Attribute catalog

This reference lists the scalar attributes exposed by the public API. C++ uses the PascalCase enumerators from Attribute, for example Attribute::Area. Stable symbolic names use uppercase snake case in string requests, returned layouts, and Python, for example "AREA" and mmcfilters.Attribute.AREA.

Every listed attribute produces one value per node in the returned AttributeNames layout. For usage patterns and output-space rules, see Attributes. Family-specific mathematical conventions are kept in focused guides such as Distance-transform attributes.

The Contract column classifies the input required by the attribute:

• Topology/support: does not read node altitudes. Some attributes use only finite smallest-node mapping; others additionally declare regular 2D geometry or adjacency requirements.
• Altitude-aware: reads the node altitude buffer and therefore requires a ValuedMorphologicalTree<T> or ValuedMorphologicalTreeView<T>.
• Tree topology: uses only parent/child relations in the hierarchy.

The Groups column lists non-ALL group memberships. Rows are sorted by the first listed group; attributes that belong to more than one group appear only once. ALL expands to every attribute in this table.

The complete capability matrix is:

Attributes	Altitude	Grid 2D	Adjacency	Monotone order	Altitude for directional adjacency	Canonical 4/8
AREA, SUBTREE_HEIGHT through BALANCE_NODE, AVG_CHILD_HEIGHT_NODE	no	no	none	no	no	no
VOLUME, RELATIVE_VOLUME, GRAY_LEVEL_HEIGHT, MEAN_GRAY_LEVEL, GRAY_LEVEL_VARIANCE	yes	no	none	no	no	no
bounding boxes, central/Hu moments, moment-derived attributes, CONTOUR_*	no	yes	none	no	no	no
BITQUAD_*	no	yes	uniform or directional	no	yes	yes
MAX_DIST_EXACT, MAX_DIST, MAX_SQUARED_DIST*, MAX_DIST_CENTER_*, DIST_*	no	yes	none	no	no	no

C++ callers can query attributes::registry::capabilityRequirements(attribute). Python callers use mmcfilters.Attribute.requirements(attribute). Group requests are expanded to scalar attributes before these requirements are validated.

C++ enumerator	Stable/Python name	Groups	Contract	Description
Attribute::Volume	VOLUME	GRAY_LEVEL	Altitude-aware	Sum of altitude-weighted support contributions over the node subtree. It behaves like the gray-level mass or integral of the image over the connected component support.
Attribute::RelativeVolume	RELATIVE_VOLUME	GRAY_LEVEL	Altitude-aware	Recursive contrast volume R(n) = area(n) + sum_c [R(c) + area(c) * abs(altitude(c) - altitude(n))] over the direct children c.
Attribute::GrayLevelHeight	GRAY_LEVEL_HEIGHT	GRAY_LEVEL	Altitude-aware	Maximum absolute altitude difference between the node and any node in its subtree. On monotone max-tree and min-tree hierarchies this reduces to the traditional one-sided span; it also applies to hierarchies with unconstrained altitude order. Leaves have value 0.
Attribute::MeanGrayLevel	MEAN_GRAY_LEVEL	GRAY_LEVEL	Altitude-aware	Arithmetic mean of the image values over the full node support: sum(f(x), x in X) / card(X).
Attribute::GrayLevelVariance	GRAY_LEVEL_VARIANCE	GRAY_LEVEL	Altitude-aware	Population variance of the image values over the full node support, with denominator card(X).
Attribute::Area	AREA	SHAPE	Topology/support	Number of pixels in the full node support. Equivalently, it is the sum of proper-part cardinalities over the node's subtree.
Attribute::BoxWidth	BOX_WIDTH	SHAPE	Topology/support	Width, in columns, of the smallest axis-aligned bounding box enclosing the node support.
Attribute::BoundingBoxHeight	BOUNDING_BOX_HEIGHT	SHAPE	Topology/support	Height, in rows, of the smallest axis-aligned bounding box enclosing the node support.
