tilewise-ccl

Fast tile-wise connected-components labeling for large N-dimensional arrays, returning a lazy array of labels.

tilewise_ccl.label_array takes any large N-D binary mask (NumPy, Zarr, or Dask backed) and returns a lazy dask array of connected-component labels, computed with a tile-local labeling pass plus a small global boundary-piece graph. It is:

• Fast: only components that touch a tile border are reconciled, through a small global graph, so the reconciliation cost stays small as the number of tiles grows.
• N-dimensional: 2D, 3D, or higher; connectivity is configurable.
• Storage- and domain-agnostic: no OME-Zarr / image-format dependency; just NumPy + SciPy + Dask.
• Dask-optional: the dyna backend (see Backends) runs the whole thing through dyna-zarr's pull model instead - no Dask task graph, and it fuses a preceding threshold into each tile read.
• Memory-bounded: peak working memory is primarily controlled by tile size and concurrency rather than the total array size, so it labels arrays far larger than RAM. (On the dask backend the output chunking matters too - see Choosing tile_shape.)
• Composable: the result is a genuine lazy dask array, so it plugs straight into other dask operations, such as da.unique, slicing, arithmetic, .to_zarr(...), region-property computation, etc.

Labels are dense integers 1..N (background 0), int32 when N < 2**31 (essentially always) else int64.

Installation

pip install tilewise-ccl
# or, from a checkout:
pip install -e .

Requires Python ≥ 3.11 and numpy, scipy, dask.

Optional extras, each needed only by the feature that names it:

pip install "tilewise-ccl[dyna]"   # backend="dyna": pull-model tile reads, no dask graph
pip install "tilewise-ccl[cc3d]"   # labeler="cc3d": a faster per-tile CCL kernel (3-D)
pip install "tilewise-ccl[all]"    # both

Each is imported lazily at the point of use, so a plain install stays light and only raises - naming the extra - if you reach for that feature without it.

Quick start

label_array expects a binary mask (anything truthy is foreground). Threshold your data first, then label:

import numpy as np
from tilewise_ccl import label_array

# any N-D array; truthy = foreground
image = np.random.default_rng(0).integers(0, 100, size=(512, 512), dtype=np.uint8)
mask = image > 80

labels = label_array(mask, tile_shape=(256, 256), connectivity=2)

labels                      # lazy dask.array.Array, dtype int32, shape (512, 512)
result = labels.compute()   # materialize to a NumPy array of labels 1..N

# opt in to diagnostics (object/graph counts, timings) -> returns a tuple
labels, diag = label_array(mask, tile_shape=(256, 256), connectivity=2, diagnostics=True)
print(diag["n_final_objects"])

On a Dask array (e.g. a large Zarr / OME-Zarr level)

The input can be lazy. label_array reads it tile by tile, so nothing needs to fit in memory at once. Note the labeling is not forced until you compute or write the result.

import dask.array as da
from tilewise_ccl import label_array

# read one array directly from a zarr store (no OME-Zarr machinery needed)
arr = da.from_zarr("dataset.zarr/0")     # e.g. a huge 3D volume, uint8/uint16
mask = arr > 128                          # lazy boolean mask

labels = label_array(mask, tile_shape=(384, 384, 384), connectivity=2, n_workers=4)

# the result is lazy. Stream it straight to disk (each chunk written once)
labels.to_zarr("labels.zarr", overwrite=True)

The same, without dask (the dyna backend)

The identical job through dyna-zarr's pull model - no Dask task graph anywhere. Install the [dyna] extra. Labels are byte-identical to the dask path; only the execution differs. See Backends for what changes and why.

from dyna_zarr.io import io as dio
from tilewise_ccl import label_array

# read one array directly from a zarr store, exactly as above
arr = dio.read("dataset.zarr/0")          # a DynamicArray, not a dask array
mask = arr > 128                          # lazy - and FUSED into each tile read

# backend is inferred from the mask type - a DynamicArray selects the dyna path
labels = label_array(mask, tile_shape=(384, 384, 384), connectivity=2, n_workers=4)

