Glossary

Every feature maskel can extract, grouped by the level it's computed at and named exactly as it appears in the corresponding CSV column (summary.csv, <image>_branches.csv, <image>_nodes.csv — see Configurable parameters for when each file is written). Generated by running maskel with every extraction option enabled on a 3D vessel volume and reading the resulting tables and code together.

Spacing-aware below means the value changes once extraction.spacing is set to a non-isotropic value instead of the default null; everything else stays in raw pixel/voxel units (or a dimensionless ratio/count) no matter what spacing is.

Object-level features (summary.csv)

One row per object per image. Requires extraction.summary (on by default); most fields need other options too, as noted.

Every mask-derived field below (vessel_area, vessel_area_fraction, and the radius/diameter statistics) is measured against the mask after preprocessing — if extraction.fill_holes or extraction.closing_iterations is set, that's the morphologically-modified mask, not the raw input crop.

• object_id — the mask's own label value for this object (1 for a plain binary mask).
• num_nodes — number of distinct graph nodes (junctions/endpoints) referenced by any branch in this object.
• num_edges — number of branches (skeleton segments) in this object. Always computed alongside the summary, regardless of whether extraction.branches is also on.
• num_endpoints — number of nodes with degree 1 (skeleton tips).
• num_bifurcations — number of nodes with degree ≥ 3 (branch points).
• total_length — sum of every branch's branch-distance. Spacing-aware.
• mean_length / std_length / max_length / min_length — mean/std/max/min of branch-distance across all branches. Spacing-aware.
• mean_tortuosity / std_tortuosity — mean/std of per-branch tortuosity (see Branch-level below), excluding branches where it's undefined (zero euclidean distance). Tortuosity is a length ratio, so unaffected by spacing even though the underlying lengths are.
• num_components — number of disjoint connected pieces in this object's branch graph. Usually 1, since each object is already its own connected foreground region before thinning — but pruning or thinning can fragment it further.
• mean_degree / max_degree — mean/max node degree over this object's graph nodes.
• fractal_dimension — box-counting fractal dimension of this object's own skeleton crop: count how many boxes of a given size contain any skeleton pixel, repeat over a range of box sizes, and fit a log-log line whose slope magnitude is the fractal dimension. Ranges ~1–2 for 2D skeletons (up to ~3 for 3D); values near the upper end mean the skeleton densely fills space, values near the lower end mean sparse, line-like coverage. Requires extraction.fractal_dimension; forced to 0.0 when spacing is set and anisotropic, since box-counting assumes isotropic voxels.
• fractal_dimension_r2 — R² goodness-of-fit of the log-log line used to compute fractal_dimension (fit-quality indicator, not a feature of the vessel itself).
• hgu — "hyphal growth unit": total_length / num_endpoints. The average uninterrupted skeleton length per tip; higher means longer stretches between endpoints. Spacing-aware (inherits from total_length).
• mean_radius / std_radius / min_radius / max_radius — statistics of the Euclidean-distance-transform radius, sampled at every skeleton pixel of this object (not per-branch — see the branch-level fields of the same name for that). Requires extraction.mask_radius. Spacing-aware (the EDT is computed with spacing as the pixel sampling distance).
• mean_diameter / std_diameter / min_diameter / max_diameter — 2 × the radius statistics above. Same requirements and spacing-awareness.
• vessel_area — foreground pixel/voxel count of this object's own (padded bounding-box) crop of the binary mask, before thinning (see note above on which mask). Despite the name, this is an area in 2D and a volume in 3D. Spacing-aware: scaled by the pixel/voxel's physical area/volume (spacing[0] * spacing[1] * ...) when set.
• vessel_area_fraction — the same foreground count as a fraction (0–1) of the crop's total pixel/voxel count. A ratio, so unaffected by spacing.
• mean_segment_volume — mean of the branch-level volume column (see below) across this object's branches. Requires extraction.mask_radius; 0.0 when there are no branches with a valid radius. Spacing-aware.
• mean_surface_area — mean of the branch-level surface_area column across this object's branches. Same requirements and spacing-awareness.

