Classification of Breast Cancer Lesions in 3D Automated Breast Ultrasound

Project page · Code · Roadmap · Results so far

Automated 3D breast ultrasound (ABUS) images the whole breast in a single sweep, but reading the resulting volumes is slow, and telling malignant lesions from benign ones remains hard.

This repository is a research reference for studying, implementing and evaluating published ABUS methods on TDSC-ABUS 2023. We select relevant and influential papers, reconstruct their methods, run experiments on a shared benchmark, and publish the evidence needed for other researchers to understand, verify and extend the work.

Our current focus is paper reproduction and evaluation. Each study connects an implementation in abus_classification, an explanatory notebook, Kaggle GPU kernels, stored results and a detailed reproduction guide. Those records explain what we did, how and why, including assumptions, differences from the paper, unexpected behavior and follow-up experiments. Original authors are welcome to review the implementation and contribute corrections; review status is recorded explicitly.

Phase 3 will study Laplace–Beltrami shape representations and their classification performance, using the reproduced methods as baselines. Our previous paper [7] motivates that investigation; its finalized source, including the CNN code, is currently awaited from the first author.

Start with the research index and research workflow. The index distinguishes current reproductions, planned studies and historical thesis experiments.

The work is carried out at the Iran Image Processing Lab (IIPL) by Ali Naderiparizi and Sepideh Barekatrezaei, under the supervision of Dr. Ehsan Kozegar and Dr. Mohsen Soryani (main supervisor). Code is released under the MIT license.

Results so far

All results below use the official TDSC-ABUS test split (70 lesions: 40 malignant, 30 benign). Published challenge scores are labeled separately from our evaluations. A completed run does not imply original-author verification or an exact reproduction of the original protocol. Always answering “malignant” scores 57.1% accuracy on it.

Comparing across rows. The reproductions here compute features from the ground-truth lesion masks, and the CNN patches are centred on those masks. Challenge entries had to locate and segment lesions themselves, so their task was harder. Closing that gap — running every method on predicted segmentations as well — is part of Phase 2.

What the Tan et al. reproductions show so far (details in 1-tao2013.ipynb):

• Coronal spiculation replicates. Tan’s spiculation features score AUC 0.80–0.81 on their own, matching the 0.81–0.83 reported on their Nijmegen data, and removing them costs the classifier 0.07 test AUC. They are not a proxy for lesion size.
• Several classic ultrasound features do not transfer. Posterior acoustic behavior falls to chance (AUC 0.50, against 0.80 in the paper), and the height-to-width ratio and margin contrast lose most of their signal.
• Shape carries most of the signal on this data. Among general radiomic features, boundary fractal dimension (AUC 0.75), surface area, compactness and sphericity (0.74) lead, while intensity features sit near chance — which motivates the shape-based approach in Phase 3.

Tan’s features on two lesions	ROC on the test split

Barekatrezaei et al. 2026 — awaiting finalized author source. The first author’s finalized source, including the CNN implementation, is pending. Provisional comparisons are omitted from this README while fidelity is unresolved. Existing runs, differences and diagnostics remain in the notebook and reproduction record; they are not a finalized assessment of the paper. See #28.

Zhou et al. 2021 (details in 3-zhou2021.ipynb):

• Different data and evaluation. The paper reports AUC 0.787, accuracy 74.1% and Dice 0.778 from four-fold cross-validation on private data. Our TDSC-ABUS evaluation gives AUC 0.67, accuracy 62.9% and Dice 0.73. These protocols do not establish a direct replication of the paper’s score.
• Refinement helps segmentation, as in the paper. The paper’s classification gain does not show here: on one seed, the full method scores AUC 0.65 against 0.74 without refinement, with overlapping confidence intervals.
• The classification head under-fits. Its loss barely falls during training and training AUC only reaches about 0.75. The cause is not yet tested.

