1 Introduction↩︎

Thyroid nodules affect a large proportion of the global population, and ultrasound (US) imaging is the primary modality for their evaluation [1]. Accurate segmentation of nodule regions is a prerequisite for downstream tasks such as risk stratification and biopsy guidance. Over the past decade, deep learning (DL) has become the de facto standard for medical image segmentation [2]. Architectures such as TransFuse [3], SwinE-Net [4], and our prior DeepLabv3+-based method [5] achieve Dice scores above 0.80 on TN3K. However, these methods share fundamental limitations:

• Opacity: Millions of learnt parameters form an opaque mapping that cannot be audited by clinicians.

• Resource intensity: Training requires GPU hardware and hours of backpropagation; CPU inference is prohibitively slow.

• Data hunger: Performance degrades sharply on small datasets without pre-training on large external corpora.

The Green Learning (GL) paradigm, introduced by Kuo et al. [6], offers an interpretable alternative. GL replaces gradient-based optimisation with sequential, closed-form subspace learning (Successive Subspace Learning, SSL), producing compact models with mathematically transparent feature representations. GL has demonstrated strong results in image classification via PixelHop [7] and in volumetric medical classification via VoxelHop [8], yet no prior work has applied GL to pixel-level segmentation of thyroid US images.

We present MedSaab-US as a first exploratory application of GL to this task. Our contributions are:

1. The first application of the Green Learning / SSL paradigm to thyroid nodule segmentation in ultrasound images.

2. A multi-scale DWT + Saab feature extraction scheme that captures nodule texture at three spatial scales without any backpropagation.

3. A reproducible non-DL baseline on TN3K, including comparisons against traditional non-DL methods.

4. An ablation study separating the effects of LAG feature selection and training-set size, and an honest analysis of the performance gap and its acoustic origins.

2 Related Work↩︎

2.1 Deep Learning for Thyroid Nodule Segmentation↩︎

Early DL approaches adopted encoder-decoder architectures [2]. Recent methods targeting TN3K include TRFE+ [9], which incorporates thyroid region-focused enhancement; SwinE-Net [4], a hybrid Swin Transformer / CNN model achieving Dice \(\approx 0.83\); and MADGNet [10], a multi-scale dual-guidance network. Our prior work [5] combined an ECB encoder, CMM module, and SSEM boundary supervision within a DeepLabv3+ framework. While these methods achieve high accuracy, they are computationally intensive and not suitable for CPU-only edge devices.

2.2 Green Learning and the Saab Transform↩︎

The Saab transform [11] replaces learnt convolution filters with principal components computed analytically on local patches. PixelHop [7] demonstrated that multi-hop Saab features suffice for image classification. VoxelHop [8] extended GL to 3-D MRI classification, and RadHop [12] achieved AUC \(>0.90\) on prostate US lesion classification. Critically, all prior GL medical imaging work addresses classification; pixel-level segmentation via GL remains unexplored, motivating MedSaab-US.

2.3 Wavelet Features in Medical Imaging↩︎

Discrete Wavelet Transform (DWT) decomposes images into approximation and detail subbands encoding low-frequency shape and high-frequency boundary information [13]. Coupling DWT with the SSL / Saab framework for US nodule segmentation has not been previously investigated.

3 Proposed Method: MedSaab-US↩︎

An overview of the four-stage MedSaab-US pipeline is illustrated in Fig. 1.

3.1 Stage 1: Multi-Level DWT Decomposition↩︎

Each grayscale US image \(\mathbf{I} \in \mathbb{R}^{H \times W}\) is decomposed using a 2-level Daubechies-4 (db4) wavelet: \[\mathcal{W}(\mathbf{I}) = \{LL_2, LH_2, HL_2, HH_2, LH_1, HL_1, HH_1\}, \label{eq:dwt}\tag{1}\] yielding 7 subbands. The \(LL\) subband captures low-frequency structural information, while the \(LH\), \(HL\), and \(HH\) subbands encode horizontal, vertical, and diagonal high-frequency boundary responses, respectively. Each subband is upsampled to \(H \times W\) via bilinear interpolation and normalised per-subband to zero mean and unit variance.

