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 Attribute class column classifies monotonicity under support inclusion. For node supports \(X\) and \(Y\) with \(X \subseteq Y\):

Increasing means that \(A(X) \leq A(Y)\) is guaranteed by the attribute contract.
Non-increasing means that this increasing-order guarantee does not hold in general. It does not assert that the attribute is monotonically decreasing.

The classification is unconditional over the full documented input contract. A property that holds only under an additional restriction is therefore Non-increasing; for example, VOLUME is increasing for non-negative altitudes, and GRAY_LEVEL_HEIGHT is increasing on globally monotone max-tree and min-tree hierarchies, but neither restriction is required by its public computation contract.

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_`, `FILLED_`, `HOLE_AREA_FRACTION`	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	Attribute class	Description
`Attribute::Volume`	`VOLUME`	`GRAY_LEVEL`	Altitude-aware	`Non-increasing`	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	`Increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Population variance of the image values over the full node support, with denominator `card(X)`.
`Attribute::Area`	`AREA`	`SHAPE`	Topology/support	`Increasing`	Number of pixels in the full node support. Equivalently, it is the sum of proper-part cardinalities over the node's subtree.
`Attribute::BoundingBoxWidth`	`BOUNDING_BOX_WIDTH`	`SHAPE`	Topology/support	`Increasing`	Width, in columns, of the smallest axis-aligned bounding box enclosing the node support.
`Attribute::BoundingBoxHeight`	`BOUNDING_BOX_HEIGHT`	`SHAPE`	Topology/support	`Increasing`	Height, in rows, of the smallest axis-aligned bounding box enclosing the node support.
`Attribute::DiagonalLength`	`DIAGONAL_LENGTH`	`SHAPE`	Topology/support	`Increasing`	Euclidean diagonal length of the bounding box, `sqrt(width^2 + height^2)`.
`Attribute::Rectangularity`	`RECTANGULARITY`	`SHAPE`	Topology/support	`Non-increasing`	Ratio `AREA / (BOUNDING_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	`Non-increasing`	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	`Non-increasing`	Minimum image column index covered by the node support.
`Attribute::BoxColumnMax`	`BOX_COLUMN_MAX`	`SHAPE`	Topology/support	`Increasing`	Maximum image column index covered by the node support.
`Attribute::BoxRowMin`	`BOX_ROW_MIN`	`SHAPE`	Topology/support	`Non-increasing`	Minimum image row index covered by the node support.
`Attribute::BoxRowMax`	`BOX_ROW_MAX`	`SHAPE`	Topology/support	`Increasing`	Maximum image row index covered by the node support.
`Attribute::MaxDistExact`	`MAX_DIST_EXACT`	`SHAPE`, `DIST_TRANSF_EXACT`	Topology/support	`Increasing`	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	`Increasing`	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	`Increasing`	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	`Increasing`	Maximum approximate squared contour-distance cost, in squared pixels.
`Attribute::DistSquaredSumExact`	`DIST_SQUARED_SUM_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Increasing`	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	`Non-increasing`	Arithmetic mean of the exact squared contour-distance field over the node support.
`Attribute::DistRmsExact`	`DIST_RMS_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Sum of the approximate squared-distance field over the node support.
`Attribute::DistSquaredMean`	`DIST_SQUARED_MEAN`	`DIST_TRANSF`	Topology/support	`Non-increasing`	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	`Non-increasing`	Root mean square distance derived from the approximate field, `sqrt(mean(cost))`, in pixel units.
`Attribute::DistSquaredVariance`	`DIST_SQUARED_VARIANCE`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Population variance of the approximate squared-distance samples.
`Attribute::MaxDistCenterRowExact`	`MAX_DIST_CENTER_ROW_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Number of support pixels attaining the exact maximum squared contour distance.
`Attribute::MaxDistPlateauCentroidRowExact`	`MAX_DIST_PLATEAU_CENTROID_ROW_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Arithmetic mean of row coordinates over the approximate maximum plateau.
`Attribute::MaxDistPlateauCentroidColumn`	`MAX_DIST_PLATEAU_CENTROID_COLUMN`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Arithmetic mean of column coordinates over the approximate maximum plateau.
`Attribute::DistSum`	`DIST_SUM`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Sum of Euclidean distances `sqrt(z)` over the approximate distance field, in accumulated pixel units.