Wang et al. 2020 (details in 4-wang2020.ipynb):

• Different data and evaluation. The paper reports AUC 0.947 with five-fold cross-validation on private data; our TDSC-ABUS Test AUC is 0.755. The dataset and protocol difference limits conclusions about the original result.
• The multiview gain does not show. The transverse view alone scores highest (0.80), and ImageNet weights give no visible gain; all confidence intervals overlap.
• Validation overstates the result. Best validation AUC averages 0.94 for CNN A on 30 lesions, against 0.74 on test.

Yu et al. 2024 (details in 6-yu2024.ipynb):

• Unresolved comparison on the paper’s data and protocol. The paper reports soft voting AUC 0.986 from five-fold cross-validation on the TDSC Train split; our reconstruction gives 0.85 under that split protocol. Several implementation details remain assumptions. Its voting rows list AUC equal to accuracy, and its hard voting sensitivity and specificity imply accuracy 0.937 rather than 0.907; these are questions for author clarification.
• Soft voting helps only a little over hard voting. It adds about 0.02 AUC, without a paired test yet.
• Training memorises quickly. Training accuracy reaches about 100%, by epoch 2 on whole slices. The likely cause is volumes being memorised; this is not yet tested.
• Early stopping did not help, so the paper defaults stay the main result. We added it because of that memorising, stopping on the official Validation split. Crops move from ensemble AUC 0.825 to 0.832, whole slices fall from 0.765 to 0.676, and no pretraining rises from 0.687 to 0.697; all paired 95% intervals include zero. Five-fold CV also falls, from 0.846 to 0.796 on crops. Validation AUC reaches 0.91–0.994 against 0.67–0.81 on Test, so 30 validation volumes are a poor guide.
• Challenge benchmark, classification only: crops rank 4 of 9 (Cls_Score 0.734) with defaults and 2 of 9 (0.844) with early stopping. AUC is close, and most of the gap is three test volumes at the 0.5 threshold. A second session with the same settings gave rank 3, so this rank is not stable. This method uses ground-truth masks, so it has no overall rank.

Laplace–Beltrami invariance (details in lb-invariance.ipynb):

• The invariances hold. Rigid motion, isometry and scale (λₖ·Area) are exact on meshes. Random rigid motions of re-voxelised lesions change λₖ·Area by about 0.2% on smoothed surfaces and 1% on staircase surfaces.
• The eigenvalues in our previous work measure size. They come from the cotangent matrix L without the mass matrix, and eig(L) ≈ λ·Area / n, with n the vertex count (ratio 0.99–1.00 here). The stored values rank lesions almost exactly by vertex count (Spearman −1.00 at k = 99), so they also depend on the voxel grid. In 29 of 200 lesions, an extra mesh piece shifts their indices.
• Little signal remains in the low modes once size is removed. On Train + Validation, cross-validated AUC is 0.59 for λₖ·Area with k = 1–20, 0.71 for volume and 0.72 for the stored values. Adding these modes to volume lowers it to 0.65. Higher modes and lighter smoothing are untested.

What the Laplace–Beltrami spectrum determines (details in lb-spectrum-content.ipynb):

• Area can be read from the spectrum, volume cannot. Weyl’s law recovers lesion area to about 4% from modes around k = 50–100. The Euler number comes back within about 0.1 on fine sphere and torus meshes, but too noisily on lesion meshes to count handles.
• Kac’s limit is real here. An isometric dent changes volume but not the spectrum, and a Sunada pair of non-isometric surfaces shares its spectrum to 3e-15.
• Area normalisation is not enough in practice. At a fixed voxel size and smoothing width, λₖ·Area at high modes still follows volume (Spearman up to 0.96).
• In a linear model, the spectrum adds nothing to volume on Train + Validation. With volume removed, AUC is at most 0.49 on every surface up to k = 100. Tan’s spiculation, which uses image gradients, keeps 0.69 under the same check. Sphericity also falls to about chance. Non-linear models and size-matched meshing are untested.

