Attribute Catalog

This reference lists the scalar attributes exposed by the public API. Use the constant directly in C++ requests, for example AREA, or through the Python facade, for example mmcfilters.Attribute.AREA.

Every row is materialized per node in the returned AttributeNames layout. For usage patterns and output-space rules, see Attributes.

The Contract column classifies the input required by the attribute:

• Topology/support: uses image-domain support, such as proper-part ownership, pixel coordinates, contours, bounding boxes, or shape moments. It does not read node altitudes.
• Altitude-aware: reads the node altitude buffer and therefore requires a WeightedMorphologicalTree<T> or WeightedTreeView<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.

Constant	Groups	Contract	Description
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.
RELATIVE_VOLUME	GRAY_LEVEL	Altitude-aware	Cumulative gray-level contrast volume: absolute parent/child altitude jumps weighted by child support area, plus the node support-area contribution.
LEVEL	GRAY_LEVEL	Altitude-aware	Altitude of the node in the morphological hierarchy. For component trees, this is the gray level at which the connected component appears.
GRAY_HEIGHT	GRAY_LEVEL	Altitude-aware	Gray-level span from the node altitude to the most extreme descendant altitude: maximum descendant level in a max-tree, minimum descendant level in a min-tree. Leaves have value 0.
MEAN_LEVEL	GRAY_LEVEL	Altitude-aware	Average gray level over the full node support. It is computed from accumulated VOLUME / AREA.
VARIANCE_LEVEL	GRAY_LEVEL	Altitude-aware	Variance of gray levels over the full node support. It uses the accumulated squared gray-level sum and the mean level.
AREA	SHAPE	Topology/support	Number of proper parts in the full node support, including all descendant supports. In image-domain trees this is the pixel count of the connected component represented by the node.
BOX_WIDTH	SHAPE	Topology/support	Width, in columns, of the smallest axis-aligned bounding box enclosing the node support.
BOX_HEIGHT	SHAPE	Topology/support	Height, in rows, of the smallest axis-aligned bounding box enclosing the node support.
DIAGONAL_LENGTH	SHAPE	Topology/support	Euclidean diagonal length of the bounding box, sqrt(width^2 + height^2).
RECTANGULARITY	SHAPE	Topology/support	Ratio AREA / (BOX_WIDTH * BOX_HEIGHT). Values closer to 1 indicate that the support fills its bounding box densely.
RATIO_WH	SHAPE	Topology/support	Bounding-box aspect ratio, max(width, height) / min(width, height) for non-degenerate boxes. Values are at least 1.
BOX_COL_MIN	SHAPE	Topology/support	Minimum image column index covered by the node support.
BOX_COL_MAX	SHAPE	Topology/support	Maximum image column index covered by the node support.
BOX_ROW_MIN	SHAPE	Topology/support	Minimum image row index covered by the node support.
BOX_ROW_MAX	SHAPE	Topology/support	Maximum image row index covered by the node support.
MAX_DIST	SHAPE	Altitude-aware	Maximum squared Euclidean distance reached from the node contour during the incremental distance-transform sweep. It is defined for max-trees and min-trees with valid adjacency metadata.
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.
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.
CENTRAL_MOMENT_11	MOMENTS, SHAPE	Topology/support	Mixed second-order central moment mu11. It measures covariance between column and row coordinates.
CENTRAL_MOMENT_30	MOMENTS, SHAPE	Topology/support	Third-order central moment mu30. It captures horizontal asymmetry of the support around its centroid.
CENTRAL_MOMENT_03	MOMENTS, SHAPE	Topology/support	Third-order central moment mu03. It captures vertical asymmetry of the support around its centroid.
CENTRAL_MOMENT_21	MOMENTS, SHAPE	Topology/support	Mixed third-order central moment mu21. It captures combined horizontal spread and vertical asymmetry.
CENTRAL_MOMENT_12	MOMENTS, SHAPE	Topology/support	Mixed third-order central moment mu12. It captures combined vertical spread and horizontal asymmetry.
HU_MOMENT_1	MOMENTS, SHAPE	Topology/support	First Hu invariant computed from normalized central moments. It follows the standard second-order Hu expression.
HU_MOMENT_2	MOMENTS, SHAPE	Topology/support	Second Hu invariant. It emphasizes anisotropy between horizontal and vertical spread while remaining invariant to translation, scale, and rotation.
HU_MOMENT_3	MOMENTS, SHAPE	Topology/support	Third Hu invariant. It captures third-order skewness and asymmetry patterns in the support distribution.
HU_MOMENT_4	MOMENTS, SHAPE	Topology/support	Fourth Hu invariant. It combines third-order normalized moments to describe diagonal and off-axis symmetry.