`Attribute::DistMean`	`DIST_MEAN`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Arithmetic mean of Euclidean distances over the approximate field, in pixels.
`Attribute::DistVariance`	`DIST_VARIANCE`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Population variance of Euclidean distances, `mean(z) - mean(sqrt(z))^2`, in squared pixels.
`Attribute::DistMedian`	`DIST_MEDIAN`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Lower empirical median of the approximate Euclidean-distance field.
`Attribute::DistMode`	`DIST_MODE`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Most frequent approximate Euclidean distance; ties select the smallest distance.
`Attribute::DistQ25`	`DIST_Q25`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Lower empirical 25th percentile of the approximate Euclidean-distance field.
`Attribute::DistQ75`	`DIST_Q75`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Lower empirical 75th percentile of the approximate Euclidean-distance field.
`Attribute::DistQ90`	`DIST_Q90`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Lower empirical 90th percentile of the approximate Euclidean-distance field.
`Attribute::DistEntropy`	`DIST_ENTROPY`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Shannon entropy in bits of the normalized approximate squared-distance histogram.
`Attribute::DistPositiveArea`	`DIST_POSITIVE_AREA`	`DIST_TRANSF`	Topology/support	`Increasing`	Number of support pixels whose approximate squared-distance cost is positive.
`Attribute::DistLevelCount`	`DIST_LEVEL_COUNT`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Number of represented approximate squared-distance levels, including zero.
`Attribute::DistWeightedCentroidRow`	`DIST_WEIGHTED_CENTROID_ROW`	`DIST_TRANSF`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Unnormalized approximate distance-weighted central column moment.
`Attribute::DistWeightedCentralMoment02`	`DIST_WEIGHTED_CENTRAL_MOMENT_02`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Unnormalized approximate distance-weighted central row moment.
`Attribute::DistWeightedCentralMoment11`	`DIST_WEIGHTED_CENTRAL_MOMENT_11`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Unnormalized approximate distance-weighted mixed row-column moment.
`Attribute::DistWeightedAxisOrientation`	`DIST_WEIGHTED_AXIS_ORIENTATION`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Principal axis of the approximate distance-weighted second moments, in degrees; isotropic fields return zero.
`Attribute::DistWeightedEccentricity`	`DIST_WEIGHTED_ECCENTRICITY`	`DIST_TRANSF`	Topology/support	`Non-increasing`	Major/minor eigenvalue ratio of the approximate distance-weighted second moments, capped at `1e6`.
`Attribute::DistSumExact`	`DIST_SUM_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Increasing`	Sum of exact Euclidean contour distances over the support, in accumulated pixel units.
`Attribute::DistMeanExact`	`DIST_MEAN_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Arithmetic mean of exact Euclidean contour distances, in pixels.
`Attribute::DistVarianceExact`	`DIST_VARIANCE_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Population variance of exact Euclidean contour distances, in squared pixels.
`Attribute::DistMedianExact`	`DIST_MEDIAN_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Lower empirical median of the exact Euclidean-distance field.
`Attribute::DistModeExact`	`DIST_MODE_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Most frequent exact Euclidean distance; ties select the smallest distance.
`Attribute::DistQ25Exact`	`DIST_Q25_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Lower empirical 25th percentile of the exact Euclidean-distance field.
`Attribute::DistQ75Exact`	`DIST_Q75_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Lower empirical 75th percentile of the exact Euclidean-distance field.
`Attribute::DistQ90Exact`	`DIST_Q90_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Lower empirical 90th percentile of the exact Euclidean-distance field.
`Attribute::DistEntropyExact`	`DIST_ENTROPY_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Shannon entropy in bits of the normalized exact squared-distance histogram.
`Attribute::DistPositiveAreaExact`	`DIST_POSITIVE_AREA_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Increasing`	Number of support pixels whose exact squared contour distance is positive.
`Attribute::DistLevelCountExact`	`DIST_LEVEL_COUNT_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Number of represented exact squared-distance levels, including zero.
`Attribute::DistWeightedCentroidRowExact`	`DIST_WEIGHTED_CENTROID_ROW_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Increasing`	Unnormalized exact distance-weighted central column moment.
`Attribute::DistWeightedCentralMoment02Exact`	`DIST_WEIGHTED_CENTRAL_MOMENT_02_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Increasing`	Unnormalized exact distance-weighted central row moment.
