## List of required and optional parameters

### Deformation and optimization parameter settings (in paramDiffeos.xml type of files)

The only compulsory parameter is kernel-width.

• kernel-width: the width of the deformation kernel. The larger the more “rigid” the deformation. The smaller, the more local variations of the space is allowed.
• kernel-type: exact (default), p3m, fgt. The method for evaluating kernels.
• sparsity-prior (default 0.0): weight of the L^1 type prior.
• smoothing-kernel-width-ratio (default 1.0): template parameters in sparseAltas are updated via a Sobolev gradient, which is computed thanks to a kernel whose width equals smoothing-kernel-width-ratio times kernel-width.
• number-of-timepoints (default 10). Number of time steps in which the unit interval is discretized. It used for the integration of the differential equations.
• initial-cp-spacing (equals kernel-width by default): the spacing of the regular lattice of control points, which is used as initialization of control points position in sparseMatching and sparseAtlas.
• freeze-cp: On, Off (default). Optimizes or not the position of control points during optimization.
• initial-momenta (default void): name of a file containing values of momentum vectors, which will be used as initial conditions in the optimization. If set, a file name in initial-cp-position should be given, otherwise this file is ignored.
• initial-cp-position (default void): name of a file containing positions of control points, which will be used as initial conditions in the optimization. If no file name is given in initial-momenta, momentum vectors are initialized to zero. In case of conflict with initial-cp-spacing. If a file name is given in initial-cp-position and initial-cp-spacing is set, the latter is ignored and control point positions in the file name are used.
• optimization-method-type: GradientDescent, ISTA, FISTA (default). If sparsity-prior is different from 0, GradientDescent is automatically switched to ISTA. If sparsity-prior = 0, FISTA is the Nesterov scheme, and ISTA is the same as GradientDescent.
• max-iterations (default 100): maximum number of iterations during the optimization. To be increased if the convergence is slow.
• adaptive-tolerance (default 1e-4): optimization stops if (E_curr – E_init) < adaptive-tolerance * E_init, where E_curr and E_init denote the current and initial value of the criterion respectively, and if the maximum number of iterations is not reached.
• max-line-search-iterations (default 10): maximum number of iterations for adapting the stepsize during one step of the optimization method, using a line search method.
• step-expand (default 2.0): factor by which the stepsize is multiplied after a success in the line search method.
• step-shrink (default 0.5): factor by which the stepsize is multiplied after a failure in the line search method.
• initial-step-multiplier (default 10): factor by which the initial stepsize is multiplied. The initial stepsize is determined by heuristics.
• p3m-padding-factor (default 3): defines a padding of the regular lattice used in p3m optimization. The lattice is extended by p3m-padding-factor times kernel-width, to avoid side effects due to the periodic boundary conditions of the FFTs.
• p3m-working-spacing-ratio (default 0.2): the ratio between the lattice step used in p3m optimization and the kernel-width. 0.2 gives an approximation error of about 5%, set to 0.3 for increased speed and an approximation error of about 10%.

### Object parameter settings (in paramObject.xml type of files)

The first two parameters are compulsory, and the third one for objects of type other than Landmark.

• deformable-object-type: Landmark, PointCloud, OrientedPolyLine, NonOrientedPolyLine, OrientedSurfaceMesh, NonOrientedSurfaceMesh. The type of object, which also determines the metric used measure similarity between objects.
• data-sigma: the weight $\sigma_k$ of this object in the cost function in sparseMatching and sparseAtlas
• kernel-width: kernel-width for the metric used for objects of type PointCloud, OrientedPolyLine, NonOrientedPolyLine, OrientedSurfaceMesh and NonOrientedSurfaceMesh, namely objects using the currents or varifold representation.
• reorient-normal: On, Off (default) uses (or not) a VTK filter to re-orient normals consistently for genus zero surface mesh. Use with care for surface mesh with holes or with several connected components. This flag is ignored for objects other than OrientedSurfaceMesh.