Anatomical Segmentation Difficulty (ASD)

• Anatomical Segmentation Difficulty (ASD) is a concept describing the challenges in segmenting anatomies caused by small scales, complex topology, ambiguous boundaries, and variability.
• Real-world manifestations include errors on tiny, tortuous, or artifact-laden structures in applications like precision surgery, radiotherapy, and shape modeling.
• Adaptive strategies—such as anatomical-aware learning, artifact decomposition, and balanced supervision—are developed to mitigate these segmentation challenges.

Anatomical Segmentation Difficulty (ASD) denotes the problem of characterizing why some anatomical segmentation tasks are systematically harder than others and of designing models and evaluation schemes that remain reliable under those hard conditions. In the recent literature, ASD is usually not introduced as a single universal scalar; rather, it is inferred from recurring empirical regularities. Segmentation becomes more difficult when the target anatomy is small, thin, tortuous, topologically constrained, spatially variable across patients, weakly separable from adjacent classes or background, corrupted by artifacts or modality shift, or available only under scarce, heterogeneous, or partial supervision. The concept therefore spans voxel-wise overlap, surface accuracy, topology preservation, feature-space separability, and downstream anatomical usability, especially in tasks such as precision surgery, radiotherapy planning, and statistical shape modeling (Wang et al., 10 Aug 2025, You et al., 2023, Khan et al., 2024).

1. Conceptual status and terminological scope

Across the cited works, ASD is mostly an implicit construct rather than a standardized benchmark quantity. "ASM-UNet" explicitly studies why fine-grained segmentation is harder than coarse-grained segmentation, but it "does not provide a formal taxonomy or mathematical definition of 'segmentation difficulty' as a general construct" (Wang et al., 10 Aug 2025). ACTION++ likewise does not explicitly define ASD as a named concept, but it gives a feature-space and long-tail account of why minority anatomy, boundary regions, and rare objects are difficult to segment (You et al., 2023). The statistical shape modeling study also does not define a formal difficulty score, yet it shows that difficulty must be understood through whether segmentations preserve meaningful modes of anatomical variation under low annotation budgets (Khan et al., 2024).

A more explicit use of the acronym appears in active learning for volumetric segmentation. There, ASD is defined as a query score that "evaluate[s] the difficulty in segmentation of anatomical structures by measuring predictive entropy from foreground regions adaptively" (Yang et al., 13 Sep 2025). This is a method-specific operationalization rather than a general consensus definition.

The acronym is also overloaded in adjacent literatures. In A$^3$DSegNet and ACTION++, ASD denotes Average Symmetric Surface Distance, an evaluation metric rather than a difficulty construct (Lyu et al., 2020, You et al., 2023). In a graph-based rs-fMRI classification study, ASD refers to Autism Spectrum Disorder, and the relevant issue is anatomical versus functional parcellation rather than anatomical segmentation in the usual mask-prediction sense (Madani et al., 3 Mar 2026). This terminological overlap makes explicit disambiguation necessary in technical writing.

2. Primary determinants of difficulty

The most recurrent anatomical source of difficulty is scale. ASM-UNet states that fine-grained anatomical segmentation is harder because the target structures are often "small-scale," "structurally intricate," and subject to "frequent individual variations." In the biliary system, the common hepatic duct is said to "typically have a diameter of less than 10 mm," while the hard classes CD and RHD are described as "extremely short and thin," "tiny," and in the case of RHD, sometimes absent under a variant anatomy (Wang et al., 10 Aug 2025). A similar size effect appears in fetal ultrasound, where the ribs are described as "small and elongated," and in chest X-ray landmarking, where the clavicles are identified as the most challenging structure (Li et al., 10 Jun 2025, Gaggion et al., 2021).

Topology and continuity constitute a second major determinant. In biliary fine-grained segmentation, the ducts are "thin, tortuous, and anatomically continuous structures" whose identity depends on continuity and branching relationships rather than on isolated voxel classification (Wang et al., 10 Aug 2025). In left atrium shape modeling, pulmonary veins are described as "a small protuberance," and their variation is systematically missed by several semi-supervised methods, indicating that localized protrusions and fine-scale geometry are especially fragile under low-label conditions (Khan et al., 2024). In mandibular landmarking, the paper separates sparsely spaced landmarks from closely spaced landmarks because the latter become geometrically ambiguous in geodesic space and require a separate LSTM-based treatment (Torosdagli et al., 2018).

