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

Abstract

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.

A Complete Method for Reconstructing an Elevation Surface of 3D Point Clouds

“…works [9,10]. Therefore, the number of boundary points and their density depend on the previous processing and the initial shape of the surface.…”

“…As we can see in Figure 2, many triangles lies outside of the boundary (the red color line). In our case, the boundary of the surface has determined and processed in [9]. After triangulating the surface [11], it also generates many undesired triangles which are outside the exterior boundary (see Figure 2(b)).…”

“…This method of course requires computing the boundary of the point set before meshing. In our case, the boundary has already been determined in [9]. Therefore, in order to compute and remove the outward triangles, we just need to follow the boundary in the clockwise direction and delete the outward triangles accordingly.…”

“…3.3.1 Determining the boundary of the holes: In order to determine the boundary of the holes, we base on the previous work [9] to find the boundary points of these holes first (see Figure 4(a): red points).…”

“…For this reason, the input data are first structured in a sparse 3D volume as defined by Philippe Verney [8]. In order to preserve the shape of the surface, the first step is extracting and simplifying the boundary of the surface [9]. The proposed method for simplifying the surface inside its boundary [10] is an important step for the further meshing step.…”