Roundness and lobulation from the spectrum (details in lb-roundness.ipynb):

• Matching meshes to lesion size fixes the size leak. Giving each lesion a grid and smoothing proportional to its size cuts the correlation of λₖ·Area with volume from up to 0.96 to at most 0.21.
• Hersch’s bound holds, and λ₁·Area / 8π mostly reads elongation. No genus-0 lesion exceeds the bound; the median ratio is 0.61 and the largest 0.88. Its Spearman correlation with elongation is −0.69.
• Lobes split eigenvalues by an exact rule, on near-round shapes only. A lobe of even degree d first splits level d/2, within about 5% of the first-order prediction, and odd degrees split only at second order. Real lesions are far outside that range.
• Little spectral signal remains beyond volume, even when sizes are matched. On Train + Validation, CV AUC after removing volume is 0.57 for λ₁·Area and at most 0.55 for all-mode sets. Adding λ₁·Area to volume gives 0.72 against 0.71. A plain extent ratio does better: 0.63 after volume, 0.75 with it. Many comparisons were made on 130 lesions.

Lobes and the levels they split	Real lesions by their distance from the round sphere

Stability of the spectrum (details in lb-stability.ipynb):

• Eigenvalues have a proved limit, with one exception. The ratio of any eigenvalue to its deformed value is bounded by how much the surface’s metric changes, for every mode. Necks escape it: a thin neck barely changes volume and strongly lowers λ₁.
• Small percent changes hide low reliability. High modes move only about 1% under 0.5 mm boundary noise, but lesions differ by about that much too. ICC at that noise is 0.81 at k = 1, 0.44 at k = 20 and 0.13 at k = 100, against 0.99 for volume.
• On real predicted masks, a lesion’s rank in the spectrum mostly disappears. With Zhou 2021’s masks (mean Dice about 0.73), Spearman between true and predicted is 0.92 for volume, 0.64 for elongation, 0.40 for λ₁·Area and about 0 from k = 20 up. Those patches are centred on the true lesion, so a full pipeline would not do better. The network also rounds shapes: median sphericity rises from 0.38 to 0.62, and 94% of predictions are rounder than their true mask.
• Simulated noise does not explain the weak class signal. AUC stays about flat up to 0.5 mm of noise. So instability is a separate limit, and the annotation error already in the true masks remains unmeasured.

A real lesion under increasing boundary noise	True and predicted surfaces, Test lesions

Spherical harmonics and the spectrum (details in lb-spherical-harmonics.ipynb):

• The two views connect exactly on near-round shapes. A lobe of degree d appears at harmonic degrees d ± 1 and first splits eigenvalue level d/2.
• Real lesions can be mapped. All 200 map to the sphere conformally, 19 after topology correction, with almost no flipped triangles. The map is the one in Hersch’s proof: its energy is within 5% of 8π, and λ₁·Area stays below it on every lesion. Thin parts shrink and reconstruct worst.
• Harmonic power is more reliable than eigenvalues at fine scales. At 0.5 mm noise, ICC is 0.70 at degree 10 (about mode 120) against 0.13 at k = 100. On predicted masks, rank is 0.48 at degree 10, where eigenvalues from k = 20 keep none. At coarse scales they are about equal. Topology correction may account for part of this.
• Reliability does not bring class signal. On Train + Validation, CV AUC after removing volume is at most 0.56 for harmonic features, against 0.70 for spiculation.

Rebuilding real lesions from harmonics	Sphere maps of real lesions

Spectral descriptors as classifiers (details in lb-descriptors.ipynb):

• Features using eigenfunctions show the first spectral signal beyond volume. On Train + Validation, CV AUC after removing volume is 0.64 for the count of heat-kernel maxima (“tips”, protrusions at a given scale) and for the WKS 95th percentile, against 0.44–0.47 for Shape-DNA. With volume, they reach about 0.77 against 0.71 for volume alone.
• Not yet established. The best gain over all 9 families beats shuffled features (p = 0.02), but each gain’s 95% interval includes zero, and that test does not correct for earlier work on the same 130 lesions. Test has not been used.
• Overlaps with spiculation. Tips add only 0.015 on top of volume and Tan’s spiculation (0.80), which remains the strongest feature here.
• The means cannot help in principle. Mean HKS is the heat trace and mean WKS is identically 1, so only their spread and maxima can add to the eigenvalues.

