Morphology (erode / dilate / open / close)

Erode (local min) or dilate (local max) a grid over a (2r+1)² square structuring element; opening is erode→dilate, closing is dilate→erode. Grey-scale by definition; a 0/1 mask is the binary special case.

What it means

• Opening removes anything thinner than the element and keeps blobs. The motivating case is LIDAR: a roof is opaque, so a building’s interior has first-minus-last return ≈ 0 — but its one-pixel perimeter (first return on the roof edge, last return on the ground beside it) reads as several metres of canopy. It is thin and canopy is not, so an r = 1 opening of the canopy mask separates them. Hedgerows survive: at 1 m they are 2–4 pixels of crown, not a line.
• A large-radius opening of a surface is a ground estimate. Opening the last-return surface with r ≈ 25 takes the local minimum and then re-expands it, flattening trees and buildings while tracking terrain — the classic morphological bare-earth filter.
• Closing is the dual: it fills gaps narrower than the element.

GPU approach

A square element is separable exactly — the min over a square is the min of per-row minima — so this is the same two-pass horizontal-then-vertical "use gpu" gather as separable convolution, with min/max in place of the weighted sum and clamp-to-edge boundaries. Because there is no arithmetic the GPU result is bit-exact against a direct 2-D window (that is what the test asserts). Opening and closing run two rounds through GPU-resident scratch; as a graph node the op is Tier-2 resident (no host round-trip between it and its neighbours).

Usage

import { morphologyGpu, openingGpu } from 'intraspatial/gpu/spatial/morphology';

const canopy = await openingGpu(mask, w, h, 1);                 // binary opening, r = 1
const ground = await morphologyGpu(lastReturn, w, h, 25, 'open'); // bare-earth estimate

As a graph node: g.op1("morphology", { grid }, { op: "open", radius: 1 }).

Composes with

• Separable convolution — the linear sibling; a box blur after an opening gives the smoothed canopy-cover fraction.
• threshold (hard or soft) before it — the canopy mask. An untested idea from the terrain work: a soft threshold feeding a grey-scale opening may behave better at woodland edges than a frozen hard mask.

Status: ✅ implemented, bit-exact against the square-window oracle and psychogeo:codec_eval/foliage.py::opening semantics · src/gpu/spatial/morphology.ts, graph op src/gpu/graph/ops/morphology.ts. Not yet nodata-aware (terrain gap 3).