Boundary ambiguity and inter-class similarity are repeatedly identified as hard-case mechanisms. ASM-UNet attributes the performance gap between coarse and fine segmentation to "the small size, ambiguous boundaries, and high inter-class similarity among the fine-grained categories" (Wang et al., 10 Aug 2025). In fetal A4C ultrasound, "ultrasound artifacts," "speckle noise," "complex background interference," "boundary ambiguity," and variation "across different gestational stages" all degrade precise delineation (Li et al., 10 Jun 2025). In multimodal brain-barrier segmentation, accuracy becomes challenging "due to the visual and anatomical differences between different modalities," namely CT, T1ce MRI, and T2-FLAIR MRI (Ning et al., 2020).

Artifact burden and domain shift create another class of difficulty. Atlas-aware ConvNet work frames robust segmentation as a challenge caused by "artifacts, pathologies, and differences in scanning setups/scanners," together with the small size of medical datasets (Liang et al., 2021). A$^3$DSegNet makes the problem concrete for intraoperative CBCT, where vertebra segmentation is hard because of "pronounced noise," "poor tissue contrast," and "metal artifacts," to the point that delineation is described as "even manually, a demanding task" (Lyu et al., 2020). The mandible CBCT study similarly emphasizes "much greater noise and artifact presence" than spiral CT, including truncation, beam hardening, low resolution, braces, implants, plates, and screws (Torosdagli et al., 2018). The unsupervised anatomical-prior model generalizes this difficulty to settings with no paired labels, low contrast in some regions, and cross-study or cross-modality transfer to T2-FLAIR (Dalca et al., 2019).

A distinct but equally important source is supervision structure. ACTION++ argues that medical segmentation often follows "long-tail distributions with heavy class imbalance," causing difficulty for "minority classes (i.e., boundary regions or rare objects)," especially under 5% or 10% label regimes (You et al., 2023). Multi-center chest X-ray segmentation with heterogeneous labels adds another supervision-driven failure mode: conventional pixel models exhibit "domain memorization issues and conflicting labels," so the same anatomy may be treated as foreground in one center and effectively absent in another (Gaggion et al., 2022). This suggests that ASD is not only a property of anatomy and imaging, but also of how supervision is distributed across classes, domains, and tasks.

3. Operationalizations, proxies, and anatomy-aware evaluation

Because a universal ASD scalar is absent, the literature relies on proxies. ACTION++ makes this explicit by proposing several measurable indicators. Difficult anatomy corresponds to low class frequency or pixel prevalence, poor latent-space separation, high embedding overlap, weak alignment under augmentation, boundary sensitivity, and poor label efficiency. The paper defines class divergence as

$$D = \max_{c \neq c'} \overline{\phi}_c \cdot \overline{\phi}_{c'},$$

and uses a positive-alignment quantity

$$A = \sqrt{ \mathbb{E}_{\mathbf{x},\tilde{\mathbf{x}}} \mathbb{E}_{c \in [K]} \mathbb{E}_{\omega_p \in Cla_c} \left[ \| f(\omega_p; \mathbf{x}) - f(\omega_p; \tilde{\mathbf{x}})\|^2 \right] }.$$

In that framing, difficult anatomy is anatomy whose features are unstable under augmentation and insufficiently separated from competing classes (You et al., 2023).

A different operationalization appears in anatomy-aware evaluation. "Anatomy-Aware Measurement of Segmentation Accuracy" argues that standard Dice and Jaccard ignore the internal anatomical relevance of different zones. It introduces a "master gold" with expert-defined internal zones and proposes combined scores such as

$$A^* = A^2 + (1-A) \times \underset{i}{\min}~ A_{Z_i} \quad \textrm{if}\quad A\geq A_{\min},$$

together with anatomy-aware Dice and Jaccard variants:

$$D^{*}_{1} = D^2+(1-D)\times \underset{i}{\min}~ D_{Z_i},$$

$$J^{*}_{1} = J^2+(1-J)\times \underset{i}{\min}~ J_{Z_i}.$$

This formulation does not measure difficulty directly, but it localizes where difficulty concentrates and shows that clinically important zones can reorder rankings that global overlap would treat as equivalent (Tizhoosh et al., 2016).

The most explicit difficulty score appears in active sample selection for foundation-model adaptation. For an unlabeled target volume $x_u$, the network outputs $$\boldsymbol{P} \in \mathbb{R}^{C \times H \times W \times D}$$, with background map $\boldsymbol{P}_0$. The method scales the background channel by

$^3$0

defines a foreground mask

$^3$1

and then computes foreground-masked entropy

$^3$2

Here ASD is a volume-level query score derived from voxel-level uncertainty in adaptively estimated foreground regions, explicitly avoiding domination by background voxels (Yang et al., 13 Sep 2025).