Protrusions by class, and the gain against shuffled features

Classification with every feature set (details in lb-classification.ipynb). These are Train + Validation estimates, made before Test was read; the Test results follow in the next section:

• Fair performance is about 0.81. With feature selection inside cross-validation, AUC is 0.81, against 0.58 at the 95th percentile with shuffled labels (p < 0.01). Testing many combinations without nesting gives higher numbers that should not be trusted.
• Spiculation is the core. It is chosen in 99% of folds and is the only group whose removal clearly hurts. It uses image gradients, so this is not purely a shape result.
• Spectral features alone are weak, but one adds to spiculation. All spectral groups together reach 0.67. The Hersch ratio λ₁·Area/8π adds 0.045 on top of size and spiculation (interval 0.006 to 0.089). With 11 additions tried, this is promising, not established.
• More features is not better. All 112 features score 0.81, below the 21 classical ones at 0.84.
• Predictions can be explained. A four-feature linear model splits each prediction into readable contributions. Its own 0.87 AUC is optimistic, since its features were picked on these lesions.

Each feature group alone	Explaining single lesions

Laplace–Beltrami features on Test, with the TDSC-ABUS benchmark (details in lb-feature-evaluation.ipynb). Models were frozen on Train + Validation from 510 combinations of 17 classifiers and 10 feature sets, then scored once on Test. All use ground-truth masks and classify only, so ranks are not like-for-like with challenge teams:

• Above 0.80 needs classical features. LB features alone do not get there, with any classifier the rule could pick. Size + spiculation clears both targets, and uses image gradients.
• The earlier spectral gain did not replicate. The Hersch ratio helped on Train + Validation and changed AUC by −0.020 (−0.086 to 0.042) on Test. At this point, no LB feature had shown independent value on held-out data.
• The best of 510 is not a result. Extra trees reached AUC 0.922 and ACC 0.857 on Test, but it was found by looking at Test. Test has now been used, so further tuning against it would be biased.
• Single lesions look different, but the classes overlap. Both classes contain round and irregular lesions, and single shape measures reach AUC 0.61–0.72.

Results on the challenge board	Class overlap per measure

What malignancy means, and what a 3D surface can show (details in lb-malignancy.ipynb). Designed on Train + Validation, then scored once on Test from a plan frozen and hashed in advance. Test had already been used once, so this is a second look at that split. True masks unless stated.

Malignancy is a behaviour of cells, invasion and spread, confirmed by histology. Shape is only its footprint, and it fails in both directions: radial scars can look spiculated and be benign, and many triple-negative cancers look circumscribed. So we turned the clinical signs into descriptors, and asked which of them hold up.

Ranks use true masks and classify only, so they are not like-for-like with challenge teams. Predicted-mask patches are centred on the true lesion. The notebook reports all 12 models. Only the primary and size were in the plan for predicted masks; the rest are post hoc.

• Tissue lines replicated. Lines in the tissue run out of malignant lesions as far as 25–30 mm, and benign lesions stay near zero, with the same profile on Test as on Train + Validation. AUC after volume is 0.77, against 0.76 for Tan’s SP90, and it does not follow size. A sham lesion elsewhere in the scan gives AUC 0.43, against 0.77 at the lesion.
• The hybrid did not beat size + spiculation. It passes 0.80 on both metrics, but its gain is −0.035 (−0.117 to 0.039). Its tilt term failed: AUC 0.49 on Test, against 0.60 on Train + Validation. Without tilt the model has the highest AUC of the 12, but being the best of 12 it is not a result, and it ties size + spiculation.
• Spiculation is not just spikes on the mask. On Train + Validation, surface signs track SP90 at Spearman 0.36 at most, while radial lines reach 0.77. Within a lesion, bumps barely sit where lines run out (0.03–0.08 across splits). Masks may simply leave thin spicules out.
• Mask shape is modest and does not survive real segmentation. Surface signs alone reach AUC 0.63 on Train + Validation and 0.73 on Test, then 0.64 with ACC 0.43 on predicted masks. Those surfaces are much smoother, so the model calls almost every lesion benign.
• Lines do survive it. On Zhou 2021’s masks the primary model keeps AUC 0.82 and ACC 0.78, where Zhou’s own classification head scores 0.67 and 62.9% on the same lesions.
• Laplace–Beltrami’s part is small. The fine area budget, built from the operator applied to the surface’s coordinates, is the first LB measure here with signal beyond volume on held-out data: AUC 0.76 (0.63–0.87), one of eight features checked. Its gain on the hybrid is not established (0.034, −0.009 to 0.079), and whether it adds to size + spiculation was not in the plan. The line excess needs no LB, and tilt matches plain surface PCA.

