Query regarding source mesh vertex correspondence in Deformetrica output

[Minuf fugf Fhgc]

I am currently using Deformetrica for diffeomorphic registration of 3D surface meshes (VTK format) and have encountered a behavior regarding the output vertex counts that I would appreciate some clarification on.

My setup involves registering a series of source surface meshes (each with approximately 20,001 vertices, e.g., P*_VZ_L.vtk) to a fixed template surface mesh (P8_VZ_L.vtk, which has 13,185 vertices). I am using the DeterministicAtlas model-type with the <freeze-template>On</freeze-template> option set in optimization_parameters.xml, and the Varifold attachment type for the SurfaceMesh objects defined in model.xml.

My observation is that the output files representing the deformation flow, starting from the very first timepoint (DeterministicAtlas__flow__...__tp_0.vtk), as well as the final DeterministicAtlas__Reconstruction__...__subject_....vtk file, all have 13,185 vertices – matching the vertex count of my template mesh, rather than the 20,001 vertices of my original source mesh.

This leads me to believe that Deformetrica, under my current configuration or perhaps by default when source and template topologies differ, might be re-sampling or projecting the geometry of my original source mesh onto the mesh structure/topology of the template mesh at the t=0 stage of the LDDMM flow. We've seen documentation (possibly for an older version, e.g., Sec 3.2 regarding dense-mode) that hints at mechanisms where control points are tied to template vertices, which might explain this behavior.

My primary goal is to establish a clear point-to-point correspondence from my original source mesh (20,001 vertices) to its deformed state after registration. Given the observed change in vertex count from tp_0.vtk onwards, this direct correspondence by index is not straightforward.

Could you please provide some insights or guidance on the following:

1. Is this behavior—where the tp_0.vtk and subsequent flow/reconstruction files adopt the template's mesh structure and vertex count—expected under certain conditions (e.g., dense-mode, or as a default when source/template topologies differ)? If so, what are these conditions?
2. If this initial re-sampling/projection onto the template's mesh structure occurs, what is the recommended method within the Deformetrica framework to understand or reconstruct the mapping from the vertices of the original source mesh (20,001 points) to this initial tp_0.vtk state (13,185 points which represents the source geometry on the template's mesh)?
3. Alternatively, is there an operational mode, output option, or a different set of parameters in Deformetrica that would ensure the LDDMM deformation is directly applied to the original source mesh's vertices, thereby preserving the 20,001 vertex count throughout the flow files and in the final Reconstruction file, which would allow for direct index-based correspondence?

Thank you for developing such a powerful tool and for any assistance you can provide on this matter. I am happy to provide my configuration files (model.xml, data_set.xml, optimization_parameters.xml) and relevant log outputs if that would be helpful.

Sincerely,