Super Generalized 4PCS for 3D Registration

The 4-Points Congruent Sets (4PCS) Algorithm is an established approach to registering two overlapping 3D point sets with partial overlap and arbitrary initial poses. 4PCS performs the registration efficiently using a special set of 4 points, also known as a base, formed by two co-planar pairs of points within a RANSAC framework. The SUPER 4PCS algorithm uses intelligent indexing to reduce the complexity of the original 4PCS algorithm. Although SUPER 4PCS is efficient, we show in this work that one can gain significant practical improvements in runtime by reducing the number of congruent 4-point bases across the two 3D point sets. We accomplish this by using a generalized 4-point base which considers non-coplanar 4-point bases as well as planar ones. We show through experimentation that the number of 4-point bases decreases, sometimes exponentially, with a non-coplanar base. Using this property, we propose the Super Generalized 4PCS algorithm which can exhibit a significant speed-up of up to 6.5x over the Super 4PCS algorithm as demonstrated experimentally.