Estimate leaf area density¶

Compute per-voxel leaf area density (LAD) over a scanned canopy. See Leaf area density for the concept — in short, LAD inverts Beer's law on the laser beams passing through each voxel, so it accounts for occluded foliage rather than just visible surface.

Prerequisites¶

One or more scans with scan parameters (scanner origin + angular sweep). Import them with their parameters (e.g. Add Scan → Import from XML) or attach parameters from the Scans panel. A scan with only point data and no parameters cannot be used.
A voxel grid — LAD requires one (unlike triangulation).
(Optional) A DEM if you want the grid to follow sloping ground — see Terrain following below.
Sky/miss points. LAD needs the beams that passed through the canopy without returning (the Beer's-law transmission denominator), so each scan must carry misses. Formats like E57 and structured PLY retain them; others can reconstruct them from a per-return timestamp and/or scan-grid row/column indices. LAD no longer recovers misses silently — run Backfill Misses first when a scan has none (the dialog tells you and offers a button). A scan with no misses and no way to recover them can't be used until re-imported in a miss-retaining format.

Steps¶

Select the scan(s) in the Scans panel first, then create the voxel grid. Click Create Voxel Grid (the box icon in the Create group). A 1×1×1 m box appears at the origin and the Transform panel opens; the scan selection is kept so you can fit the box in one click.
- Click Fit to selected scan(s) in the Transform panel to resize and center the box around the selected scan(s) (with a small buffer so edge points aren't clipped). The button is enabled whenever one or more scans with points are selected, and you can re-fit at any time.
- Adjust the box (Position / Scale) if you want a tighter or different region. The box is its own object in the scene. Changing its Position (origin) or Scale re-frames the viewport on the box's new location, so it stays in view as you move it away from the default unit cube at the origin — the view updates when you commit a value (press Enter or click away / pause typing), not on every keystroke. Rotating the box about the vertical axis is honored — the LAD voxels are computed in the rotated frame and the result grid lines up with the box you laid out (e.g. to follow a planted row that isn't axis-aligned).
- Set Grid Resolution (Nx × Ny × Nz) to the number of voxels you want along each axis. Use 1×1×1 for a single canopy-wide value, or subdivide for a 3-D density field. A wireframe shows the cells when any axis is greater than 1.
- Alternatively, if your Helios scan XML defines a <grid> block, the voxel grid is created automatically on import — no need to build it by hand.
Backfill misses if needed. If a selected scan has no sky/miss points yet, run Backfill Misses (Pre-processing group) to recover them — see Backfill misses. The LAD dialog also surfaces this: it disables Compute LAD and shows a banner with a one-click Backfill Misses button for any selected scan still missing them. Clicking it runs the backfill and then reopens the LAD dialog with the same scan selection once it finishes, so you're back where you were. Scans imported from a miss-retaining format (E57 / structured PLY) skip this step.
Open the LAD tool (the grid icon, next to Triangulate). The button is disabled until both a parameterized scan is selected and a voxel box exists — the tooltip tells you which is missing.
In the dialog:
- G(θ) source. First choose how the leaf-projection coefficient G(θ) — the term that converts beam attenuation into leaf area — is obtained:
  - Derive from triangulation (default) — mesh the hit points and estimate G(θ) per voxel from the leaf-surface orientations. This is the original workflow; the triangulation choice below applies.
  - Supply G(θ) directly — prescribe the leaf-angle distribution / G(θ) yourself and skip triangulation entirely. See Override G(θ) directly below. Moving-platform scans always use this path (they can't be triangulated).
- Triangulation. (Derive-from-triangulation only.) If you've already triangulated over a voxel grid — either a Helios triangulation, or a per-scan Ball Pivot mesh pinned to a grid — choose Reuse: \<that mesh> here. The inversion then uses that mesh directly — the exact triangles you see (with the current Lmax / aspect filter applied) are sent to the inversion and used as-is, skipping the re-triangulation entirely. This reproduces the mesh's G-function and, on a heavy scan, saves the minutes a fresh triangulation would take. The scan picker, grid selector, and filter fields below are hidden (locked to the mesh). Choose Run a new triangulation to set everything yourself instead. (This selector only appears when a reusable triangulation exists — one built with a voxel grid. When one does, it's pre-selected by default, since reusing it skips the redundant re-triangulation; pick Run a new triangulation if you'd rather not.) A ball-pivot mesh that can't be reused — merged, not pinned to a grid, or from a scan with no scanner position — appears greyed-out here with the reason, so you can fix it (re-triangulate per-scan, pinned to a grid) rather than wonder why it's missing.
  
