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Robust affine point matching via quadratic assignment on Grassmannians

Alexander Kolpakov, Michael Werman

Abstract

Robust Affine Matching with Grassmannians (RoAM) is a new algorithm to perform affine registration of point clouds. The algorithm is based on minimizing the Frobenius distance between two elements of the Grassmannian. For this purpose, an indefinite relaxation of the Quadratic Assignment Problem (QAP) is used, and several approaches to affine feature matching are studied and compared. Experiments demonstrate that RoAM is more robust to noise and point discrepancy than previous methods.

Robust affine point matching via quadratic assignment on Grassmannians

Abstract

Robust Affine Matching with Grassmannians (RoAM) is a new algorithm to perform affine registration of point clouds. The algorithm is based on minimizing the Frobenius distance between two elements of the Grassmannian. For this purpose, an indefinite relaxation of the Quadratic Assignment Problem (QAP) is used, and several approaches to affine feature matching are studied and compared. Experiments demonstrate that RoAM is more robust to noise and point discrepancy than previous methods.
Paper Structure (14 sections, 14 equations, 25 figures, 1 algorithm)

This paper contains 14 sections, 14 equations, 25 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Algorithm RoAM
  3. Correctness
  4. Robustness to noise
  5. Point discrepancy
  6. Finding feature matching
  7. Experiments
  8. Random point clouds
  9. Caerbannog point clouds
  10. Partial scans of the same object
  11. Comparison to other algorithms
  12. Conclusions
  13. Acknowledgements
  14. Appendix: numerical tests

Figures (25)

  • Figure 1: "Teapot" cloud: the initial point cloud $X$ (blue) and its image $Y$ (red) under a linear transformation $L$ with $\mathrm{cond}\,L = 4.0$. The feature matching is shown: side view (top) and top view (bottom).
  • Figure 2: "Teapot" cloud: specimen $X$ (yellow) and preimage $L^{-1}_0\, Y$ (red). Points of $X$ having no correspondence in $Y$ are marked (blue).
  • Figure 3: "Bunny" cloud: specimen $X$ (yellow) and preimage $L^{-1}_0\, Y$ (red). Points of $X$ having no correspondence in $Y$ are marked (blue).
  • Figure 4: "Cow" cloud: specimen $X$ (yellow) and preimage $L^{-1}_0\, Y$ (red). Points of $X$ having no correspondence in $Y$ are marked (blue).
  • Figure 5: "Teapot" cloud: $\delta_L$ as a function of $\lambda$ (discrepancy level, horizontal) and $\sigma$ (noise level, vertical)
  • ...and 20 more figures