Tracking optimisation in DefSLAM

Source: lamarca-2020

Optimisation function

• Minimises
  • reprojection error (in the image)
  • deformation energy (of the template)
  • boundary nodes of the local zone are fixed (i.e. not set as arguments to the optimisation function)
    • this makes the absolute camera pose observable how?
    • in order to constrain the gauge freedoms
• Initial guess: values from previous optimisation (i.e. previous frame: t-1)

Reprojection error

robust against outliers due to Huber robust kernel

Deformation energy

Deformation energy = stretching energy + bending energy + temporal term

• “involves two spatial and one temporal constraint”

• requires the derivatives of each term/regulariser

• stretching energy: change in edge lengths in the local zone (w.r.t. shape at rest)

• bending energy: change in node mean curvatures (w.r.t. shape at rest)

  • Node mean curvature: estimated using the discrete Laplacian operator

• temporal term/reference regulariser: smoothness between estimates

  • to prevent abrupt changes between frames
  • to keep the template as close as possible to its initial position