# the result is a lazy DynamicArray - write it with dyna-zarr's writer, which
# picks up the tile grid automatically (see the note below).
dio.write(labels, "labels.zarr", chunks=(96, 96, 96),
          max_workers=8, overwrite=True)

Two differences worth noting against the dask version above:

• The threshold costs nothing extra. arr > 128 is never materialized - each tile applies the comparison as it is pulled, so there is no intermediate mask array on disk and no per-tile scheduler overhead.
• The writer follows the tile grid on its own. label_array records its tile_shape on the returned array, and dio.write reads it, so the write regions line up with the tiles and each tile is read and labeled exactly once. You do not have to restate the tiling. (chunks is separate and can stay small for fast downstream reads.)

Downstream composability

The labeling is lazy, and so is everything you build on it. A useful consequence: properties=True gives you every object's size and bounding box as metadata, without a second pass over the data - it reuses the tiles Phase A already read, so you can find an object of interest and then read back only the box it occupies.

import numpy as np

labels, diag = label_array(mask, tile_shape=(128, 128, 128), connectivity=2,
                           n_workers=4, properties=True)

# area / bbox come from the per-tile pass - no extra read of the array
i    = int(np.argmax(diag["area"]))          # the largest object
lbl  = int(diag["label_values"][i])
lo, hi = diag["bbox_start"][i], diag["bbox_stop"][i]

# read back ONLY that object's bounding box (.compute() works on both backends)
crop = labels[tuple(slice(int(a), int(b)) for a, b in zip(lo, hi))].compute()
obj  = crop == lbl                            # the object itself, isolated

Only the box is materialized during Phase B; the rest of the labeled output is never computed.

The same laziness applies to ordinary array work:

import dask.array as da

# count objects an independent way (excludes background 0)
n_objects = int(np.count_nonzero(da.unique(labels).compute()))

# write at the tile shape: Phase B emits one block per tile, so this needs no
# split on the way out (see "Choosing tile_shape" for why smaller chunks cost more)
labels.to_zarr("labels.zarr", overwrite=True)

API

label_array(mask, tile_shape=None, connectivity=2, n_workers=1, diagnostics=False, properties=False, verbose=False, backend="auto", executor="thread", labeler="scipy")

Label connected components of a binary N-D mask into a lazy dask array.

Returns:

• By default (diagnostics=False): just output_labels, a lazy array of dense labels 1..N (background 0), same shape as mask. dtype is int32 when N < 2**31, else int64. It is a dask.array.Array with the default backend="dask", and a dyna_zarr DynamicArray with backend="dyna".
• With diagnostics=True: a tuple (output_labels, diag), where diag is a dict of object/graph counts and timings (see below).

labels = label_array(mask)                          # -> dask.array.Array
labels, diag = label_array(mask, diagnostics=True)  # -> (dask.array.Array, dict)

Parameters

Note. tile_shape must have the same length as mask.ndim; a mismatch raises ValueError.

diag fields (returned only when diagnostics=True)

Connectivity

connectivity selects the neighborhood via scipy.ndimage.generate_binary_structure(ndim, connectivity). An offset counts as a neighbor iff its number of nonzero components is ≤ connectivity:

Cross-tile connections (including diagonal corner/edge crossings between tiles) are handled correctly for every connectivity, so the label result is identical to a single whole-array scipy.ndimage.label, independent of tile_shape.

Choosing tile_shape

tile_shape is a pure performance/parallelism knob and does not affect the result. Guidance:

• Bigger tiles → more objects fit entirely inside one tile → fewer boundary pieces → smaller reconciliation graph and less per-tile overhead. The cost is more memory per tile (one scipy.ndimage.label call on a haloed tile) and coarser parallelism.

• The default is usually fine. With tile_shape=None, label_array targets a ~256 MiB int32 working set over the trailing three axes and snaps it to whole storage chunks, so the tile is always a chunk multiple and no chunk is read twice. On a 3-D array chunked at 96³ that lands on 384³; on a 5-D (t, c, z, y, x) it tiles z/y/x only and leaves t/c at 1.

• Override it when you have memory to spare. Phase A holds a few tiles at once, so its cost scales with n_workers × (tile voxels): at 128³ tiles and 4 workers that measured ~350 MiB, and at 256³ tiles ~1 GiB. Bigger tiles mean fewer boundary pieces and a smaller reconciliation graph, at that cost.

