SigOrbit

Rotation-robust handwritten-signature embeddings with continuous SO(2) canonicalization and steerable C4/C8 backbones. Created and maintained by Jordi Murgó (GitHub · jordi.murgo@gmail.com · jordi.murgo@gft.com).

SigOrbit turns a cropped signature image into a deterministic, L2-normalized 256-dimensional vector. It is designed for retrieval, clustering and downstream verification systems that must tolerate arbitrary in-plane rotation without making mirrored signatures equivalent.

Demo

The analyzed signatures are compared with six references while rotation, scale, noise, blur and contrast vary. The matching reference remains identifiable in the per-reference cosine-similarity traces.

Watch or download the MP4 version.

Alpha release. SigOrbit generates embeddings; it is not a complete fraud detector, legal signature verifier, document detector, identity database or anti-spoofing system. Do not use one model score as the sole basis for legal, financial or access-control decisions.

Why the name?

A group action moves an input through its orbit. SigOrbit learns a canonical SO(2) pose and embeds signatures consistently across that rotation orbit. sigorbit was clear on PyPI and had no exact GitHub repository collision when checked on 2026-08-07. This is not a trademark opinion.

Architecture

• C4: 2,254,466 trainable parameters (2.2 M); C8: 4,276,354 (4.3 M)
• 257×257 grayscale input
• 256-dimensional float32 output
• continuous SO(2) rotation canonicalization; no scale or reflection canonicalization
• C4 or C8 regular representations and invariant group pooling; the canonicalizer handles continuous rotation, so C4 equivariance (90° symmetry) is sufficient for signatures and trains 2.7× faster

See the architecture notes and model card.

The end-to-end workflow wraps three training stages:

1. validate an immutable local manifest and a separate rights attestation;
2. train the C4 or C8 backbone from random weights with PK sampling, discrete rotation augmentation and a temporary ArcFace head;
3. restore the best backbone and train only the SO(2) canonicalizer against known synthetic angles;
4. jointly optimize canonicalizer, backbone and ArcFace head using identity, circular-orientation and cosine-consistency objectives;
5. evaluate on signer-disjoint validation identities, restore the best joint checkpoint and export an inference-only SigOrbit artifact.

There are no reflections: the symmetry is SO(2)+C_N (N = group_order), not O(2)/D_N. The ArcFace classifier, optimizers and schedulers exist only in recovery checkpoints; the deployable artifact contains the canonicalizer and backbone.

Training and model lineage

The runtime package owns the exact model and preprocessing classes. The companion sigorbit-trainer package imports those classes directly rather than maintaining a second architecture. Its current from-scratch protocol has three stages:

1. train the C4 or C8 backbone and a temporary ArcFace classifier;
2. restore the best backbone, freeze it, and pretrain only the SO(2) canonicalizer against known synthetic angles;
3. jointly fine-tune canonicalizer, backbone and ArcFace head with identity, circular-orientation and embedding-consistency losses.

The ArcFace head exists only during training and is not part of an exported encoder. The published package still identifies the historically selected checkpoint as sigorbit-c8-257-v1; that checkpoint used an older C8 initializer whose complete resume history was not archived. The auditable trainer produces two from-scratch model IDs: sigorbit-c8-257-retrained-v1 (C8, batch 32) and sigorbit-c4-257-b64 (C4, batch 64). Neither claims a byte-for-byte reproduction of the deployed model. See training and reproducibility for all lineages.

Install

Python 3.10+ is supported. Install the correct PyTorch build for your CPU, CUDA or ROCm platform first, then install SigOrbit:

python -m pip install sigorbit
# Optional FastAPI example:
python -m pip install "sigorbit[api]"

For an unreleased commit, installation directly from GitHub is also supported:

python -m pip install "sigorbit @ git+https://github.com/jordi-murgo/sigorbit.git@main"

For NVIDIA/ROCm, follow the official PyTorch selector rather than relying on the CPU wheel chosen by a generic resolver.

Python API

from sigorbit import SignatureEncoder

encoder = SignatureEncoder(
    checkpoint="/secure/path/sigorbit-c8-257-v1.pt",
    device="auto",
)
vector = encoder.embed("signature.png")

print(vector.shape)  # (256,)
print(vector.dtype)  # float32
print(float(vector @ vector))  # ~1.0
print(encoder.model_id)  # sigorbit-c8-257-v1
print(encoder.preprocess_version)  # sigorbit-gray-square-257-v1

Batch inference preserves order:

vectors = encoder.embed_batch(["a.png", "b.png"], batch_size=16)
assert vectors.shape == (2, 256)

Accepted inputs are PIL.Image, NumPy arrays, encoded bytes and file paths. Inputs must already be cropped signatures. Never compare embeddings generated by different model_id or preprocess_version values.