Attribute::DiagonalLength	DIAGONAL_LENGTH	SHAPE	Topology/support	Euclidean diagonal length of the bounding box, sqrt(width^2 + height^2).
Attribute::Rectangularity	RECTANGULARITY	SHAPE	Topology/support	Ratio AREA / (BOX_WIDTH * BOUNDING_BOX_HEIGHT). Values closer to 1 indicate that the support fills its bounding box densely.
Attribute::RatioWh	RATIO_WH	SHAPE	Topology/support	Bounding-box aspect ratio, max(width, height) / min(width, height) for non-degenerate boxes. Values are at least 1.
Attribute::BoxColumnMin	BOX_COLUMN_MIN	SHAPE	Topology/support	Minimum image column index covered by the node support.
Attribute::BoxColumnMax	BOX_COLUMN_MAX	SHAPE	Topology/support	Maximum image column index covered by the node support.
Attribute::BoxRowMin	BOX_ROW_MIN	SHAPE	Topology/support	Minimum image row index covered by the node support.
Attribute::BoxRowMax	BOX_ROW_MAX	SHAPE	Topology/support	Maximum image row index covered by the node support.
Attribute::MaxDistExact	MAX_DIST_EXACT	SHAPE, DIST_TRANSF_EXACT	Topology/support	Maximum exact Euclidean distance, in pixels, from a support pixel to the foreground 4-connected contour. It is the square root of MAX_SQUARED_DIST_EXACT.
Attribute::MaxDist	MAX_DIST	SHAPE, DIST_TRANSF	Topology/support	Maximum of the approximate distance field, in pixels. It is the square root of MAX_SQUARED_DIST and may differ from MAX_DIST_EXACT.
Attribute::MaxSquaredDistExact	MAX_SQUARED_DIST_EXACT	DIST_TRANSF_EXACT	Topology/support	Maximum exact squared Euclidean contour distance, in squared pixels. This exposes the maximum integer cost of the exact field without applying a square root.
Attribute::MaxSquaredDist	MAX_SQUARED_DIST	DIST_TRANSF	Topology/support	Maximum approximate squared contour-distance cost, in squared pixels.
Attribute::DistSquaredSumExact	DIST_SQUARED_SUM_EXACT	DIST_TRANSF_EXACT	Topology/support	Sum of the exact squared Euclidean distance to the foreground A4 contour over every support pixel.
Attribute::DistSquaredMeanExact	DIST_SQUARED_MEAN_EXACT	DIST_TRANSF_EXACT	Topology/support	Arithmetic mean of the exact squared contour-distance field over the node support.
Attribute::DistRmsExact	DIST_RMS_EXACT	DIST_TRANSF_EXACT	Topology/support	Root mean square Euclidean contour distance, sqrt(mean(d^2)), in pixel units. This is not the arithmetic mean of d.
Attribute::DistSquaredVarianceExact	DIST_SQUARED_VARIANCE_EXACT	DIST_TRANSF_EXACT	Topology/support	Population variance of the exact squared contour-distance samples, mean((d^2)^2) - mean(d^2)^2, in fourth-power pixel units.
Attribute::DistSquaredSum	DIST_SQUARED_SUM	DIST_TRANSF	Topology/support	Sum of the approximate squared-distance field over the node support.
Attribute::DistSquaredMean	DIST_SQUARED_MEAN	DIST_TRANSF	Topology/support	Arithmetic mean of the approximate squared-distance field over the node support. It need not equal DIST_SQUARED_MEAN_EXACT.
Attribute::DistRms	DIST_RMS	DIST_TRANSF	Topology/support	Root mean square distance derived from the approximate field, sqrt(mean(cost)), in pixel units.
Attribute::DistSquaredVariance	DIST_SQUARED_VARIANCE	DIST_TRANSF	Topology/support	Population variance of the approximate squared-distance samples.
Attribute::MaxDistCenterRowExact	MAX_DIST_CENTER_ROW_EXACT	DIST_TRANSF_EXACT	Topology/support	Zero-based row of the exact support pixel attaining MAX_DIST_EXACT. If several pixels attain the maximum, the smallest row-major pixel is selected.
