Boundary extraction and simplification of a surface defined by a sparse 3D volume

Reconstructing surfaces with data coming from an automatic acquisition technique always entails the problem of mass of data. It leads to a mandatory data reduction process. Applying the process to the whole set of points induces an important risk of surface shrinking so that the initial boundary extraction is an important step permitting a simplification inside it. The global surface shape will then be better kept. It is nevertheless required to simplify the boundary, which can be done on the extracted boundary. In this paper, we present a new method to extract and simplify the boundary of an elevation surface given as voxels in a large 3D volume having the characteristics to be sparse since many data are missing. We first present our boundary definition based on mathematical relations between a point and its square neighborhoods. Second, we introduce algorithms to extract such a boundary. Third, we simplify this boundary.