Anatomical Normality Modeling

• Anatomical normality modeling is a framework that defines typical anatomical structure by learning a reference distribution from healthy subjects.
• It employs methods like statistical shape models, implicit neural representations, and subject-specific predictors to quantify deviations.
• The approach supports clinical tasks such as anomaly detection, surgical planning, and tracking neurodegenerative progression while addressing challenges like registration accuracy.

Anatomical normality modeling denotes a family of methods that learn a reference distribution, manifold, or trajectory of anatomically typical structure and then quantify deviation from that reference. In normative modeling, one first defines a reference distribution of normal anatomy or morphology, typically from cognitively normal controls, and then quantifies how much an individual deviates from that distribution; when trained only on healthy subjects, a model can instead provide a subject-specific healthy anatomical trajectory against which observed follow-up anatomy is compared (Zhang et al., 2024, Dalca et al., 2020). Across current work, the modeled object may be a corresponded surface, a morphometric parameter vector, a cortical feature map on a sphere, a deformation field, a whole-body pose-normalized shape space, or a group-level anatomical connectivity architecture (Boutillon et al., 2022, Shetty et al., 2023, Wang et al., 2023).

1. Conceptual foundations

At its core, anatomical normality modeling is a deviation-from-reference problem. In the shape-normality setting, normality means consistency with the learned distribution of anatomical shape variation around a population mean shape, abnormality means deviation from that learned distribution, and severity quantification is a continuous measure of degree of deviation rather than only binary normal/abnormal classification (Tao et al., 2020). This framing is especially attractive when pathological samples are scarce, heterogeneous, or inconsistently labeled, because several methods are explicitly designed to learn only from normal samples and zero knowledge about the pathology (Tao et al., 2020).

The reference itself may be population-level or subject-conditional. A population-level model summarizes typical variation across a cohort; a subject-conditional model estimates what would be normal for a specific anatomy, age, sex, or baseline scan. This distinction is technically important. A population Gaussian in shape space, a conditional diffusion model on the cortical surface, and a baseline-conditioned longitudinal predictor all instantiate “normality,” but they do so with different objects: a density over corresponded shapes, a sample-based conditional normal distribution, or a personalized healthy trajectory (Zhang et al., 2024, Dalca et al., 2020).

2. Representations of anatomical normality

The dominant classical representation is the statistical shape model built from dense correspondences. Point distribution models represent the anatomical surface via a dense set of correspondences, with local coordinates describing the geometrical features of each individual anatomical surface and world coordinates representing the population-level statistical shape information after removing global alignment differences across samples in the given cohort; a joint deep model can learn these two coordinate spaces directly from volumetric images, with world correspondences used for shape analysis and local correspondences used for anatomy segmentation (Tao et al., 2022).

A parallel line of work makes the latent space anatomically interpretable rather than purely geometric. In the anatomically parameterized statistical shape model, a standard Gaussian SSM with coefficients $\alpha$ is re-expressed through clinically meaningful morphometric parameters $\beta$ via a learned linear mapping $\beta = Q\alpha$, leading to $ANAT_{SSM} = \mu + P D Q^{+}\beta$ and an induced parameter distribution $\beta \sim \mathcal{N}(0,QQ^T)$ (Boutillon et al., 2022). This removes the limited clinical interpretability of standard SSMs and turns normal variation into a model over named anatomical measures such as neck-shaft angle, glenoid version, or scapula length (Boutillon et al., 2022).

Recent representations relax fixed-topology assumptions. Implicit neural representations model anatomy as the zero level set of a signed distance function and naturally support topology changes, which is especially useful when anatomically plausible normal variation includes connected and disconnected configurations, as in the thyroid with and without isthmus agenesis (Wilde et al., 4 Apr 2025). Semi-implicit medial representations instead approximate the medial axis transform through learned unsigned distance fields and reconstruct smooth watertight surfaces via convolution surfaces; this is topology-aware and simulation-ready, but it is an enabling representation rather than a probabilistic normality model by itself (Pepe et al., 2024).

A different representation treats normality as spatial organization. BodyGPS maps query locations to atlas coordinates via regression, directly producing absolute, interpretable coordinates in a canonical atlas frame; this makes it natural to model normal anatomical layout as coherent subject-to-atlas correspondence rather than as texture or appearance alone (Yerebakan et al., 12 May 2025).