  You don't need a Helios mesh first
  
  Run a new triangulation with your scans + grid is the full workflow on its own. It runs a real Helios triangulation first — the same one the standalone Triangulate tool produces, with the max edge length auto-estimated from the data — adds that surface mesh to the Meshes panel, then inverts Beer's law on it. So the inversion's G(θ) is computed on a surface you can actually see and check. If it looks wrong (e.g. long triangles bridging gaps between separate leaves, which flatten the normals and depress G(θ)), adjust its Lmax / aspect filter in the Meshes panel, then reopen this dialog and choose Reuse: \<that mesh> to recompute on the corrected surface. If a reused mesh's source scans are no longer all present, the tool blocks the run rather than silently changing the result. - Pick the voxel grid to use (required — no auto-grid). (New triangulation only.) - Max Edge Length (Lmax) and Max Aspect Ratio control the triangulation that estimates the G-function. Leave Lmax on Auto (the placeholder) to size it from the data — an Otsu estimate over the candidate edge lengths, the same default the standalone Triangulate tool seeds — or type a value to force it. The resulting mesh lands in the Meshes panel either way, where you can fine-tune the filter and re-run via Reuse (see the note above). (New triangulation only.) - Min Voxel Hits skips voxels with too few returns to solve reliably. - Element width (m) is the characteristic width of a leaf or needle. It sets the sampling-uncertainty interval reported with the result (Pimont et al. 2018). Use the Broadleaf (0.05) or Conifer (0.002) preset, or type your own value. It does not change the LAD point estimate, only the confidence interval. - On sloping ground, snap the grid to the terrain first (Meshes panel → expand the grid → Snap to ground) so each column follows the ground; the dialog then shows "This grid is snapped to ground." See Terrain following below. - The return type is shown read-only; it follows each scan's own parameters. Multi-return scans need per-pulse metadata in the source (see the concept page).
Click Compute LAD. The calculation runs on the backend (the first run can take a while as PyHelios warms up). A Leaf Area Density entry appears in the scene panel when it finishes.

Reading the result¶

Voxels are drawn as translucent colored cells; the color maps LAD through the shared colormap, with a colorbar in m²/m³.
Hover a cell to read its exact LAD, G(θ), and hit count.
In the result's row you can toggle visibility, adjust opacity, hide empty voxels (default on), and change the colormap.
Selecting the result also shows a group-scale confidence interval (e.g. Mean LAD 1.23 [1.15–1.31] m²/m³, 95% CI), computed across all solved voxels following Pimont et al. (2018). This is the recommended aggregate — it is far tighter and more trustworthy than a single voxel's interval. It reflects sampling uncertainty conditional on the beams that entered the voxels; it does not capture occlusion bias (foliage no beam ever reached). If the interval falls outside the method's validity range, it is not reported.

Terrain following — snap the grid to the ground¶

A flat voxel grid assumes level ground: voxel layer k is at the same absolute height everywhere, so on a slope the bottom layer can be buried in soil on the uphill side and floating above the canopy downhill. Snap to ground fixes this by shifting each vertical column of voxels so its bottom rides a DEM surface, keeping every column a constant height above the local ground. The grid visibly displaces in the viewport, and that displaced grid is exactly what the LAD inversion uses — what you see is what is computed.

To use it:

Generate a DEM from the cloud first (Generate DEM). The DEM is the ground surface the grid will follow; it appears in the Meshes panel.
Create and place the voxel grid as usual (size it to the canopy height you want above the ground, not to absolute elevations).
In the Meshes panel, expand the grid's row and click Snap to ground (under Terrain follow). Pick the DEM (if more than one exists) and set the clearance — the gap kept between the ground and the lowest cell, as a fraction of one voxel's height (so it scales with grid resolution). The grid's columns immediately shift to follow the terrain in the viewport.
Open the LAD tool and pick that grid. A note confirms "This grid is snapped to ground." Compute LAD — the inversion runs against the displaced grid, so the result voxels track the ground.