Attribute::MaxDistCenterColumnExact	MAX_DIST_CENTER_COLUMN_EXACT	DIST_TRANSF_EXACT	Topology/support	Zero-based column of the same deterministic exact maximum-distance center. Request row and column together to recover its position.
Attribute::MaxDistCenterRow	MAX_DIST_CENTER_ROW	DIST_TRANSF	Topology/support	Zero-based row of the support pixel attaining the approximate maximum. The same smallest-row-major tie rule is applied.
Attribute::MaxDistCenterColumn	MAX_DIST_CENTER_COLUMN	DIST_TRANSF	Topology/support	Zero-based column of the same deterministic approximate maximum-distance center. Approximate and exact centers may differ even when their maximum values agree.
Attribute::MaxDistPlateauAreaExact	MAX_DIST_PLATEAU_AREA_EXACT	DIST_TRANSF_EXACT	Topology/support	Number of support pixels attaining the exact maximum squared contour distance.
Attribute::MaxDistPlateauCentroidRowExact	MAX_DIST_PLATEAU_CENTROID_ROW_EXACT	DIST_TRANSF_EXACT	Topology/support	Arithmetic mean of the row coordinates over the exact maximum-distance plateau. It may be fractional.
Attribute::MaxDistPlateauCentroidColumnExact	MAX_DIST_PLATEAU_CENTROID_COLUMN_EXACT	DIST_TRANSF_EXACT	Topology/support	Arithmetic mean of the column coordinates over the exact maximum-distance plateau. It may be fractional.
Attribute::MaxDistPlateauArea	MAX_DIST_PLATEAU_AREA	DIST_TRANSF	Topology/support	Number of support pixels attaining the approximate maximum. It may differ from the exact plateau area.
Attribute::MaxDistPlateauCentroidRow	MAX_DIST_PLATEAU_CENTROID_ROW	DIST_TRANSF	Topology/support	Arithmetic mean of row coordinates over the approximate maximum plateau.
Attribute::MaxDistPlateauCentroidColumn	MAX_DIST_PLATEAU_CENTROID_COLUMN	DIST_TRANSF	Topology/support	Arithmetic mean of column coordinates over the approximate maximum plateau.
Attribute::DistSum	DIST_SUM	DIST_TRANSF	Topology/support	Sum of Euclidean distances sqrt(z) over the approximate distance field, in accumulated pixel units.
Attribute::DistMean	DIST_MEAN	DIST_TRANSF	Topology/support	Arithmetic mean of Euclidean distances over the approximate field, in pixels.
Attribute::DistVariance	DIST_VARIANCE	DIST_TRANSF	Topology/support	Population variance of Euclidean distances, mean(z) - mean(sqrt(z))^2, in squared pixels.
Attribute::DistMedian	DIST_MEDIAN	DIST_TRANSF	Topology/support	Lower empirical median of the approximate Euclidean-distance field.
Attribute::DistMode	DIST_MODE	DIST_TRANSF	Topology/support	Most frequent approximate Euclidean distance; ties select the smallest distance.
Attribute::DistQ25	DIST_Q25	DIST_TRANSF	Topology/support	Lower empirical 25th percentile of the approximate Euclidean-distance field.
Attribute::DistQ75	DIST_Q75	DIST_TRANSF	Topology/support	Lower empirical 75th percentile of the approximate Euclidean-distance field.
Attribute::DistQ90	DIST_Q90	DIST_TRANSF	Topology/support	Lower empirical 90th percentile of the approximate Euclidean-distance field.
Attribute::DistEntropy	DIST_ENTROPY	DIST_TRANSF	Topology/support	Shannon entropy in bits of the normalized approximate squared-distance histogram.
Attribute::DistPositiveArea	DIST_POSITIVE_AREA	DIST_TRANSF	Topology/support	Number of support pixels whose approximate squared-distance cost is positive.