• It is decoupled from storage chunking: label_array reads whatever tile size you ask for directly, regardless of how the data is chunked on disk, so there is no need to rechunk the input first. This keeps it efficient even on natively small-chunked data.

• On the dask backend, keep the output chunk equal to tile_shape. Phase B emits one block per tile, so writing to a smaller chunk makes dask split every block on the way out, and that split - not the labeling - dominates peak memory (128³ tiles, 4 workers):

  input	chunks == tile	chunks = tile/2
  1 GiB	563 MiB	965 MiB
  8 GiB	728 MiB	1780 MiB
  15.6 GiB	1066 MiB	2662 MiB

  Labeling with large tiles and then writing to small chunks is the combination to avoid. If you need small storage chunks, use the dyna backend, which writes them directly.

Phase A's memory is n_workers × (tile voxels) × (a few bytes) - ~300-400 MiB on every volume above. The write is what varies; see the table.

How it works: interior–boundary reconciliation

tilewise-ccl is a tile-wise connected-components labeler: label each tile on its own, then merge the components that meet across tile borders. It adapts that classic idea with two moves that keep it fast and memory-bounded:

1. Interior–boundary separation shrinks what must be reconciled. A component touching none of its tile's borders is already a finished object and is set aside at once. Only components touching a border (the ones that might continue into a neighbour) are reconciled. So the global step is a small graph over border pieces, whose size tracks the tiles' seam area, not the object count, and stays flat as the number of tiles grows.

2. Plan first, materialize once defers ever touching the data. The first pass reads each tile but keeps only compact metadata (which pieces merge, plus a per-tile lookup table) and allocates no output array. The labels are a lazy dask graph that materializes exactly once, on .compute() / .to_zarr(...), relabelling each block in a single pass. Peak memory scales with tile size × concurrency (a handful of tiles), never the whole array, and no voxel is written twice.

In short: most objects sit inside a single tile and are finished there (cheap); only the few that straddle a seam between tiles ever need the reconciliation graph.

The two phases

flowchart TB
    T["Tile the N-D mask"] --> L

    subgraph PA["① Phase A · per tile, in parallel · metadata only, no array built"]
      L["label a 1-voxel-haloed tile<br/>(scipy.ndimage.label)"] --> Q{"touches a<br/>tile border?"}
      Q -->|no| I["<b>interior</b> piece<br/>→ a finished object"]
      Q -->|yes| Bd["<b>boundary</b> piece<br/>→ cache its border slabs"]
    end

    subgraph RC["② Reconcile · metadata only (the whole plan)"]
      Bd --> M["match facing border slabs<br/>of adjacent tiles → edges"]
      M --> U["union-find over<br/>boundary pieces"]
    end

    I --> LUT["per-tile lookup table:<br/>local id → dense final id 1..N"]
    U --> LUT
    LUT --> PB["③ Phase B · lazy dask map_overlap<br/>relabel each block once + apply its LUT<br/>(runs only on .compute() / .to_zarr())"]

1. Phase A (eager, one tile at a time, in parallel; metadata only). Read a 1-voxel-haloed tile and label it with scipy.ndimage.label. Split its components into interior (touch no border → finished) and boundary (touch a border → deferred, their border slabs cached). Only small per-tile metadata is kept (never voxel data), so memory is bounded by tile size × n_workers and the pass runs safely across a thread pool. No output array is allocated.

2. Reconcile (metadata only). Compare the facing border slabs of adjacent tiles (faces, plus edge/corner diagonals for higher connectivity); where foreground meets foreground, link the two boundary pieces. A union-find over those pieces merges them into whole objects, and each tile gets a lookup table from its local ids to dense final ids 1..N. This little plan is the entire global result.

3. Phase B (lazy; materialize once). A dask.array.map_overlap relabels each block and applies that tile's lookup table, emitting final labels directly, with no read-modify-write of an output buffer. Nothing runs until you .compute() or .to_zarr(...), and each chunk is produced exactly once.

