3.2.5. Advancing Front Surface Reconstruction

There are two forms of surface description of the objects processed by the proposed system: triangulated mesh (explicit representation), used to generate the deformation graph and the model; and TSDF volume (implicit representation), used to perform the fusion between the input surface and the model. The technique used to reconstruct the triangulated mesh was the Advancing Front [73,74]. This technique is based on the Delaunay triangulation, but has higher performance in terms of accuracy and quality, since the best triangles are formed sequentially. Another advantage of this technique is the ability to fill holes without having to perform this operation as preprocessing.

In the Advancing Front algorithm the initial triangle for mesh processing is defined by the size of the radius of the Delaunay triangles, defined by the circle passing over the three vertices of the triangle; the triangle with the smallest radius serves as the starting point of the algorithm. Then, the algorithm creates and maintains a list of candidate triangles to integrate the reconstructed surface. The list update happens every time a new triangle is incorporated into the partial surface, since new edges are made available for the reconstruction to move forward. For this list formation, there are four possibilities for a triangle to be a candidate to compose the surface: by extension; hole filling; ear filling; and glueing [73,74].

From the list of candidates, the triangle that has the highest plausibility degree is incorporated into the partial surface. The algorithm performs the update and definition of new triangles until all edges are verified. If a discontinuity occurs, the system performs the radius verification of the Delaunay triangles again, starting from the triangle with the smallest radius [73,74]. Figure 9 presents an example of surface reconstruction using the Advancing Front technique.

Advancing Front surface reconstruction. (a) Input point cloud and (b) surface reconstructed with the Advancing Front technique.