Attribute::DistLevelCount	DIST_LEVEL_COUNT	DIST_TRANSF	Topology/support	Number of represented approximate squared-distance levels, including zero.
Attribute::DistWeightedCentroidRow	DIST_WEIGHTED_CENTROID_ROW	DIST_TRANSF	Topology/support	Zero-based row centroid weighted by approximate Euclidean distance. All-zero fields use the ordinary support centroid.
Attribute::DistWeightedCentroidColumn	DIST_WEIGHTED_CENTROID_COLUMN	DIST_TRANSF	Topology/support	Zero-based column centroid weighted by approximate Euclidean distance. All-zero fields use the ordinary support centroid.
Attribute::DistWeightedCentralMoment20	DIST_WEIGHTED_CENTRAL_MOMENT_20	DIST_TRANSF	Topology/support	Unnormalized approximate distance-weighted central column moment.
Attribute::DistWeightedCentralMoment02	DIST_WEIGHTED_CENTRAL_MOMENT_02	DIST_TRANSF	Topology/support	Unnormalized approximate distance-weighted central row moment.
Attribute::DistWeightedCentralMoment11	DIST_WEIGHTED_CENTRAL_MOMENT_11	DIST_TRANSF	Topology/support	Unnormalized approximate distance-weighted mixed row-column moment.
Attribute::DistWeightedAxisOrientation	DIST_WEIGHTED_AXIS_ORIENTATION	DIST_TRANSF	Topology/support	Principal axis of the approximate distance-weighted second moments, in degrees; isotropic fields return zero.
Attribute::DistWeightedEccentricity	DIST_WEIGHTED_ECCENTRICITY	DIST_TRANSF	Topology/support	Major/minor eigenvalue ratio of the approximate distance-weighted second moments, capped at 1e6.
Attribute::DistSumExact	DIST_SUM_EXACT	DIST_TRANSF_EXACT	Topology/support	Sum of exact Euclidean contour distances over the support, in accumulated pixel units.
Attribute::DistMeanExact	DIST_MEAN_EXACT	DIST_TRANSF_EXACT	Topology/support	Arithmetic mean of exact Euclidean contour distances, in pixels.
Attribute::DistVarianceExact	DIST_VARIANCE_EXACT	DIST_TRANSF_EXACT	Topology/support	Population variance of exact Euclidean contour distances, in squared pixels.
Attribute::DistMedianExact	DIST_MEDIAN_EXACT	DIST_TRANSF_EXACT	Topology/support	Lower empirical median of the exact Euclidean-distance field.
Attribute::DistModeExact	DIST_MODE_EXACT	DIST_TRANSF_EXACT	Topology/support	Most frequent exact Euclidean distance; ties select the smallest distance.
Attribute::DistQ25Exact	DIST_Q25_EXACT	DIST_TRANSF_EXACT	Topology/support	Lower empirical 25th percentile of the exact Euclidean-distance field.
Attribute::DistQ75Exact	DIST_Q75_EXACT	DIST_TRANSF_EXACT	Topology/support	Lower empirical 75th percentile of the exact Euclidean-distance field.
Attribute::DistQ90Exact	DIST_Q90_EXACT	DIST_TRANSF_EXACT	Topology/support	Lower empirical 90th percentile of the exact Euclidean-distance field.
Attribute::DistEntropyExact	DIST_ENTROPY_EXACT	DIST_TRANSF_EXACT	Topology/support	Shannon entropy in bits of the normalized exact squared-distance histogram.
Attribute::DistPositiveAreaExact	DIST_POSITIVE_AREA_EXACT	DIST_TRANSF_EXACT	Topology/support	Number of support pixels whose exact squared contour distance is positive.
Attribute::DistLevelCountExact	DIST_LEVEL_COUNT_EXACT	DIST_TRANSF_EXACT	Topology/support	Number of represented exact squared-distance levels, including zero.
Attribute::DistWeightedCentroidRowExact	DIST_WEIGHTED_CENTROID_ROW_EXACT	DIST_TRANSF_EXACT	Topology/support	Zero-based row centroid weighted by exact Euclidean distance. All-zero fields use the ordinary support centroid.
