Fitting and recognition of geometric primitives in segmented 3D point clouds using a localized voting procedure

Recognizing geometric primitives in 3D point clouds of mechanical CAD objects

“…The recent advances in the use of the algebraic functions [8] are paving the road to a larger use of the HT for recognising more complex families of geometric primitives. To the best of our knowledge, the sole approaches that exploit this idea were proposed in [31], for the recognition of an ellipsoid in a free-form model; and in [9], for the recognition of spheres, (circular) cylinders, (circular) cones and tori in presegmented point clouds, as a way to post process faulty segmentations. The work in [9] also addresses the problem of reducing the number of the parameters of the primitive representation when the point cloud corresponds to a patch of a primitive: in this case, the point cloud is opportunely rototranslated in a space embedding so that it can be fit by a primitive in a standard form.…”

“…In addition to the simple geometric primitives of Figure 1 (plane, cylinder, cone, sphere, and torus) -see [9] for their recognition in presegmented point clouds -in this section, we introduce a set of complex geometric primitives that to the best of our knowledge have never been used before for recognition by HT.…”

“…A strategy to obtain the standard form in an automatic way starting from a point cloud is provided in [9], and it can be naturally extended to complex primitives.…”

“…For our purposes the orientation of the normal vector is not relevant, as we are only interested in aligning the most voted normal direction to the z-axis. We can therefore use the approach introduced in [9], which estimates the normal vectors through a voting procedure. For convenience, when P is clean we can also consider the method presented in [34], which is available in MATLAB with the pcnormals function; for each input point in P, the method selects the k points of P closest to that input point and then uses principal component analysis (PCA) to estimate the normal vector.…”

“…To this end, we aggregate the primitives found on the basis of their size and space embedding, whenever possible. Our strategy also reduces the oversegmentation of the output and we exploit the strategy proposed in [9] to decrease the computational complexity of methods based on the HT thanks to an opportune preprocessing of the point cloud and its subparts. Our experiments confirm the robustness and completeness of the method, and the comparisons made exhibit its competitiveness with respect to the methods proposed so far in the literature.…”