Crown metrics

A crown fit approximates a tree's foliage envelope with a simple geometric shape and derives structural metrics from it. It answers questions a bounding box or raw point cloud can't summarise at a glance: how tall is the tree, how much space does its crown occupy, where is it centred, and how wide is it?

Crown fitting is the geometric counterpart to a QSM: a QSM reconstructs the woody structure cylinder by cylinder, while a crown fit characterises the foliage as a single bounding solid. Both are computed per tree.

The shapes

Four shapes trade off tightness against simplicity:

Shape	Volume	Notes
Ellipsoid	4⁄3·π·a·b·c	Independent X, Y, Z semi-axes from the crown's per-axis spread. Smooth, forgiving.
Rectangular prism	box volume	The axis-aligned bounding box of the crown. Dimensions are its edge lengths.
Cone	1⁄3·π·r²·h	Upright, apex at the crown top; base radius from the widest (lower) part of the crown. Suits conifers.
Alpha shape	mesh volume (convex-hull fallback)	A smooth, watertight concave hull that hugs the crown outline — the most faithful shape. The radius auto-grows until the surface closes into one connected component; override it to hug more or less tightly.

All four shapes are axis-aligned — the parametric shapes (ellipsoid, prism, cone) are fit upright and square to the world axes, so their reported dimensions read directly as width × depth × height.

The metrics

Every fitted crown reports metrics computed from the fitted shape's geometry (so they describe the solid you see, consistently across all four shapes):

• Tree height — the crown top minus the ground baseline. When the scan carries ground_class labels the baseline is the minimum height of the labelled ground; otherwise it's the tree's own lowest point. (This is measured from the crown points — the real tree height — since a fitted shape's top can clip, e.g. a cone tip.)
• Crown volume — the fitted shape's volume (see the table above). Analytic formulas are used for the parametric shapes; the alpha shape uses its watertight mesh volume, falling back to the convex-hull volume when the mesh isn't closed. The value is never negative.
• Crown center — the center of the fitted shape (its bounding-box center), in world coordinates.
• Crown dimensions — the width, depth, and height of the fitted shape's bounding box.
• Surface area and the number of points the fit used.

Fuzzy trimming

Real crowns have the occasional branch shooting well outside the general foliage envelope. If the shape had to bound those outliers it would enclose a lot of empty space, over-stating the volume and dimensions. The fuzziness parameter controls how aggressively such outliers are trimmed before fitting:

Fuzziness ranges from 0 to 0.5 (default 0.2):

• At 0, the shape fully encloses the crown — every point lies on or inside the fitted surface, so nothing protrudes.
• As it rises toward 0.5, the outermost points are dropped more aggressively, so a lone branch no longer inflates the fit (the shape may then clip that branch).

Cones and the crown tip

A cone narrows to a point at its apex, so the tapering top of a crown — where foliage still spreads laterally — can't be enclosed by any cone without the base radius exploding. The cone therefore encloses everything below the top sliver and clips that tip, by design. The ellipsoid, prism, and alpha shape enclose the full crown at fuzziness 0.

The trim works per vertical slice: within each horizontal band of the crown, points whose lateral distance from the vertical axis exceeds a percentile (set by the fuzziness) are dropped. Trimming by lateral distance within a slice — rather than by raw distance to the centroid — preserves a crown's natural vertical taper, so a tall or conical crown isn't decapitated. A floor guarantees the trim can never collapse the crown to too few points.

Which points form the crown

• If the scan has leaf/wood labels (wood_class), the crown is fit to the leaf points only — the cleanest definition.
• Otherwise the crown is fit to all non-ground points, so it includes the trunk and branches. (You're warned about this in the setup modal.)

See Fit a crown & metrics to run it, and Separate leaf and wood to produce the labels for a leaf-only crown.