Attribute::DistWeightedCentroidColumnExact	DIST_WEIGHTED_CENTROID_COLUMN_EXACT	DIST_TRANSF_EXACT	Topology/support	Zero-based column centroid weighted by exact Euclidean distance. All-zero fields use the ordinary support centroid.
Attribute::DistWeightedCentralMoment20Exact	DIST_WEIGHTED_CENTRAL_MOMENT_20_EXACT	DIST_TRANSF_EXACT	Topology/support	Unnormalized exact distance-weighted central column moment.
Attribute::DistWeightedCentralMoment02Exact	DIST_WEIGHTED_CENTRAL_MOMENT_02_EXACT	DIST_TRANSF_EXACT	Topology/support	Unnormalized exact distance-weighted central row moment.
Attribute::DistWeightedCentralMoment11Exact	DIST_WEIGHTED_CENTRAL_MOMENT_11_EXACT	DIST_TRANSF_EXACT	Topology/support	Unnormalized exact distance-weighted mixed row-column moment.
Attribute::DistWeightedAxisOrientationExact	DIST_WEIGHTED_AXIS_ORIENTATION_EXACT	DIST_TRANSF_EXACT	Topology/support	Principal axis of the exact distance-weighted second moments, in degrees; isotropic fields return zero.
Attribute::DistWeightedEccentricityExact	DIST_WEIGHTED_ECCENTRICITY_EXACT	DIST_TRANSF_EXACT	Topology/support	Major/minor eigenvalue ratio of the exact distance-weighted second moments, capped at 1e6.
Attribute::CentralMoment20	CENTRAL_MOMENT_20	MOMENTS, SHAPE	Topology/support	Second-order central moment mu20 around the support centroid. It measures horizontal spread using column coordinates as x.
Attribute::CentralMoment02	CENTRAL_MOMENT_02	MOMENTS, SHAPE	Topology/support	Second-order central moment mu02 around the support centroid. It measures vertical spread using row coordinates as y.
Attribute::CentralMoment11	CENTRAL_MOMENT_11	MOMENTS, SHAPE	Topology/support	Mixed second-order central moment mu11. It measures covariance between column and row coordinates.
Attribute::CentralMoment30	CENTRAL_MOMENT_30	MOMENTS, SHAPE	Topology/support	Third-order central moment mu30. It captures horizontal asymmetry of the support around its centroid.
Attribute::CentralMoment03	CENTRAL_MOMENT_03	MOMENTS, SHAPE	Topology/support	Third-order central moment mu03. It captures vertical asymmetry of the support around its centroid.
Attribute::CentralMoment21	CENTRAL_MOMENT_21	MOMENTS, SHAPE	Topology/support	Mixed third-order central moment mu21. It captures combined horizontal spread and vertical asymmetry.
Attribute::CentralMoment12	CENTRAL_MOMENT_12	MOMENTS, SHAPE	Topology/support	Mixed third-order central moment mu12. It captures combined vertical spread and horizontal asymmetry.
Attribute::HuMoment1	HU_MOMENT_1	MOMENTS, SHAPE	Topology/support	First Hu moment invariant computed from normalized central moments. It follows the standard second-order Hu expression.
Attribute::HuMoment2	HU_MOMENT_2	MOMENTS, SHAPE	Topology/support	Second Hu moment invariant. It emphasizes anisotropy between horizontal and vertical spread while remaining invariant to translation, scale, and rotation.
Attribute::HuMoment3	HU_MOMENT_3	MOMENTS, SHAPE	Topology/support	Third Hu moment invariant. It captures third-order skewness and asymmetry patterns in the support distribution.
Attribute::HuMoment4	HU_MOMENT_4	MOMENTS, SHAPE	Topology/support	Fourth Hu moment invariant. It combines third-order normalized moments to describe diagonal and off-axis symmetry.
Attribute::HuMoment5	HU_MOMENT_5	MOMENTS, SHAPE	Topology/support	Fifth Hu moment invariant. It is sensitive to more complex orientation-dependent asymmetries and reflection-related differences.