HU_MOMENT_5	MOMENTS, SHAPE	Topology/support	Fifth Hu invariant. It is sensitive to more complex orientation-dependent asymmetries and reflection-related differences.
HU_MOMENT_6	MOMENTS, SHAPE	Topology/support	Sixth Hu invariant. It combines second- and third-order normalized moments to capture elliptical asymmetry and curvature-related shape variation.
HU_MOMENT_7	MOMENTS, SHAPE	Topology/support	Seventh Hu invariant. It is highly sensitive to fine asymmetries and helps distinguish mirror-related shapes.
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 invariant.
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.
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.
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.
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.
AXIS_ORIENTATION	MOMENTS, SHAPE	Topology/support	Principal-axis orientation in degrees, 0.5 * atan2(2*mu11, mu20 - mu02), normalized to a non-negative angle.
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.
BITQUADS_AREA	BOUNDARY, SHAPE	Topology/support	Duda-style sub-pixel area estimator derived from aggregated 2x2 bitquad pattern counts.
BITQUADS_NUMBER_EULER	BOUNDARY, SHAPE	Topology/support	Euler characteristic estimated from bitquad counters, representing connected components minus holes under the selected connectivity projection.
BITQUADS_NUMBER_HOLES	BOUNDARY, SHAPE	Topology/support	Number of holes inferred from the bitquad Euler characteristic for a single connected support.
BITQUADS_PERIMETER	BOUNDARY, SHAPE	Topology/support	Discrete boundary-length estimate from bitquad edge-contributing patterns.
BITQUADS_PERIMETER_CONTINUOUS	BOUNDARY, SHAPE	Topology/support	Smoothed continuous perimeter estimate from bitquad counters, using weighted transitions across local 2x2 configurations.
BITQUADS_CIRCULARITY	BOUNDARY, SHAPE	Topology/support	Bitquad compactness measure (4*pi*BITQUADS_AREA) / BITQUADS_PERIMETER_CONTINUOUS^2. Values closer to 1 indicate rounder supports. Degenerate zero-perimeter supports return 0.
BITQUADS_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.
BITQUADS_LENGTH_AVERAGE	BOUNDARY, SHAPE	Topology/support	Average longitudinal extent proxy, derived as half of the average continuous perimeter. Euler estimates <= 0 return 0.
BITQUADS_WIDTH_AVERAGE	BOUNDARY, SHAPE	Topology/support	Average transverse extent proxy, computed as 2 * BITQUADS_AREA / BITQUADS_PERIMETER_CONTINUOUS with a zero fallback when the continuous perimeter is degenerate.
CONTOUR_PIXELS	BOUNDARY, SHAPE	Topology/support	Number of support pixels that touch the 4-neighbour complement by at least one side.
CONTOUR_PERIMETER	BOUNDARY, SHAPE	Topology/support	Total number of exposed 4-neighbour sides over the support. This is the side-count perimeter, not a Euclidean perimeter estimate.
CONTOUR_SIDE_NORTH	BOUNDARY, SHAPE	Topology/support	Number of exposed north-facing sides over support pixels.
CONTOUR_SIDE_WEST	BOUNDARY, SHAPE	Topology/support	Number of exposed west-facing sides over support pixels.
CONTOUR_SIDE_EAST	BOUNDARY, SHAPE	Topology/support	Number of exposed east-facing sides over support pixels.
CONTOUR_SIDE_SOUTH	BOUNDARY, SHAPE	Topology/support	Number of exposed south-facing sides over support pixels.
HEIGHT_NODE	TREE_TOPOLOGY	Tree topology	Longest child-edge path from the node to any leaf in its subtree. Leaves have height 0.
DEPTH_NODE	TREE_TOPOLOGY	Tree topology	Number of parent-edge steps from the node to the root. The root has depth 0.
IS_LEAF_NODE	TREE_TOPOLOGY	Tree topology	Boolean scalar encoded as 1 when the node has no children and 0 otherwise.
IS_ROOT_NODE	TREE_TOPOLOGY	Tree topology	Boolean scalar encoded as 1 for the tree root and 0 for all other nodes.
NUM_CHILDREN_NODE	TREE_TOPOLOGY	Tree topology	Number of direct child nodes. It measures the immediate branching factor of the hierarchy at the node.
NUM_SIBLINGS_NODE	TREE_TOPOLOGY	Tree topology	Number of other nodes sharing the same parent. The root has 0 siblings.
NUM_DESCENDANTS_NODE	TREE_TOPOLOGY	Tree topology	Number of internal tree nodes strictly below this node in its subtree.
NUM_LEAF_DESCENDANTS_NODE	TREE_TOPOLOGY	Tree topology	Number of leaf nodes in the node subtree. A leaf node contributes 1 for itself.
LEAF_RATIO_NODE	TREE_TOPOLOGY	Tree topology	Ratio of leaf descendants to subtree size, leaf_descendants / (descendants + 1). Leaves return 1.
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.
AVG_CHILD_HEIGHT_NODE	TREE_TOPOLOGY	Tree topology	Average height of direct child subtrees. Leaves return 0; non-leaf nodes average direct child heights.