nanofractal

Fast fractal fiducial-marker detection for Python. Fractal markers are nested square markers: they stay detectable under heavy occlusion and over a wide range of distances, and every visible level contributes corner correspondences for accurate pose.

nanofractal wraps an optimised C++ pipeline with nanobind: zero-copy NumPy ↔ cv::Mat, the GIL is released during detection, multi-threaded single-frame detection, and a parallel batch API.

Since 0.6 the library is fractal-only (the ArUco detector was removed). 0.7 reads far markers the reference detector misses (2.6–3 px per cell), explains rejected candidates (diagnose), drops levels that do not fit the rest, finds every copy of a marker, reports pose uncertainty, scales the tracker to the marker size and adds NEON code for aarch64. 0.7.1 finds markers seen from very close on dark frames (a second threshold pass); 0.7.2 reports the reading quality of every level and keeps a marker that flickers at the edge of range (prior / FractalTracker(use_prior=True)). 0.7.3 picks up a marker that is in view but never read yet, once it holds its place for a few frames (FractalTracker(capture_frames=3)). 0.7.4 reads a far marker with a looser tolerance when its size is known from the height (expected_side_px), reports lookalikes, and gives one number for the pose uncertainty (Pose.sd_t).

📖 User guide — markers and printing, detection, pose, video, how to use it most efficiently, parameter tuning, API reference, troubleshooting. Every Python example in it, and in this README, is executed by the test-suite.

Performance

The hot path (adaptive threshold, contour tracing, polygon fitting, decoding) is a purpose-built reimplementation: every level the reference detector finds comes back with bit-identical corners (checked by the test-suite against _reference_detect), and it runs on all cores within a single frame.

Median latency per frame, FRACTAL_5L_6, synthetic scenes from nanofractal.bench, i5-12400 (6 cores / 12 threads), NF_MARCH=x86-64-v3, OpenCV 4.10 — the configuration of the published wheels:

0.7.3 measured 2026-11-03 (one core pinned with taskset); 0.5 on the same machine earlier. A frame with no marker costs 0.1–0.7 ms more than in 0.6: it is thresholded a second time for markers seen from very close (params.close_pass = False skips that).

With OpenCV 5.0 (whose own findContours is already ~3× faster than 4.10's) 0.6 is 2–2.5× faster than 0.5 on one core and 3–8.5× with all cores, e.g. 1080p detect 4.66 → 0.92 ms and 4K 15.9 → 4.14 ms.

0.7 adds a SIMD prefix-scan threshold (detect on one core ×1.17–1.34 at 4K, ×1.05–1.12 at 1080p) and NEON code for aarch64 (Raspberry Pi 5, one core: 1.5–2× faster than the scalar build). The second bit reading costs nothing measurable on scenes the reference already reads. Every push is timed against the previous commit in CI and fails on a slowdown.

Reproduce on your machine:

python -m nanofractal.bench --resolution 1920x1080 --scene perspective
python benchmarks/fractal_bench.py run --resolutions 1920x1080 3840x2160 --batch

Levers:

• nf.set_num_threads(n) — threads used inside one detect() call (default: all cores; 1 = sequential, best for many concurrent detectors). Next to video capture/encoding, fewer threads are often faster (Raspberry Pi 5 with a 60 fps camera and preview: 2 threads 57.5 frames/s, 4 threads 32.5) — start with half the cores and measure the whole pipeline.
• params.detection_scale — runs the threshold/contour stage on a downscaled frame (corners are still refined at full resolution); 0.5 is roughly 3–4× faster at 4K.
• FractalTracker — for video: searches near the previous frame's markers (whole frame when they are lost), with identical accuracy; ~2× faster at 4K and 1.4–1.8× at 1080p on a moving-marker sequence. With auto_scale=True it also shrinks the searched region to the marker size (corners still refined on the full frame): 4K, one core, ×5.7 vs detect.
• detect_batch — parallelises across frames for offline throughput.

Installation

pip install nanofractal

Wheels are available for Linux x86_64/aarch64, macOS arm64/x86_64 (macOS 11+) and Windows AMD64, CPython 3.9–3.14 (x86_64 wheels require AVX2, i.e. Haswell 2013 or newer). They bundle a minimal OpenCV, so no system OpenCV is required at runtime.