Attribute::HuMoment6	HU_MOMENT_6	MOMENTS, SHAPE	Topology/support	Sixth Hu moment invariant. It combines second- and third-order normalized moments to capture elliptical asymmetry and curvature-related shape variation.
Attribute::HuMoment7	HU_MOMENT_7	MOMENTS, SHAPE	Topology/support	Seventh Hu moment invariant. It is highly sensitive to fine asymmetries and helps distinguish mirror-related shapes.
Attribute::Inertia	INERTIA	MOMENTS, SHAPE	Topology/support	Sum of normalized second-order central moments, mu20 / area^2 + mu02 / area^2. This is the same scalar expression as the first Hu moment invariant.
Attribute::Compactness	COMPACTNESS	MOMENTS, SHAPE	Topology/support	Area normalized by second-order dispersion, (1 / (2*pi)) * area / (mu20 + mu02) when the denominator is positive. Higher values indicate more compact supports.
Attribute::Eccentricity	ECCENTRICITY	MOMENTS, SHAPE	Topology/support	Ratio of the largest to smallest eigenvalue of the second-moment matrix. Values near 1 indicate isotropic shapes; larger values indicate elongation. Degenerate line-like supports saturate at the finite value 1e6.
Attribute::LengthMajorAxis	LENGTH_MAJOR_AXIS	MOMENTS, SHAPE	Topology/support	Length proxy for the major axis of the equivalent second-moment ellipse, derived from the largest inertia eigenvalue and area.
Attribute::LengthMinorAxis	LENGTH_MINOR_AXIS	MOMENTS, SHAPE	Topology/support	Length proxy for the minor axis of the equivalent second-moment ellipse, derived from the smallest inertia eigenvalue and area.
Attribute::AxisOrientation	AXIS_ORIENTATION	MOMENTS, SHAPE	Topology/support	Principal-axis orientation in degrees, 0.5 * atan2(2*mu11, mu20 - mu02), normalized to a non-negative angle.
Attribute::Circularity	CIRCULARITY	MOMENTS, SHAPE	Topology/support	Ratio lambda2 / lambda1 of second-moment eigenvalues. Values near 1 indicate circular or isotropic supports; values near 0 indicate elongation.
Attribute::BitquadArea	BITQUAD_AREA	BOUNDARY, SHAPE	Topology/support	Duda-style sub-pixel area estimator derived from aggregated 2x2 bitquad pattern counts.
Attribute::BitquadNumberEuler	BITQUAD_NUMBER_EULER	BOUNDARY, SHAPE	Topology/support	Euler characteristic estimated from bitquad family counts under an explicit connectivity projection. For a tree of shapes, non-root connectivity is selected from exact lower/upper shape polarity; the root has no polarity.
Attribute::BitquadNumberHoles	BITQUAD_NUMBER_HOLES	BOUNDARY, SHAPE	Topology/support	Number of holes inferred from the bitquad Euler characteristic for a single connected support.
Attribute::BitquadPerimeter	BITQUAD_PERIMETER	BOUNDARY, SHAPE	Topology/support	Discrete boundary-length estimate from bitquad edge-contributing patterns.
Attribute::BitquadPerimeterContinuous	BITQUAD_PERIMETER_CONTINUOUS	BOUNDARY, SHAPE	Topology/support	Smoothed continuous perimeter estimate from bitquad counters, using weighted transitions across local 2x2 configurations.
Attribute::BitquadCircularity	BITQUAD_CIRCULARITY	BOUNDARY, SHAPE	Topology/support	Bitquad compactness measure (4*pi*BITQUAD_AREA) / BITQUAD_PERIMETER_CONTINUOUS^2. Values closer to 1 indicate rounder supports. Degenerate zero-perimeter supports return 0.
Attribute::BitquadPerimeterAverage	BITQUAD_PERIMETER_AVERAGE	BOUNDARY, SHAPE	Topology/support	Average continuous perimeter per connected component, computed from bitquad perimeter and Euler-count estimates. Euler estimates <= 0 return 0.
