Surface alignment in DefSLAM

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Parent:  Mapping step-by-step in DefSLAM
Source: lamarca-2020

Goal:

  • to scale the up-to-scale surface (output of NRSfM ) to the proper dimensions
  • get an idea of the proper dimensions from the already estimated map
    • i.e. resulting surface must match the scale of the template $\mathcal{T}_{k-1}$
    • $\mathcal{T}{k-1}$: deformed map generated by the tracker at the instance of KF $=k$ insertion, with shape-at-rest of $\mathcal{S}{k-1}$ generated from KF: $(k-1)$
  • result: scale-corrected shape-at-rest $\mathcal{S}_k$

Method:

  • alignment of the map points using Sim(3)

  • Sim(3): basically a transformation that enlarges/shrinks by a certain scale (as far as I understand it). For more info see Wiki . unknown_filename.png scale $\hat{\mathcal{S}}$ to $\mathcal{S}$

  • Minimise the error between transformation of map points in $\hat{\mathcal{S}}$ and the map points in $\mathcal{S}$ unknown_filename.1.png where the arguments are the transformation parameters

Generating of the new template $\mathcal{T}_{k}$ from $\mathcal{S}_k$

  • Use Delaunay triangulation to make a triangular mesh from $\mathcal{S}_k$
  • New map point poses are computed
    • from the camera observation
    • by constraining them to be on the surface $\mathcal{S}_k$ (embedding of the re-observed map points)