Build from source

You need a C++17 compiler, CMake ≥ 3.18 and a development OpenCV — 4.x (core, imgproc, calib3d, features2d) or 5.x (core, imgproc, geometry, features):

sudo apt-get install -y build-essential cmake libopencv-dev   # Debian/Ubuntu
pip install .
NF_MARCH=x86-64-v3 pip install .     # AVX2 build (what the x86_64 wheels use)

Quick start

Inputs are plain NumPy uint8 arrays — (H, W) / (H, W, 1) grayscale or (H, W, 3) BGR, C-contiguous.

Generate a marker

import nanofractal as nf

marker = nf.generate_fractal("FRACTAL_5L_6", size_px=1200)   # every nested level
outer = nf.generate_fractal("FRACTAL_5L_6", size_px=1200, nested=False)  # external level only

The image spans the marker's black border exactly; leave a white quiet zone around it when printing. Configs: FRACTAL_2L_6, FRACTAL_3L_6, FRACTAL_4L_6, FRACTAL_5L_6 (number of nested levels).

Detect

import numpy as np
import nanofractal as nf

# a test frame: the marker on a white page (or image = cv2.imread("scene.png"))
image = np.full((900, 1200), 255, np.uint8)
image[150:750, 300:900] = nf.generate_fractal("FRACTAL_5L_6", 600)
det = nf.FractalDetector("FRACTAL_5L_6", marker_size=0.2)  # side in metres

res = det.detect(image)
print(res.ids)       # int32 (N,)      — one entry per visible marker level
print(res.corners)   # float32 (N,4,2) — outer corners, sub-pixel
for level_id, corners in res:
    print(level_id, corners[0])
assert 0 in res.ids

Pose (occlusion-robust)

estimate_pose returns (rvec, tvec, reproj_err) or None. It uses every visible inner and outer corner correspondence when available and falls back to the outer corners of every detected level otherwise (each at its true size, so the scale is right even when only an inner level is visible); reproj_err (RMS px) lets you gate noisy poses.

camera_matrix = np.array([[1000.0, 0, 600], [0, 1000.0, 450], [0, 0, 1]])
dist_coeffs = np.zeros(5)

res = det.detect(image, with_inner_points=True)
pose = det.estimate_pose(res, camera_matrix, dist_coeffs)       # fisheye=True for the fisheye model
if pose is not None:
    rvec, tvec, reproj_err = pose
    print(tvec.ravel(), reproj_err)    # marker 0.2 m wide, 600 px: about 0.33 m away
    vis = det.draw(image, res, camera_matrix, dist_coeffs, rvec, tvec)   # outlines + axes

The raw correspondences are exposed too: res.points_2d float32 (M, 2), res.points_3d float32 (M, 3) (planar, z = 0) and res.points_level, the level of each point.

estimate_pose(..., full=True) returns a Pose with the method used, the number of points and inliers, the 6×6 covariance cov of (rvec, tvec) and the other planar solution (rvec_alt, tvec_alt, reproj_err_alt): when reproj_err_alt is close to reproj_err the tilt is ambiguous.

Tune detection

p = nf.DetectorParams()
p.detection_scale = 0.5      # downscaled threshold/contour stage
p.min_contour_size = 60      # detect smaller markers (default 120 px perimeter)
p.adaptive_block_size = 21   # threshold window (odd, >= 3; -1 = auto)
p.adaptive_c = 7.0           # threshold constant
p.approx_poly_rate = 0.05    # polygon fit epsilon = perimeter * rate
p.subpix_win_size = 4        # corner refinement half-window (0 = off)
p.kfilter_min_dist = 10.0    # min distance between inner-corner keypoints
p.close_pass = True          # retry empty frames with a large threshold block (very close markers)
det = nf.FractalDetector("FRACTAL_5L_6", params=p)
det.params.adaptive_c = 5.0  # changes apply to the next detect()

Video

frames = [np.roll(image, 20 * k, axis=1) for k in range(5)]   # stand-in for a camera
tracker = nf.FractalTracker(det, auto_scale=True, use_prior=True)   # margin=0.25, pad=16
for frame in frames:
    res = tracker.detect(frame)           # det.detect(frame), plus levels read through the last result
    print(res.cell_px, res.contrast, res.bit_errors)   # reading quality per level

# on a drone's approach: also pick up the marker before it is first read
tracker = nf.FractalTracker(det, use_prior=True, capture_frames=3)