`Attribute::DistWeightedCentralMoment11Exact`	`DIST_WEIGHTED_CENTRAL_MOMENT_11_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	Unnormalized exact distance-weighted mixed row-column moment.
`Attribute::DistWeightedAxisOrientationExact`	`DIST_WEIGHTED_AXIS_ORIENTATION_EXACT`	`DIST_TRANSF_EXACT`	Topology/support	`Non-increasing`	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	`Non-increasing`	Major/minor eigenvalue ratio of the exact distance-weighted second moments, capped at `1e6`.
`Attribute::CentralMoment20`	`CENTRAL_MOMENT_20`	`MOMENTS`, `SHAPE`	Topology/support	`Increasing`	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	`Increasing`	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	`Non-increasing`	Mixed second-order central moment `mu11`. It measures covariance between column and row coordinates.
`Attribute::CentralMoment30`	`CENTRAL_MOMENT_30`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	Third-order central moment `mu30`. It captures horizontal asymmetry of the support around its centroid.
`Attribute::CentralMoment03`	`CENTRAL_MOMENT_03`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	Third-order central moment `mu03`. It captures vertical asymmetry of the support around its centroid.
`Attribute::CentralMoment21`	`CENTRAL_MOMENT_21`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	Mixed third-order central moment `mu21`. It captures combined horizontal spread and vertical asymmetry.
`Attribute::CentralMoment12`	`CENTRAL_MOMENT_12`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	Mixed third-order central moment `mu12`. It captures combined vertical spread and horizontal asymmetry.
`Attribute::HuMoment1`	`HU_MOMENT_1`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Seventh Hu moment invariant. It is highly sensitive to fine asymmetries and helps distinguish mirror-related shapes.
`Attribute::Inertia`	`INERTIA`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	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::RawInertia`	`RAW_INERTIA`	`MOMENTS`, `SHAPE`	Topology/support	`Increasing`	Unnormalized polar second central moment, `mu20 + mu02`. Equivalently, it is the sum of squared Euclidean distances from support pixels to the support centroid.
`Attribute::Compactness`	`COMPACTNESS`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	Area normalized by second-order dispersion, `(1 / (2pi)) area / (mu20 + mu02)` when the denominator is positive. Higher values indicate more compact supports.
`Attribute::Eccentricity`	`ECCENTRICITY`	`MOMENTS`, `SHAPE`	Topology/support	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Duda-style sub-pixel area estimator derived from aggregated `2x2` bitquad pattern counts.
`Attribute::BitquadNumberEuler`	`BITQUAD_NUMBER_EULER`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	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	`Non-increasing`	Number of holes inferred from the bitquad Euler characteristic for a single connected support.
`Attribute::BitquadPerimeter`	`BITQUAD_PERIMETER`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	Discrete boundary-length estimate from bitquad edge-contributing patterns.
`Attribute::BitquadPerimeterContinuous`	`BITQUAD_PERIMETER_CONTINUOUS`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	Smoothed continuous perimeter estimate from bitquad counters, using weighted transitions across local `2x2` configurations.
`Attribute::BitquadCircularity`	`BITQUAD_CIRCULARITY`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	Bitquad compactness measure `(4piBITQUAD_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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	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	`Non-increasing`	Number of support pixels that touch the 4-neighbor complement by at least one side.
`Attribute::ContourPerimeter`	`CONTOUR_PERIMETER`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	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	`Non-increasing`	Number of exposed north-facing sides over support pixels.
`Attribute::ContourSideWest`	`CONTOUR_SIDE_WEST`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	Number of exposed west-facing sides over support pixels.
`Attribute::ContourSideEast`	`CONTOUR_SIDE_EAST`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	Number of exposed east-facing sides over support pixels.
`Attribute::ContourSideSouth`	`CONTOUR_SIDE_SOUTH`	`BOUNDARY`, `SHAPE`	Topology/support	`Non-increasing`	Number of exposed south-facing sides over support pixels.
`Attribute::SubtreeHeight`	`SUBTREE_HEIGHT`	`TREE_TOPOLOGY`	Tree topology	`Increasing`	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	`Non-increasing`	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	`Non-increasing`	Boolean scalar encoded as `1` when the node has no children and `0` otherwise.
`Attribute::IsRootNode`	`IS_ROOT_NODE`	`TREE_TOPOLOGY`	Tree topology	`Increasing`	Boolean scalar encoded as `1` for the tree root and `0` for all other nodes.