Branch-level features (<image>_branches.csv)

One row per branch (skeleton edge between two graph nodes). Requires extraction.branches (and output.write_branch_csv to actually write the CSV). Most columns other than object_id, tortuosity, straightness, and the radius/diameter/volume/surface_area group come directly from skan's summarize().

• object_id — added by maskel; the object this branch belongs to.
• skeleton-id — which connected skeleton fragment (within this object) the branch belongs to, in case num_components > 1. Not the same as object_id.
• node-id-src / node-id-dst — the two endpoint nodes' ids in this object's own graph (matches node_id in <image>_nodes.csv for the same object).
• branch-distance — the branch's path length along the skeleton (sum of step-to-step distances, not a straight line). Spacing-aware.
• branch-type — 0 = endpoint-to-endpoint (an isolated segment, both ends degree 1), 1 = endpoint-to-junction (a tip), 2 = junction-to-junction, 3 = isolated cycle (a closed loop with no branch point, so both ends are the same node).
• mean-pixel-value / stdev-pixel-value — mean/std of the skeleton array's own pixel values along the branch's path. Since maskel's skeleton is a binary 0/1 array (not a grayscale intensity image), this is essentially always 1.0/0.0 — kept for compatibility with skan's schema rather than being informative here.
• image-coord-src-0, image-coord-src-1, (image-coord-src-2) / image-coord-dst-* — the source/destination node's raw pixel-index coordinates, one column per axis, in this object's local (cropped) coordinate system. Never spacing-scaled.
• coord-src-* / coord-dst-* — the same coordinates scaled by spacing (identical to the image-coord-* values when spacing is null). Spacing-aware.
• euclidean-distance — straight-line distance between the source and destination nodes, computed from the spacing-scaled coord-src/coord-dst values. Spacing-aware.
• tortuosity — branch-distance / euclidean-distance; NaN when euclidean-distance is 0 (a cycle). A length ratio, so unaffected by spacing even though both inputs are spacing-aware.
• straightness — the inverse, euclidean-distance / branch-distance; NaN when branch-distance is 0. Also spacing-independent.
• mean_radius / std_radius / min_radius / max_radius — EDT radius statistics sampled along just this branch's path (as opposed to the object-level fields of the same name, which cover the whole object). Requires extraction.mask_radius. Spacing-aware.
• mean_diameter / std_diameter / min_diameter / max_diameter — 2 × the radius statistics above. Same requirements and spacing-awareness.
• volume — this branch modeled as a chain of frustums between consecutive skeleton pixels along its path: each step's physical length (diagonal- and spacing-aware) weighted by the average radius of its two endpoints, summed as π × Σ(r_mid² × step_length). Requires extraction.mask_radius. Spacing-aware.
• surface_area — the same frustum chain's lateral surface area, 2π × Σ(r_mid × step_length). Same requirements and spacing-awareness.

Node-level features (<image>_nodes.csv)

One row per graph node (junction, endpoint, or pass-through point). Requires extraction.nodes (and output.write_node_csv to write the CSV) — unlike napari-maskel's node layer, which only displays branch/end nodes, this CSV includes every node, including pass-through ones.

• object_id — added by maskel; the object this node belongs to.
• node_id — this node's id in the object's own graph (matches node-id-src/node-id-dst in <image>_branches.csv for the same object).
• coord_0, coord_1, (coord_2) — the node's raw pixel-index coordinates, one column per axis, already offset into the full image's coordinate system (unlike the branch CSV's local-crop coordinates). Never spacing-scaled.
• degree — number of branches meeting at this node.
• is_endpoint — true when degree == 1 (a skeleton tip).
• is_junction — true when degree >= 3 (a branch point).
• is_pass_through — true when degree == 2 (a point along a straight, unbranched run — not a true topological feature, just where skan happened to place a node).
• radius — the EDT radius sampled at this node's exact pixel. Requires extraction.mask_radius. Spacing-aware.