Because most objects are interior, the reconciliation graph is pure metadata over border pieces, and the array is only ever built lazily, cost stays low even for pathological inputs: an object spanning hundreds of tiles still reconciles in well under a second.

Backends

backend selects how tiles are READ and how Phase B is expressed. Both produce byte-identical labels - it is purely an execution choice.

backend="auto" (default)

Picks "dyna" when mask is a dyna_zarr DynamicArray, "dask" otherwise. The mask type already determines which path is viable - the dyna path accepts nothing else - so the backend is normally not worth stating. Pass it explicitly only to force the dask path for a DynamicArray mask (which works: each tile is materialized as it is pulled).

backend="dask"

mask may be a NumPy, Zarr, or Dask array. Phase B is a da.map_blocks over the mask, so the result is a genuine dask.array.Array that composes with the rest of dask (see Downstream composability).

backend="dyna"

Selected automatically when mask is a dyna-zarr DynamicArray (install the [dyna] extra). Phase A pulls each tile directly through dyna's pull model, and Phase B is a native dyna map_overlap - no dask graph anywhere. Two things make this fast:

• A lazy threshold is fused into the tile read. io.read(path) > 128 is not materialized; each tile applies the comparison as it is pulled, so there is no separate mask array on disk and no scheduler overhead per tile.
• Reads are memory-bounded by construction: a tile pull reads exactly the region asked for.

The returned array is a lazy DynamicArray, so write it with dyna-zarr's writer rather than .to_zarr() - see the worked example above.

• It writes the chunks you ask for, directly. There is no block-splitting step, so fine output chunks cost nothing extra in memory - the case where the dask path is most expensive. On a 15.6 GiB volume with 128³ tiles and 64³ output chunks, dyna peaked at 990 MiB against dask's 2662 MiB, and its Phase A was ~7x faster (29 s vs 225 s). If you need small storage chunks on large data, this is the backend to use.

Any DynamicArray works as the mask - however you obtained it, and with any chain of lazy dyna operations already applied.

Picking a backend

Measured on a 1024³ uint8 volume (1 GiB) of mixed-scale objects - 17,086 components from ~20-voxel specks up to a 386×589×311 structure crossing four tiles - stored in 64³ chunks and written back to 64³ chunks, 4 workers. Each backend runs at the tile size that suits it: dask writes at its tile shape (no block splitting), dyna writes the requested chunks directly. Both produce byte-identical labels (17,086 objects, 2.5 MiB on disk):

dyna is ~3x faster end to end on about half the memory, and the margin is widest in Phase A (~9x here): dask assembles each tile from many small chunk reads through its task graph, which is GIL-bound, while dyna pulls the region directly. The finer the input chunking, the bigger the gap - with coarse 128³ input chunks it narrows to ~1.2x, and with small 32³ chunks it grows to ~3.5x.

Peak memory follows the tile: dyna at 256³ tiles peaks near 1 GiB, at 128³ near 350 MiB. Set tile_shape to the memory you can afford.

What a crop actually costs

Phase A runs once over the whole volume; after that the labels are lazy, so the write cost tracks the region you ask for. Same volume as above, writing each target on its own:

Peak RSS stays flat down each column - ~630-650 MiB for dask, ~360-400 MiB for dyna - because it is set by tile_shape × n_workers, not by how much you write.

Note the crossover at the bottom: dask's 64³ tiles make sub-tile crops cheaper than dyna's 128³ ones, since a crop smaller than a tile still labels whole tiles. That is a tile_shape effect, not a backend one - drop dyna to 64³ tiles and it matches. The trade is worth it in the other direction: the larger tile is what makes dyna's Phase A ~9x faster.

One machine's numbers: the qualitative behaviour should generalize, but the absolute timings and ratios depend on hardware, chunking, tile size and workload.

The mask is shipped to each worker once via the pool initializer, and lazy masks (zarr / dask / dyna) pickle as small references, so no array data is copied. Process pools fall back to threads automatically for an in-memory NumPy mask (which would be copied per worker) and for grids too small to amortize start-up.

labeler="cc3d" follows the same logic: it is faster per call but holds the GIL, so pair it with executor="process" or not at all.