3.2 Stage 2: Multi-Scale Channel-Wise Saab Transform↩︎

For each subband \(\mathbf{S}_k\) and patch size \(p \in \{5, 11, 21\}\), we extract overlapping \(p \times p\) patches centred at every pixel. The Saab transform [11] is applied independently per (subband, scale) pair: \[\mathbf{F}_{k,p} = \text{PCA}_{k,p}\!\left(\mathbf{x} - \boldsymbol{\mu}_{k,p}\right), \label{eq:saab}\tag{2}\] where \(\mathbf{x} \in \mathbb{R}^{p^2}\) is a flattened patch, \(\boldsymbol{\mu}_{k,p}\) is the empirical mean over 40,000 randomly sampled patches from 400 training images, and \(\text{PCA}_{k,p}\) retains the top 8 principal components. All Saab filter parameters are determined analytically in a single pass through the training data — no iterative optimisation is required at this stage. The three patch scales capture local texture (\(p=5\)), mid-range structural context (\(p=11\)), and global neighbourhood shape (\(p=21\)), yielding \(7 \times 3 \times 8 = 168\) features per pixel.

3.3 Stage 3: Positional Encoding and LAG Feature Selection↩︎

Three normalised spatial coordinates \([\tilde{r}, \tilde{c}, d_c]\) are appended to each pixel’s feature vector, where \(\tilde{r} = r/H\), \(\tilde{c} = c/W\), and \(d_c\) is the normalised Euclidean distance from the image centre. These encode the spatial prior that thyroid nodules preferentially appear in the inferior-central region of TN3K images. We note, however, that this fixed spatial prior is dataset-specific; it may not generalise to different ultrasound acquisition protocols, probe positions, or field-of-view crops, and should be treated with caution in cross-institutional deployment. Protocol-agnostic spatial priors represent an important direction for future work.

The resulting 171-dimensional feature vector is pruned using Label-Assisted Greedy (LAG) selection [7], which ranks features by mutual information with the binary label and retains the top 60. LAG selection is a purely statistical, non-iterative operation.

3.4 Stage 4: XGBoost Pixel-Wise Classification↩︎

The 60-dimensional feature vector for each pixel is classified by an XGBoost gradient-boosted tree ensemble [14] (600 estimators, max depth 7, learning rate 0.05). Training uses balanced class sampling (400 foreground + 400 background pixels per image). We emphasise that XGBoost employs iterative greedy tree construction and involves tuned hyperparameters; it is backpropagation-free but is not closed-form in the sense that the Saab and LAG stages are. The pipeline as a whole eliminates backpropagation and gradient computation, while individual stages differ in their mathematical character: Saab transforms are analytically determined, LAG selection is statistical, and XGBoost is iterative and non-gradient. The classification threshold is calibrated on a held-out validation split (last 150 training images) by maximising pixel-level Dice.

4 Experiments↩︎

4.1 Dataset and Implementation Details↩︎

We evaluate on TN3K [1], comprising 3,493 thyroid US images (2,879 train / 614 test) with pixel-level nodule masks. Images are resized to \(256 \times 256\) pixels. All experiments run on CPU only (Intel Xeon @ 2.0 GHz, 2 cores, Kaggle CPU-only session; no GPU). Code is implemented in Python using PyWavelets, scikit-learn, and XGBoost.

4.2 Evaluation Metrics↩︎

We report mean Dice similarity coefficient (DSC), Intersection over Union (IoU), Precision, Recall, and Specificity over the 614 test images.

4.3 Comparison with Existing Methods↩︎

Table 1 compares MedSaab-US to DL methods and to two traditional non-DL baselines: (i) Otsu thresholding with morphological post-processing (Otsu+Morph) and (ii) a Random Forest classifier trained on Haralick texture features extracted from \(7\times7\) patches (RF+Haralick). Both baselines run on the same CPU environment without GPU resources.

MedSaab-US achieves Dice 0.4784 without any neural network or GPU, which substantially exceeds both non-DL baselines (\(+\)​0.127 over RF+Haralick). This confirms that multi-scale SSL features provide a stronger representation than hand-crafted texture descriptors for thyroid US segmentation. However, the 0.37-point Dice gap relative to the best DL method reflects fundamental limitations of local, patch-based approaches, as discussed in Section 4.5. We present MedSaab-US strictly as an exploratory baseline that establishes the achievable frontier of non-DL methods on TN3K, not as a replacement for DL in accuracy-critical clinical settings.

