Comparison of methods for axis detection of high-density acquired axially-symmetric surfaces

Axis evaluation is a fundamental preliminary step for several applications, from archaeology to geometric inspection of mechanical workpieces. The axis of symmetry is the situation feature of axially-symmetric surfaces, but also a reference for the evaluation of specific geometric properties (roundness, cylindricity and straightness of the axis). Since it is a non-physical geometric entity, it is not directly measurable from the surface, but can nevertheless be derived from the surface. For discretised models, defined by point clouds or triangular meshes, the axis of symmetry detection is a very complex task to accomplish. In this paper three methods for axis estimation of high-density acquired axially-symmetric surfaces are reviewed and compared in the common cases. The methods comparison, performed in this work, doesn’t consist just in an ordinary implementation of methods already described in the literature. These methods involve some auxiliary processing tools (mainly devoted to evaluate geometric differential properties) which characterise the implemented version and its performances. For each of these methods various versions have been considered and implemented which diversify each other for the criterion used for geometrical differential properties of the tessellated model. The methods for axis estimation are compared in the interpretation of the axes of axially-symmetric geometries (analytical and generic, partial and complete) for several types of discretization (size and regularity of the mesh). The results show that in the case of complete axially-symmetric features (analytical or generic), the three analysed methods perform similar results. In presence of not complete axially-symmetric features the methods show very different performances. The methods for axes estimation are of particular interest in several applications where precision and reliability are required. In this paper the main characteristics of the most important methods are identified and some guidelines for their use are given.