Hierarchical Segmentation of Sparse Surface Data Using Energy-Minimization Approach Raid Al-Tahir Centre for Caribbean Land and Environmental Appraisal Research (CLEAR) Department of Surveying and Land Information The University of the West Indies, Trinidad and Tobago rtahir@eng.uwi.tt Abstract: The main objective for this research is to develop an algorithm that produces a dense representation of a surface from a sparse set of observations and facilitates preliminary labeling of discontinuities in the surface. The solution to these issues is of a great interest to the new trends and applications in digital photogrammetry, particularly for large-scale urban imagery. This study adopts the approach of a concurrent interpolation of the surface and detection of its discontinuities by the weak membrane. The solution was achieved through developing a multigrid implementation of the Graduate Non-Convexity (GNC) algorithm. The conducted experiments proved that the developed method is adequate and applicable for dealing with large-scale images of urban areas as it was successful in producing a realistic surface representation and fulfilling other set criteria. Key words: Surface Reconstruction, Discontinuioty Detection, Multigrid Regularization. 1 Introduction Surface interpolation is a common and important task for several disciplines and applications in geosciences and engineering. This topic has regain research interest with the emergence of new trends and technologies in the collection of geo-spatial data such as digital photogrammetry and lidar. Such systems provide a large amount of data in the form of discrete points of three-dimensional coordinates. Photogrammetry is a 3-dimensional coordinate measuring technique that uses mainly aerial photographs as the fundamental medium for measurements. The basic mode of operation is based on taking photographs from at least two different view points; light rays are then traced back from each photograph to points on the