Each sign on shapes built to show it	Lines around six real lesions

Predicted and true tumors, Zhou et al. 2021	Ablations against the paper

Roadmap

Status: ✅ recorded work completed within its stated scope · 🔄 in progress · ⬜ planned. These symbols do not indicate original-author verification; see the research index.

Phase 0 — Foundations ✅

Phase 1 — Reproduce classical radiomics ✅

Phase 2 — Reproduce the strongest published results 🔄

The shared target protocol fits Train + Validation (130 volumes) and evaluates the official Test split (70), with malignant as the positive class, three seeds and AUC confidence intervals. Original-paper protocols and variants are reported separately. For example, holding out Validation for early stopping fits only Train (100); it must not be described as the same training protocol. Each volume’s slices and patches stay together when creating splits. Pairwise statistical comparisons and evaluation using predicted segmentations remain planned where not explicitly reported.

Each study also reports the challenge benchmark on the published leaderboard (abus_classification/challenge.py). So far that covers classification only (#34).

Phase 3 — Mathematical foundations of Laplace–Beltrami shape representation 🔄

Our previous work [7] motivates studying Laplace–Beltrami spectra of lesion surfaces. Foundational invariance work has begun alongside the benchmark studies; full descriptor classification comparisons remain pending. This phase investigates which properties of a tumor’s shape the spectrum provably captures, which it cannot, how stable it is under the imperfections of real ultrasound segmentations, and how it relates to spherical harmonic decompositions. Every claim is paired with an empirical check on TDSC-ABUS, and the theory is used to derive better-founded descriptors.

The feature sets in 3D

lb-features-3d.ipynb shows what each one measures, on reference shapes and real TDSC-ABUS lesions chosen by volume percentile. These illustrate one lesion per class and are not evidence of a class difference.

The real surfaces. Staircase meshes from binary masks, and the same lesions after light smoothing.

Shape-DNA, the eigenvalues: the pitches a surface vibrates at, a global description that ignores pose and, multiplied by area, size. Shape appears as the departure from Weyl’s line.

Eigenfunctions: the vibration patterns. Low modes split a shape along its long extents; higher modes make finer patches.

Heat diffusion: heat placed at one point spreads over time, and how much returns underlies the heat trace.

Heat kernel signature: how much heat stays at each point. It stays longest on tips, so dark regions mark protrusions at the scale set by time.

Wave kernel signature: a band-pass version that isolates one range of modes.

Global point signature: a new embedding where distance reflects how the surface connects, not how it sits in space.

Spherical harmonics: the sphere’s own vibration patterns, used as a basis for rebuilding a surface mapped onto the sphere. Unlike the spectrum, they see how a surface sits in space.

What it cannot see: an isometric dent keeps the spectrum and changes the volume, and Sunada surfaces share a spectrum without being isometric.

Phase 4 — Paper ⬜

Datasets

TDSC-ABUS 2023

The public dataset of the TDSC-ABUS 2023 challenge: 200 ABUS volumes acquired with a GE Invenia ABUS at Harbin Medical University Cancer Hospital, each with a voxel-level tumor mask and a malignant/benign label.

Access requires a signed data use agreement; see the dataset page.

Voxels are not cubes. The volumes are 843–865 × 546–682 × 270–354 voxels at 0.200 mm along the transducer, 0.073 mm in depth and 0.476 mm between slices, and the NRRD files do not record this. All features and figures here use physical units; measured in voxels, lesions appear up to five times thinner along one axis than they are.