Downstream-shape work suggests an additional family of proxies. When the end task is statistical shape modeling, difficulty is better reflected by whether segmentations preserve compactness, generalization, specificity, Grassmannian subspace structure, and meaningful dominant modes of variation. The key empirical observation is that some methods produce "noisy segmentation," which is "very unfavorable" for SSM because the first mode of variation can capture prediction noise rather than anatomy (Khan et al., 2024). This suggests that ASD cannot be reduced to overlap alone when the downstream objective is correspondence-based shape analysis.

4. Difficulty-aware modeling strategies

One major response is to make scanning or context aggregation adaptive to anatomy. ASM-UNet is a 3D U-Net-like encoder-decoder with six encoder blocks, six decoder blocks, and adaptive scanning Mamba blocks. Its central claim is that fixed manually defined scanning orders limit adaptability to inter-individual fine-grained anatomical variation, so it introduces adaptive scan scores that combine "group-level commonalities and individual-level variations" to guide scanning order dynamically (Wang et al., 10 Aug 2025). The architectural motivation is directly difficulty-driven: long-range dependency modeling is inserted where spatial dimensions are large and global context is hardest to capture efficiently.

A second response treats ASD as a representation-geometry problem. ACTION++ adds supervised adaptive anatomical contrastive learning, precomputed uniformly distributed class centers on the unit sphere, online adaptive center allocation, and an anatomical-aware temperature scheduler

$^3$3

with default $^3$4 and $^3$5 (You et al., 2023). The method is explicitly designed for difficult anatomies that appear as minority, boundary, or small-region classes under scarce labels. Its core idea is that hard anatomy fails because the learned embedding geometry is biased toward dominant classes, so balanced target geometry and dynamic temperature are used to preserve margins for tails.

A third strategy injects explicit anatomical priors. The unsupervised structural brain MRI model learns a deep prior over segmentation maps,

$^3$6

with a decoder that outputs voxelwise label probabilities $^3$7, allowing segmentation when no paired image–segmentation data are available for the target modality (Dalca et al., 2019). Atlas-aware ConvNet augments a backbone UNet, VNet, or HCNet with a Constraint Adoption Module that fuses appearance, prior, and smoothness terms inside a locally connected CRF, thereby reinforcing anatomical consistency under artifacts, pathology, and scanner variation (Liang et al., 2021). HybridGNet uses graph convolutional decoding so that outputs lie on a learned manifold of anatomically plausible shapes, which improves robustness to occlusion and yields more plausible landmark-based segmentations (Gaggion et al., 2021). In multi-center heterogeneous-label training, the same landmark/graph formulation reduces domain memorization and naturally yields more domain-invariant representations than pixel-level baselines (Gaggion et al., 2022).

A fourth strategy targets modality corruption and artifact entanglement directly. A$^3$8DSegNet decomposes CBCT into content and artifact latents, learns unpaired CT/CBCT translation together with vertebra segmentation, and introduces anatomy-aware de-normalization so that synthesis does not "wash away the anatomical information" (Lyu et al., 2020). For fetal ultrasound, DCD adds Dense ASPP and CBAM to DeepLabv3+ in order to improve multi-scale detail preservation and feature emphasis under artifacts, speckle, and ambiguous boundaries (Li et al., 10 Jun 2025). In mandible CBCT, the pipeline combines a modified Fully Convolutional DenseNet for segmentation, geodesic-space landmark learning for sparsely spaced landmarks, and an LSTM for closely spaced landmarks that are not reliably separable with standard detection (Torosdagli et al., 2018). In multimodal brain-barrier segmentation, a residual U-shaped model uses the Tversky loss to address "class imbalance between different foreground and the background classes," followed by ensembling to remove outliers (Ning et al., 2020).

5. Empirical manifestations across anatomies and tasks

The empirical literature shows that difficulty is anatomy-specific rather than uniform. In biliary fine-grained segmentation, CD and RHD are explicitly designated hard classes, and several methods produce Dice scores of zero on tiny-volume categories; by contrast, the gallbladder is easier and is said to benefit from larger volume (Wang et al., 10 Aug 2025). In fetal A4C ultrasound, DCD reports IoU values of 55.71 for IS and 55.98 for RiB, whereas larger or broader structures such as RA (88.48), RL (87.57), and LL (87.75) are much easier. The same paper explicitly attributes rib difficulty to a "small and elongated" structure and notes that several baselines yield discontinuous rib segmentations (Li et al., 10 Jun 2025). These results support a stable pattern: broad, homogeneous, high-area structures are easier than thin septa, walls, ducts, protrusions, or elongated bones.