Attribute::BitquadLengthAverage	BITQUAD_LENGTH_AVERAGE	BOUNDARY, SHAPE	Topology/support	Average longitudinal extent proxy, derived as half of the average continuous perimeter. Euler estimates <= 0 return 0.
Attribute::BitquadWidthAverage	BITQUAD_WIDTH_AVERAGE	BOUNDARY, SHAPE	Topology/support	Average transverse extent proxy, computed as 2 * BITQUAD_AREA / BITQUAD_PERIMETER_CONTINUOUS with a zero fallback when the continuous perimeter is degenerate.
Attribute::ContourPixels	CONTOUR_PIXELS	BOUNDARY, SHAPE	Topology/support	Number of support pixels that touch the 4-neighbor complement by at least one side.
Attribute::ContourPerimeter	CONTOUR_PERIMETER	BOUNDARY, SHAPE	Topology/support	Total number of exposed 4-neighbor sides over the support. This is the side-count perimeter, not a Euclidean perimeter estimate.
Attribute::ContourSideNorth	CONTOUR_SIDE_NORTH	BOUNDARY, SHAPE	Topology/support	Number of exposed north-facing sides over support pixels.
Attribute::ContourSideWest	CONTOUR_SIDE_WEST	BOUNDARY, SHAPE	Topology/support	Number of exposed west-facing sides over support pixels.
Attribute::ContourSideEast	CONTOUR_SIDE_EAST	BOUNDARY, SHAPE	Topology/support	Number of exposed east-facing sides over support pixels.
Attribute::ContourSideSouth	CONTOUR_SIDE_SOUTH	BOUNDARY, SHAPE	Topology/support	Number of exposed south-facing sides over support pixels.
Attribute::SubtreeHeight	SUBTREE_HEIGHT	TREE_TOPOLOGY	Tree topology	Longest child-edge path from the node to any leaf in its subtree. Leaves have height 0.
Attribute::DepthNode	DEPTH_NODE	TREE_TOPOLOGY	Tree topology	Number of parent-edge steps from the node to the root. The root has depth 0.
Attribute::IsLeafNode	IS_LEAF_NODE	TREE_TOPOLOGY	Tree topology	Boolean scalar encoded as 1 when the node has no children and 0 otherwise.
Attribute::IsRootNode	IS_ROOT_NODE	TREE_TOPOLOGY	Tree topology	Boolean scalar encoded as 1 for the tree root and 0 for all other nodes.
Attribute::NumChildrenNode	NUM_CHILDREN_NODE	TREE_TOPOLOGY	Tree topology	Number of direct child nodes. It measures the immediate branching factor of the hierarchy at the node.
Attribute::NumSiblingsNode	NUM_SIBLINGS_NODE	TREE_TOPOLOGY	Tree topology	Number of other nodes sharing the same parent. The root has 0 siblings.
Attribute::NumDescendantsNode	NUM_DESCENDANTS_NODE	TREE_TOPOLOGY	Tree topology	Number of internal tree nodes strictly below this node in its subtree.
Attribute::NumLeafDescendantsNode	NUM_LEAF_DESCENDANTS_NODE	TREE_TOPOLOGY	Tree topology	Number of leaf nodes in the node subtree. A leaf node contributes 1 for itself.
Attribute::LeafRatioNode	LEAF_RATIO_NODE	TREE_TOPOLOGY	Tree topology	Ratio of leaf descendants to subtree size, leaf_descendants / (descendants + 1). Leaves return 1.
Attribute::BalanceNode	BALANCE_NODE	TREE_TOPOLOGY	Tree topology	Difference between maximum and minimum child-subtree heights. It is 0 for leaves and increases when child depths are uneven.
Attribute::AvgChildHeightNode	AVG_CHILD_HEIGHT_NODE	TREE_TOPOLOGY	Tree topology	Average height of direct child subtrees. Leaves return 0; non-leaf nodes average direct child heights.