FastAPI example

pip install -e '.[api]'
export SIGORBIT_CHECKPOINT=/secure/path/sigorbit-c8-257-v1.pt
export SIGORBIT_CHECKPOINT_SHA256=ec8d99f887f5a2658d93b14a14911b29a1411e9cf142efa85862a47b30cd233e
export SIGORBIT_API_KEY=replace-with-a-secret-from-your-secret-manager
SIGORBIT_DEVICE=auto sigorbit-api

Then, from an authorized client:

curl http://127.0.0.1:8000/health
curl -X POST http://127.0.0.1:8000/embed \
  -H "Authorization: Bearer $SIGORBIT_API_KEY" \
  -F 'file=@signature.png'

The response includes the model/preprocess identity, predicted canonicalization angle and 256 normalized floats. Interactive docs are at /docs.

Configuration:

Uploaded filenames are ignored: the API passes bytes to the decoder and never constructs or writes a filesystem path from client input. Encoded inputs are restricted to PNG, JPEG and WebP. The in-process Python API deliberately accepts trusted str/Path inputs, so applications must not forward a remote filename to SignatureEncoder.embed().

See the security review for the threat model, adversarial tests and residual risks.

The server binds to loopback by default. Before binding to a non-loopback address, configure bearer authentication and place it behind a TLS reverse proxy with request/time/rate limits. The built-in limits reduce accidental and simple resource exhaustion; they are not a replacement for an edge proxy or process isolation.

The example intentionally has no signer database and no hard-coded MATCH threshold. Thresholds are catalogue-, domain- and reference-count-specific.

Measured behavior

On the held-out 33-signer/792-image BHSig260 Bengali test split, the 257px checkpoint achieved:

• clean leave-one-out top-1: 100.0% (792/792);
• clean median margin: +0.3196;
• model-canvas non-zero-angle mean top-1: 98.04%;
• square-expand mean top-1: 98.16%;
• raw-expand mean top-1: 89.87%;
• real-signature all-triplet mean top-1: 87.64%.

These numbers describe one dataset/protocol, not a universal error rate. See the model card for exact protocols, limitations and the 129px comparison.

Development

python -m pip install -e '.[api,dev]'
ruff check .
pytest
python -m build

Repository layout:

src/sigorbit/model.py          architecture
src/sigorbit/checkpoint.py     safe artifact loading and identity
src/sigorbit/preprocessing.py  versioned image contract
src/sigorbit/encoder.py        public Python API
src/sigorbit/api.py            minimal FastAPI example
docs/                          architecture, model card, training and release notes
CITATION.bib                   project and technical bibliography

Responsible use and release status

Handwritten signatures are biometric personal data. Do not log uploads or embeddings unnecessarily, and establish retention, consent, access control and deletion policies before deployment.

The source code is MIT licensed. The repository contains no training images. Before publishing the trained checkpoint, read the completed dataset licence audit and complete RELEASING.md. All 7,560 aggregate images were matched pixel-for-pixel to genuine CEDAR and BHSig260 samples. CEDAR has no explicit licence grant, while the BHSig260 authors state only “for research purposes”. The Hub uploader's MIT tag therefore does not establish a sublicence chain. The local checkpoint is present to validate this extraction; do not push or publish it until upstream permission or counsel approval is recorded.

License and citation

Source code: MIT. Third-party notices: NOTICE. Repository: https://github.com/jordi-murgo/sigorbit.

If SigOrbit is useful in research, cite the software as:

@software{murgo2026sigorbit,
  author  = {Jordi Murgó},
  title   = {{SigOrbit}: Rotation-Robust Handwritten-Signature Embeddings},
  year    = {2026},
  version = {0.1.0},
  url     = {https://github.com/jordi-murgo/sigorbit},
  license = {MIT}
}

The complete BibTeX bibliography—including the e2cnn, CEDAR and BHSig260 references—is in CITATION.bib; machine-readable citation metadata is in CITATION.cff. Citing a dataset does not imply that it has an open licence; consult the dataset licence audit.