`Attribute::NumChildrenNode`	`NUM_CHILDREN_NODE`	`TREE_TOPOLOGY`	Tree topology	`Non-increasing`	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	`Non-increasing`	Number of other nodes sharing the same parent. The root has `0` siblings.
`Attribute::NumDescendantsNode`	`NUM_DESCENDANTS_NODE`	`TREE_TOPOLOGY`	Tree topology	`Increasing`	Number of internal tree nodes strictly below this node in its subtree.
`Attribute::NumLeafDescendantsNode`	`NUM_LEAF_DESCENDANTS_NODE`	`TREE_TOPOLOGY`	Tree topology	`Increasing`	Number of leaf nodes in the node subtree. A leaf node contributes `1` for itself.
`Attribute::LeafRatioNode`	`LEAF_RATIO_NODE`	`TREE_TOPOLOGY`	Tree topology	`Non-increasing`	Ratio of leaf descendants to subtree size, `leaf_descendants / (descendants + 1)`. Leaves return `1`.
`Attribute::BalanceNode`	`BALANCE_NODE`	`TREE_TOPOLOGY`	Tree topology	`Non-increasing`	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	`Non-increasing`	Average height of direct child subtrees. Leaves return `0`; non-leaf nodes average direct child heights.
`Attribute::FilledArea`	`FILLED_AREA`	`FILLED_SHAPE`	Topology/support	`Increasing`	Number of pixels enclosed by the unique external boundary, including holes; requires exactly one external boundary per live node.
`Attribute::FilledCentroidRow`	`FILLED_CENTROID_ROW`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Zero-based mean row of the filled region pixels.
`Attribute::FilledCentroidColumn`	`FILLED_CENTROID_COLUMN`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Zero-based mean column of the filled region pixels.
`Attribute::FilledLengthMajorAxis`	`FILLED_LENGTH_MAJOR_AXIS`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Major-axis length proxy of the filled region, in pixels; follows `LENGTH_MAJOR_AXIS`.
`Attribute::FilledLengthMinorAxis`	`FILLED_LENGTH_MINOR_AXIS`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Minor-axis length proxy of the filled region, in pixels; follows `LENGTH_MINOR_AXIS`.
`Attribute::FilledAxisOrientation`	`FILLED_AXIS_ORIENTATION`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Non-negative principal column-axis orientation in degrees; isotropic regions return `0`.
`Attribute::FilledAxisOrientationSigned`	`FILLED_AXIS_ORIENTATION_SIGNED`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Signed principal column-axis orientation in degrees, `0.5 * atan2(2*mu11, mu20-mu02)`, in `[-90,90]`; positive row direction is downward. Isotropic regions return `0`. The existing `FILLED_AXIS_ORIENTATION` remains its absolute value.
`Attribute::FilledEccentricity`	`FILLED_ECCENTRICITY`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Major/minor eigenvalue ratio of the filled region moments, capped at `1e6`; one pixel returns `1`.
`Attribute::FilledInertia`	`FILLED_INERTIA`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Sum of the filled region second central moments divided by squared filled area.
`Attribute::HoleAreaFraction`	`HOLE_AREA_FRACTION`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Fraction of filled area occupied by holes: `1 - AREA / FILLED_AREA`.
`Attribute::FilledCentroidDisplacementNormalized`	`FILLED_CENTROID_DISPLACEMENT_NORMALIZED`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Euclidean distance between support and filled-region centroids divided by the square root of filled area.
`Attribute::FilledCompactness`	`FILLED_COMPACTNESS`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	`FILLED_AREA / (2pi(mu20 + mu02))`, using filled-region second central moments; zero dispersion returns `0`.
`Attribute::FilledCircularity`	`FILLED_CIRCULARITY`	`FILLED_SHAPE`	Topology/support	`Non-increasing`	Minor/major eigenvalue ratio of the filled-region second moments; one pixel returns `1` and a nontrivial line returns `0`.
`Attribute::AxisOrientationSigned`	`AXIS_ORIENTATION_SIGNED`	`SHAPE`, `MOMENTS`	Topology/support	`Non-increasing`	Signed principal column-axis orientation of the node support: `0.5 * atan2(2*mu11, mu20-mu02)` in degrees, in `[-90,90]`; positive row direction is downward. Isotropic and one-pixel supports return `0`; the axis is defined modulo 180 degrees. `AXIS_ORIENTATION` remains its absolute value.