Notes:

The whole cell clears the ground, not just its center: each column is lifted so its bottom face sits above the highest ground across its footprint (plus the clearance). On a slope that means a column rides on its uphill edge, so no part of the grid dips into the soil. Columns over small DEM holes inherit the nearest measured elevation; columns whose footprint lies entirely outside the DEM are dropped (a toast reports how many).
Keep the grid short enough. Because each column is lifted to clear its highest ground, a tall grid on a steep slope can push the uphill columns above the canopy. Size the grid's height (z) to the canopy you want to capture above ground, and prefer finer columns (more Nx/Ny) on steep terrain so each footprint spans less rise.
Editing the grid clears the snap. Moving, resizing, rotating, or re-dividing a snapped grid resets it to flat (the offsets would no longer match) — just Snap to ground again. Use Clear snap to remove it manually.
Terrain following only shifts columns vertically — it does not tilt or rotate the grid. Combine it with an azimuthal grid rotation (above) for a row that is both sloping and off-axis.
The snap survives export. Exporting the scene to Helios scan XML writes the per-column offsets into the <grid> block, so re-importing the XML brings the grid back already snapped — no need to re-run the DEM and snap. See the file-format reference.

Override G(θ) directly¶

Instead of deriving G(θ) from a triangulated surface, you can prescribe the leaf-angle distribution / G(θ) yourself. Choose Supply G(θ) directly under G(θ) source, then pick:

Vary with height?
- Constant — one G(θ) applied to every voxel.
- Vertical profile — G(θ) varies with height. You pick the method once, then enter its value for each z-level of the grid (level 1 = lowest band). Use this when leaf inclination differs between the lower and upper canopy. A Apply level 1 to all button fills the column from the first row.
Method (how each value is obtained):
- Constant value — type G(θ) directly (0.5 = spherical). A Spherical (0.5) preset is provided.
- de Wit — choose a classical leaf-inclination distribution (spherical, planophile, erectophile, plagiophile, extremophile, uniform). G(θ) is derived by integrating the Ross projection kernel over the actual distribution of beam zenith angles in your scan(s) — so it reflects your acquisition geometry, not a single nominal angle.
- Beta (μ, ν) — Goel–Strebel parameters (ν = toward-vertical weight, μ = toward-horizontal; mean inclination fraction ν/(ν+μ)), the same convention used by Adjust leaf angles. G(θ) is derived as for de Wit. See Leaf-angle distributions and G(θ) for the math.

This path skips triangulation, so the Lmax / aspect fields are hidden. When you use a vertical profile, the result reports the resolved G(θ) per level, and the per-voxel G(θ) you read on hover varies by height accordingly.

Moving-platform scans¶

If a scan carries a platform trajectory, LAD is computed with a beam-based inversion: every return is traced from its own per-beam origin (the platform pose when that pulse fired), joined to the trajectory by the return's timestamp. This path does not triangulate the scan — a moving sweep has no fixed angular grid to mesh — so it always uses the Supply G(θ) directly path (the G(θ) source is forced to supplied). The simplest choice is a constant mean G(θ) of 0.5 (spherical / randomly-oriented leaves; set it to match the canopy if known), but the de Wit and Beta methods — and the vertical profile — work for moving scans too, since their per-beam directions are known. The point cloud must carry a per-return timestamp column (for the trajectory join) and miss points — run Backfill Misses first if the scan has a timestamp but no recorded misses, as for any LAD.

Clock alignment matters. The return timestamps and the trajectory must use the same clock. If they don't overlap in time (a common cause: a LAS recorded in GPS Week Time combined with an absolute trajectory, or a ~1e9 s Standard vs Adjusted-Standard GPS offset), the join would otherwise clamp every return to a single pose — so LAD fails with an explicit error naming both time ranges rather than producing wrong origins. If only part of the scan falls inside the trajectory's time span, you get a partial-coverage warning and the out-of-range returns are clamped to the nearest endpoint. A scan whose LAS carries explicit per-beam origin ExtraBytes skips the join entirely and uses those origins directly.

Tips¶

If no triangles are produced (G-function can't be estimated), set an explicit Lmax (larger than Auto chose) or loosen Max Aspect Ratio, or inspect the mesh that was created in the Meshes panel and loosen its filter there. (Moving-platform scans skip triangulation; this doesn't apply to them.)
The G(θ) you see when hovering a LAD voxel is now computed on the same filtered surface shown in the Meshes panel. If it looks too low, the mesh likely has long triangles bridging gaps between separate leaves — tighten its Lmax filter and recompute via Reuse.
Segment out ground and trunk first if you only want foliage density — the inversion counts every return inside the grid.
If you crop a scan after backfilling its misses, the result warns that the misses are stale (they were computed against the pre-crop hits, so the hit/miss ratio is off). Re-run Backfill Misses on the cropped cloud before trusting the LAD.
For a single canopy-wide LAI, use a 1×1×1-cell grid sized to the whole canopy and read the single voxel's LAD × its height.