of Radiation) scanning. In this context, two problems were explored. The first corresponds to the adaptive determination of the parameter α of the alpha-shape algorithm, used to extract the approximate contour, from the available point cloud. The second refers to the regularization/modeling of building boundaries in the three-dimensional space, including buildings formed by curved segments of high complexity. Regarding the first problem, two approaches were proposed, both based on average point spacing. The main contribution of the approaches is related to the adaptive determination of α, allowing to minimize the influence of the point density variation. In order to solve the problem related to boundary regularization, a method based on the concept of CD-Spline (Changeable Degree Spline) was developed. The CD-Spline has ability to model boundaries formed by segments with different levels of complexity in n-dimensional space, which are modeled by polynomial functions of different degrees. In order to select the polynomial function automatically, an iterative approach of the CD-Spline was proposed. In this methodology, the polynomial function that best models each segment is selected by means of the statistical analysis of the residuals in each iteration. Two LiDAR datasets were considered to validate the proposed approaches. The first corresponds to the Unesp Photogrammetric Dataset of Presidente Prudente/Brazil, whereas the second corresponds to Vaihingen/Germany, being made available by German Association of Photogrammetry. Considering the determination of the parameter α, the qualitative and quantitative analyzes indicated that the proposed approaches are robust to density variation and have potential in the building boundary extraction, having better results when compared to a simpler approach, for example, the use of a global parameter. With respect to boundary regularization, the results indicated that the proposed method has ability to model of different types of boundaries, having satisfactory results even in contours formed by curved segments of different complexity. In addition, the approach was able to recover the contour in occlusion regions, caused by vegetation, and was robust in different densities. (AU)