4-Points Congruent Sets for Robust Pairwise Surface Registration Date : 01/01/26 Reporter : 鄒嘉恆 CVPR 2008

Introduction They introduce 4PCS, a fast and robust alignment scheme for 3D point sets that uses wide bases, which are known to be resilient to noise and outliers.

Outline Motivation Problem Approximate congruent 4-Points The 4PCS Algorithm Experimental results Conclusions

Motivation Two scans Corrupted with noise and outliers. In arbitrary initial poses with unknown overlap Refer to Dror A.’s slide on SIGGRAPH 2008

Problem Using wide base, not narrow-base Registration first, denoising later. [Goodrich et al. 1994]

Approximate congruent 4-Points

Approximate congruent 4-Points Affine invariants of 4-points set

Approximate congruent 4-Points Affine invariants of 4-points set Refer to Dror A.’s slide on SIGGRAPH 2008

Approximate congruent 4-Points Affine invariants of 4-points set Refer to Dror A.’s slide on SIGGRAPH 2008

Approximate congruent 4-Points Affine invariants of 4-points set Refer to Dror A.’s slide on SIGGRAPH 2008

Approximate congruent 4-Points Affine invariants of 4-points set Refer to Dror A.’s slide on SIGGRAPH 2008

Approximate congruent 4-Points Affine invariants of 4-points set Refer to Dror A.’s slide on SIGGRAPH 2008

Approximate congruent 4-Points Affine invariants of 4-points set Refer to Dror A.’s slide on SIGGRAPH 2008

The 4PCS Algorithm Refer to Dror A.’s slide on SIGGRAPH 2008

The 4PCS Algorithm Refer to Dror A.’s slide on SIGGRAPH 2008

The 4PCS Algorithm Refer to Dror A.’s slide on SIGGRAPH 2008

The 4PCS Algorithm Refer to Dror A.’s slide on SIGGRAPH 2008

The 4PCS Algorithm

The 4PCS Algorithm

Experimental results LD-RANSAC Local descrptors: spin images [Li and Guskov 2005]

Experimental results LD-RANSAC Local descrptors: spin images + integral invariants [Pottmann et al. 2007]

Experimental results Trial 1

Experimental results Trial 2

Experimental results Trial 2

Experimental results Trial 3

Experimental results

Experimental results

Experimental results

Experimental results Limitation

Conclusions A coplanar 4-points base allow us to employ a technique the efficiently matches pairs of affine invariants ratios in 3D. More faster. Prevent noise and outliers.