Among the 614 test images, MedSaab-US achieves Dice \(>0.70\) on 104 cases (16.9%), reaching a maximum Dice of 0.9184 — demonstrating that precise segmentation is attainable for cases with strong acoustic contrast.

4.4 Ablation Study↩︎

Table 2 presents an ablation study isolating the contribution of each pipeline component, including a split between the effect of LAG feature selection and increased training-set size (1000 vs. images).

Multi-scale patch extraction (row 3 vs.row 2) yields the largest single gain (\(+\)​0.172 Dice), confirming that contextual information at the 11- and 21-pixel scales is essential. Comparing rows 4 and 5 shows that LAG selection provides a +0.006 Dice improvement independent of data volume, primarily by reducing feature redundancy. Increasing training data from 1000 to 2000 images (row 5 to row 6) contributes a further +0.008 Dice, confirming that both factors contribute incrementally and independently.

4.5 Analysis: The Performance Gap and Its Origin↩︎

The 0.37-Dice gap between MedSaab-US and the best DL method reflects two root causes.

Isoechoic nodule prevalence. XGBoost feature importance analysis shows that \(LL_2\) Saab components dominate (PC5, PC3, PC1 are the three highest-ranked features), with \(HH\) boundary features ranked lower. This is consistent with the acoustic properties of TN3K: many nodules are isoechoic — their intensity is similar to surrounding tissue — yielding weak high-frequency wavelet responses that confound boundary detection.

Global context limitation. DL encoders capture long-range spatial dependencies via stacked convolutions and attention. A patch-based XGBoost classifier with a maximum receptive field of \(21 \times 21\) pixels cannot access image-level context (e.g., thyroid gland boundary, trachea position), which is a fundamental limitation of local non-DL approaches.

Dice score distribution. Per-image Dice scores show a bimodal pattern: a peak near 0.0–0.1 (isoechoic, difficult cases) and a peak near 0.5–0.6 (hypoechoic, tractable cases). This suggests that a nodule echotexture classifier could route difficult images to a DL model and tractable images to MedSaab-US, forming a hybrid interpretable-DL system.

5 Discussion and Conclusion↩︎

We presented MedSaab-US, the first exploratory application of the Green Learning paradigm to pixel-level thyroid nodule segmentation in ultrasound images. By combining 2-level DWT with multi-scale Saab PCA transforms and LAG feature selection, MedSaab-US achieves Dice 0.4784 on TN3K — substantially above traditional non-DL baselines (RF+Haralick: 0.3518, Otsu+Morph: 0.2341) — without any backpropagation, neural network weights, or GPU resources.

The ablation study reveals that multi-scale feature extraction is the dominant factor: expanding from single-scale (Dice 0.26) to three scales (Dice 0.45) yields a gain of \(+\)​0.19 Dice, demonstrating that US nodule texture is intrinsically multi-scale. LAG selection and increased training data each contribute further, independently verifiable gains.

We explicitly frame this result as an exploratory baseline rather than a deployment-ready system. The 0.37-point gap relative to the best DL method reflects the prevalence of isoechoic nodules and the inherent locality of patch-based features. Additionally, the fixed spatial prior used in Stage 3 is specific to TN3K’s acquisition protocol and may not generalise to different probe positions, field-of-view settings, or institutions; external validation is an important requirement before any real-world use.

Two directions for future work emerge from this analysis: (i) GL-compatible global feature aggregation (e.g., superpixel-level Saab transforms) to address the locality limitation; and (ii) a hybrid pipeline routing tractable hypoechoic cases to MedSaab-US and difficult isoechoic cases to a lightweight DL model, preserving interpretability where the non-DL method is reliable.

In summary, MedSaab-US demonstrates that backpropagation-free segmentation of thyroid nodules is feasible on CPU-only hardware, establishes a reproducible non-DL reference point for TN3K, and characterises both the potential and the current limits of Green Learning in medical image segmentation.

References↩︎