IIPL-3D-ABUS

A private dataset of 70 ABUS volumes (55 malignant, 15 benign) collected at the Iran Image Processing Lab and segmented under the supervision of two expert radiologists. It cannot be shared; for enquiries, contact [email protected].

Getting started

Install

The project is managed with uv, which also installs a suitable Python:

curl -LsSf https://astral.sh/uv/install.sh | sh
git clone https://github.com/mralinp/abus-classification.git
cd abus-classification
uv sync

uv.lock currently resolves for macOS, where PyTorch uses the Apple Silicon mps backend. To run on Linux with CUDA, remove environments under [tool.uv] in pyproject.toml and run uv lock.

Data

Place the TDSC-ABUS splits under data/tdsc/:

data/tdsc/
├── Train/        DATA/, MASK/, labels.csv, bbx_labels.csv
├── Validation/
└── Test/

from tdsc_abus2023_pytorch import TDSC, DataSplits
from abus_classification.features import tan

dataset = TDSC(path="data/tdsc", split=DataSplits.TRAIN, download=True)
volume, mask, label, bbox = dataset[0]          # label: 0 = malignant, 1 = benign

features = tan.extract_tan_features(volume, mask)   # millimetre-aware, uses TDSC-ABUS spacing

Passing download=True makes the dataset automatically downloaded if its not present on the system.

Run

uv run pytest test/features_tests test/utils_tests test/papers_tests   # library and paper tests
uv run jupyter lab                                   # after: uv add --group notebooks jupyterlab

Training runs on Kaggle GPU kernels (see kaggle/README.md). Notebooks load the stored outputs in results/, so they open without a long run. To run a reproduction yourself:

uv run python -m abus_classification.papers.zhou2021 --epochs 100

Google Colab

!git clone https://github.com/mralinp/abus-classification.git
%cd abus-classification
!pip install -e .

Repository layout

References

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2. T. Tan, B. Platel, T. Twellmann, G. van Schie, R. Mus, A. Grivegnée, R. M. Mann, N. Karssemeijer. Evaluation of the effect of computer-aided classification of benign and malignant lesions on reader performance in automated three-dimensional breast ultrasound. Academic Radiology 20(11):1381–1388, 2013. doi:10.1016/j.acra.2013.07.013
3. T. Tan. Automated 3D breast ultrasound image analysis. PhD thesis, Radboud University Nijmegen, 2014. pdf
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5. G. Luo, M. Xu, H. Chen, X. Liang, X. Tao, D. Ni, et al. Tumor detection, segmentation and classification challenge on automated 3D breast ultrasound: the TDSC-ABUS challenge. arXiv:2501.15588, 2025. arXiv
6. Y. Zhou, H. Chen, Y. Li, Q. Liu, X. Xu, S. Wang, D. Shen, P.-T. Yap. Multi-task learning for segmentation and classification of tumors in 3D automated breast ultrasound images. Medical Image Analysis 70:101918, 2021. ScienceDirect
7. S. Barekatrezaei, A. Naderiparizi, E. Kozegar, J. Ghofrani, M. Soryani. Breast mass classification in 3D ABUS based on Laplace-Beltrami spectra and dual path CNN. Expert Systems with Applications 299:129973, 2026. doi:10.1016/j.eswa.2025.129973
8. S. Yu, X. Liang, S. Zhao, Y. Xie, Q. Sun. Three-dimensional automated breast ultrasound (ABUS) tumor classification using a 2D-input network: soft voting or hard voting? Applied Sciences 14(24):11611, 2024. doi:10.3390/app142411611
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Citation

A paper is in preparation. Until then, please cite this repository:

@misc{naderiparizi_abus_classification,
  author       = {Ali Naderiparizi and Sepideh Barekatrezaei and Ehsan Kozegar and Mohsen Soryani},
  title        = {Classification of Breast Cancer Lesions in 3D Automated Breast Ultrasound},
  year         = {2026},
  howpublished = {\url{https://github.com/mralinp/abus-classification}}
}

License and contact

Code: MIT License. The TDSC-ABUS data is subject to the challenge’s data use agreement. Questions and collaboration: [email protected]