This file type is designed to store the critical points and arcs of the Morse-Smale complex (i.e. one dimensionnal filamentary structures). In skeleton files, the filamentary network is described as lists of nodes representing critical points or bifurcation points if available (see option -breakdown of skelconv), lists of segments tracing the local geometry of arcs and filaments originating from and leading to nodes and described as lists of segments. The base skeleton format is NDskl which is used internally, but this format may be converted to several other more or less complex formats of skeleton files adapted to different applications (see option -to in program skelconv, a list of available formats is displayed when running the program without argument).
nb: Within skeleton files, the segments are always oriented in the ascending direction of the arcs, which does *NOT* necessarily mean that the value of the field is necessarily increasing locally ! Indeed, the value is locally allowed to fluctuate within the persistence threshold, so the field value does not have to be strictly increasing locally along an arc.

Available formats:

  • -NDskl (Read / Write):
    This is the format of the skeleton files created with mse. It is a relatively complex binary format that contains all the information on the geometry and connectivity of the arcs of the Morse-Smale complex (i.e. filaments).

  • -NDskl_ascii (Write only):
    This ASCII format contains the same amount of information as NDskl files, but organized in a different way. In particular, filaments are not described as lists of segments but rather each filament is described by an origin node, a destination node, and a set of sampling points.

  • -segs_ascii and crits_ascii (Write only):
    This is a simplified ASCII file format designed to be easily readable but that only contains a subset of the information available in NDskl files. In particular, segs_ascii files contain a list of individual segments describing the local orientation of the arcs as well as some limited information on the filament they belong to, while crits_ascii contain information on the critical points and bifurcation points only.

  • -vtk, vtk_ascii, vtp and vtp_ascii (Write only):
    These formats are binary and ASCII legacy and XML VTK formats that are readable by several 3D visualization tools, such as VisIt or ParaView for instance.

Additional data: In addition to the topology and geometry of filamentary structures, more complete formats (i.e. NDskl, NDskl_ascii and all vtk formats) may store arbitrary additional information associated to filaments and nodes that can be used by skelconv (run skelconv filename.NDskl -info for a list of additional data available in skeleton file filename.NDskl). By default, mse stores the following additional data in skeleton type files:

  • -persistence / persistence_ratio / persistence_nsigmas (Nodes only) :
    The persistence (expressed as a difference, ratio or in number of sigmas) of the persistence pair containing the corresponding critical point. A negative or null value indicates that the node is not a critical point or that it does not belong to a persistence pair.

  • -persistence_pair (Nodes only):
    The index of the node that corresponds to the other critical point in the persistence pair (indices start at 0). The value is the index of the current node itself when it is not a critical point or it does not belong to a persistence pair.

  • -parent_index / parent_log_index (Nodes only):
    For each extrema only (i.e. minima and maxima), the index of the node that corresponds to the other extremum into which it would be merged if its persistence pair was canceled (indices start at 0). This can be used to reconstruct the tree of the hierarchy of maxima and minima. The value is -1 for non extrema critical points. The difference between the two versions is that the second (parent_log_index) is the hierarchy computed from the logarithm of the field. This second version is useful only for discrete point samples whose MS-complex is obtained from the delaunay tessellation computed with delaunay_nD. Practically, parent_log_index can be used whenever persistence pairs are cancelled in order of increasing ratio (option -nsig in mse), and parent_index whenever persistence pairs are cancelled in order of increasing difference (option -cut in mse).

  • -field_value / log_field_value (Nodes and Segments) :
    The value of the field and it logarithm. For segments, the suffix _p1 and _p2 is added to indicate which extremity of the segment it corresponds to.

  • -cell (Nodes and Segments) :
    The type and index of the cell corresponding to the node / segment in the initial network (i.e. from which the skeleton was computed). For segments, the suffix _p1 and _p2 is added to indicate which extremity of the segment it corresponds to. The value is a double precision floating number whose integer part is the index of the cell and decimal part its type. For instance, the 156th vertex (i.e. 0-cell) in the cell complex is represented as 156.0, while the 123th tetrahedron is 123.3. Note that the index of the 0-cell correpond to the index of the pixel / vertices in the original network from which the skeleton was computed.

  • -robustness / robustness_ratio (Nodes and Segments) :
    The robustness of the node / segment. Robustness is a local measure of how contrasted the critical point / filament is with respect to its local background, and it is therefore a good way to select only highly contrasted subsets of the filamentary structures (see option -trimBelow in skelconv). Note that robustness, like persistence, is defined as a difference or ratio between the value of the field in two points, so the robustness threshold has the same order of magnitude as the persistence threshold.

  • - type (Segments only) :
    The type of arc the segment belongs to. The value corresponds to the lowest critical index of the two critical points at the extremities of the arc the segments belongs to. For instance, in dimension D, the ridges (filaments) have type D-1.