Low-label studies further show that difficult anatomy benefits disproportionately from targeted methods. ACTION++ reports larger gains on challenging ACDC structures such as RV and Myo than on LV, and the appendices state that the method improves predictions "especially for small regions" and yields "sharper and accurate object boundaries" (You et al., 2023). In shape-model benchmarking, the left atrium is harder than the femur because pulmonary vein variation is not preserved well, and several semi-supervised methods yield "non-smooth surfaces" whose first mode of variation reflects prediction noise rather than anatomically meaningful variation (Khan et al., 2024). This is a stronger claim than ordinary overlap failure: it shows that some errors are geometrically and statistically toxic even when scalar segmentation scores appear acceptable.

Heterogeneous-label multi-center learning reveals a different manifestation of ASD. When organ labels are removed from one chest X-ray dataset during training, naive UNet and nnUNet collapse on the missing structure, with Dice values near zero in controlled experiments, whereas HybridGNet still recovers the anatomy with substantial overlap (Gaggion et al., 2022). The difficulty here is neither small structure size nor imaging artifact alone, but the interaction between domain identity and incomplete supervision. This extends ASD from anatomy/image properties to label semantics and center-specific annotation policy.

Parcellation studies suggest that analogous difficulty can arise at the region-definition stage. In rs-fMRI graph classification, the substitution of functional MSDL parcels for anatomical AAL parcels yields a 10.7-point accuracy gain, and the authors interpret this as evidence that rigid anatomical boundaries are poorly aligned with "heterogeneous and idiosyncratic connectivity patterns" in ASD neuropathology (Madani et al., 3 Mar 2026). A plausible implication is that, in some settings, segmentation difficulty begins upstream with the choice of anatomical partition itself.

6. Open problems, ambiguities, and synthesis

The main unresolved issue is the absence of a unified definition. Most papers treat ASD implicitly and task-specifically: fine-grained biliary segmentation associates difficulty with tiny volumes, variants, and ambiguous boundaries; long-tail semi-supervised learning ties difficulty to minority classes and poor feature geometry; shape-model studies tie it to noisy surfaces and corrupted modes of variation; active learning defines it as foreground-masked predictive entropy (Wang et al., 10 Aug 2025, You et al., 2023, Khan et al., 2024, Yang et al., 13 Sep 2025). These views are compatible, but they are not yet collapsed into a single formal theory.

A second unresolved issue is metric mismatch. Global overlap can conceal failures in clinically important subregions, leading anatomy-aware scores to lower performance estimates and even reorder user rankings (Tizhoosh et al., 2016). Surface distance can capture boundary failure but not necessarily mode-of-variation corruption. Dice may correlate only partially with SSM quality (Khan et al., 2024). A plausible implication is that ASD is inherently multi-objective: a case can be easy for voxel overlap yet hard for topology, anatomically salient zones, feature separability, or downstream shape analysis.

A third issue concerns the trade-off between robustness and fidelity. Atlas and shape priors improve robustness to artifacts, pathology, scanner variation, occlusion, and label heterogeneity (Liang et al., 2021, Gaggion et al., 2021, Gaggion et al., 2022). At the same time, some studies show that overly rigid assumptions can erase difficult local details. A$^3$9DSegNet reports that an artifact-consistency term can mistakenly encode "sharp edges" as metal artifacts, causing smoothed vertebra boundaries (Lyu et al., 2020). The SSM benchmark shows that smoothness alone is insufficient if pulmonary vein variation is lost (Khan et al., 2024). This suggests that ASD mitigation requires priors strong enough to stabilize anatomy but not so strong that they suppress rare, thin, or variant structures.

Taken together, the literature supports a broad but coherent interpretation. Anatomical Segmentation Difficulty is best understood as the composite hardness induced by anatomical scale, topology, inter-subject variation, boundary ambiguity, artifact burden, domain shift, supervision sparsity, label heterogeneity, and the anatomical plausibility requirements of the downstream task. Current research has produced several partial operationalizations and a large repertoire of difficulty-aware modeling strategies, but no single accepted ASD index. The field therefore treats ASD less as a settled metric than as a unifying explanatory framework for why anatomies such as biliary ducts, pulmonary veins, fetal septa and ribs, clavicles, mandibular landmark clusters, and vertebrae in artifact-laden CBCT remain persistently challenging across imaging regimes and learning paradigms.