More

• detect(image, roi=(x, y, w, h)) — detect in a zero-copy sub-rectangle; corners come back in full-image coordinates.
• detect_batch(images, num_threads=0, roi=None) — parallel over frames.
• detect(image, all_instances=True) — every copy of the marker in view; res.instance(k) is copy k, ready for estimate_pose.
• res.inconsistent_ids — levels dropped because they do not fit the larger levels (a marker-like pattern elsewhere in the frame).
• detect(image, prior=last_result) — a level the plain reading misses by a few cells where it was a moment ago is kept and marked by bit_errors > 0 (outer levels only; flight video: 10 more frames of 203).
• FractalTracker(det, capture_frames=3) — a quad within the same tolerance of a level's code that stays in place for 2 frames is read with it as prior in the 3rd (flight videos: the marker read 8–39 s earlier on the approach; no candidate on 2400 frames without it).
• detect(image, expected_side_px=(lo, hi)) — the marker's size from the height (rangefinder): that size is read with a looser tolerance and res.lookalikes lists near misses with centre, border errors and contrast (flight videos: 4780 frames with the marker instead of 4480, first read 7–36 s earlier; no false read or lookalike without a marker).
• res.cell_px, res.contrast, res.bit_errors — reading quality of every level, to weigh a detection instead of a yes/no; Pose.sd_t / Pose.sd_rot_deg — one number for the pose uncertainty.
• diagnose(image) — every candidate quad with the reason it was kept or dropped ("duplicate", "border", "bits", "inconsistent"), its closest code and cell contrast: why a marker is not found.
• refine_corners(image, corners, win_size=5) — standalone cornerSubPix.
• PoseSmoother(process_noise, measurement_noise, mode="kalman"|"ema") — temporal pose smoothing.
• draw(..., inplace=False) — draw on a copy.

Errors: wrong dtype / non-contiguous input → TypeError; unsupported shape, empty frame, invalid config or parameters, invalid intrinsics → ValueError.

How it is fast

• Fused adaptive threshold. Separable box sums (horizontal first, uint16, ring buffer + running vertical window), reproducing OpenCV's fixed-point / float rounding of the mean exactly, written straight into a zero-bordered buffer together with 8-neighbour occupancy masks. Horizontal sums come from a SIMD prefix scan (AVX2 / NEON). Row stripes run in parallel.
• Contour tracing. Suzuki–Abe border following identical to cv::findContours(RETR_LIST, CHAIN_APPROX_NONE) (sequential), with SIMD start detection, one mask load per step and no allocation for contours below the minimum size. Isolated speckle pixels (most contours in noisy frames) are skipped without tracing. Row bands are traced in parallel: each band keeps its own pixel labels and a contour is kept by the band holding its start, the ownership rule also used by OpenCV's data-race-free TRUCO tracer; the test-suite checks the result against findContours on millions of contours, including bands one row high. It is 2–3× faster than OpenCV 5.0's own parallel findContours at every thread count (1080p, 12 threads: 0.31 vs 0.72 ms).
• Polygon fit + decoding in parallel per contour, with exact replicas of OpenCV 4's and OpenCV 5's approxPolyDP (they differ) and no per-frame heap traffic. A quad the reference reader rejects is read again with each cell sampled exactly at its centre (the reference sampler is up to a pixel off, a whole cell for far markers).
• Inner points. FAST runs only around the marker; keypoint filtering and matching use grids instead of O(n²) scans.
• Tracking (FractalTracker): region-of-interest search around the previous detection, after Romero-Ramirez et al., Speeded up detection of squared fiducial markers (2018). Their other lever — shrinking the image to the previous marker size — was tested and rejected: it raised the corner error from 0.39 to 1.3 px.
• Zero-copy input, GIL released, a detector pool for detect_batch.

Intentional differences from the reference detector: the second bit reading finds more levels (far, blurred, steeply tilted markers) — levels the reference finds are unchanged; a frame where nothing is found is thresholded again with a large block (close_pass, markers seen from very close); levels that do not fit the larger levels are dropped (inconsistent_ids); with with_inner_points=True, the FAST response threshold is computed over the marker's neighbourhood instead of the whole frame. Reading with a prior is off unless asked for.

Changelog

See CHANGELOG.md.

Citation

If you use this in research, please cite the original work:

• F. J. Romero-Ramirez, R. Muñoz-Salinas, R. Medina-Carnicer, "Fractal Markers: A New Approach for Long-Range Marker Pose Estimation Under Occlusion", IEEE Access, 7, 2019.
• F. J. Romero-Ramirez, R. Muñoz-Salinas, R. Medina-Carnicer, "Speeded up detection of squared fiducial markers", Image and Vision Computing, 76, 2018.

License

Apache-2.0. The vendored fractal detector is © its authors and used under its terms; see third_party/ and PATCHES.md.