3. Statistical and generative formulations

One formulation models normal anatomy explicitly as a Gaussian population. The “Shape Normality Metric” work represents shapes by landmarks automatically inferred from the data and models the normal group by a multivariate Gaussian distribution, thereby turning abnormality into deviation from a learned normal shape distribution (Tao et al., 2020). In linear statistical shape models, compactness, specificity, and generalization remain central because the learned normal manifold is only useful if its samples remain anatomically plausible and its latent coordinates preserve interpretable variation (Boutillon et al., 2022).

A more recent formulation is conditional and sample-based rather than closed-form. The anatomy-guided surface diffusion model for Alzheimer’s disease learns a conditional normal distribution of cortical thickness and shape index on the spherical cortical surface, conditioned on age, gender, and a gyral/sulcal segmentation mask. For each test subject, it generates $N$ normal samples and defines an ROI-level abnormal score

$$Z_i = \frac{x_i-mean([x_{(i,1)}...x_{(i,N)}])}{std_j([x_{(i,1)}...x_{(i,N)}])},$$

so the normative signal is a subject-specific z-score-like deviation from a generated conditional reference set rather than a closed-form likelihood (Zhang et al., 2024).

Counterfactual healthy reconstruction is another major formulation. UNA reconstructs the healthy anatomical content underlying an observed brain image even when pathology corrupts appearance and locally destroys or obscures tissue, and then uses the voxelwise absolute difference $|I-\widetilde{I}|$ as an anomaly map (Liu et al., 23 Jan 2025). This is not a conventional latent density over normal anatomy; rather, it is a subject-conditional healthy reconstructor trained on synthetic and real data so that pathology becomes measurable as residual deviation from a reconstructed healthy counterpart (Liu et al., 23 Jan 2025).

4. Subject-specific and longitudinal normal references

Subject-specific normality models treat the expected anatomy of an individual as a function of baseline state and covariates. In predictive modeling of anatomy with genetic and clinical data, longitudinal change is written as

$$\Delta y_t = \Delta x_t \bar{\beta} + \Delta x_t\big(h_G(g)+h_C(c)+h_I(f_b)\big) + \epsilon,$$

with Gaussian-process priors on the modality-specific functions $h_G$, $\beta$0, and $\beta$1. When trained only on healthy subjects, the model yields a subject-specific healthy anatomical trajectory, and deviation from that predicted healthy follow-up can be visualized as a spatial abnormality map (Dalca et al., 2020).

Longitudinal mesh models make the same idea explicit on corresponded surfaces. TransforMesh represents the left hippocampus as a sequence of 3D meshes, encodes each visit with SpiralNet++, models temporal dependence with a bidirectional transformer encoder, and predicts a deformation field $\beta$2 relative to baseline so that $\beta$3 (Sarasua et al., 2021). This turns normality into expected temporal evolution of subject-specific anatomy rather than only closeness to a static atlas. The anomaly visualization experiment then treats vertex-wise absolute reconstruction error in subjects converting from MCI to dementia as a candidate structural abnormality signal (Sarasua et al., 2021).

This longitudinal perspective changes the interpretation of “normal.” A shape may be normal cross-sectionally yet abnormal dynamically if its future deformation is inconsistent with the learned trajectory model. That distinction is increasingly important in neurodegeneration, where individualized progression often matters more than a single time-point classification (Dalca et al., 2020, Sarasua et al., 2021).

5. Correspondence, atlas space, and anatomy-aware structure

Normality models are only as reliable as their correspondence and alignment machinery. On cortical surfaces, one of the central difficulties is residual anatomical mismatch after registration: gyri and sulci do not match perfectly because cortical folding patterns differ considerably across individuals. Anatomy-guided conditioning on a subject’s own gyral/sulcal segmentation therefore serves not merely as auxiliary input, but as a mechanism to generate normal references whose morphology is consistent with that subject’s anatomy and to reduce anatomical variance in the generated reference set (Zhang et al., 2024).

For point-based statistical shape modeling, correspondence quality is itself a methodological bottleneck. Adaptive particle-based shape modeling introduces a neighborhood correspondence loss and a geodesic correspondence algorithm so that particles can move toward locally informative geometry while maintaining consistent particle configurations across a cohort (Xu et al., 10 Jul 2025). This is directly relevant to anatomical normality modeling because poor correspondence inflates variance, distorts mean shapes, and confounds biological variation with registration error; better adaptive correspondence yields cleaner normal manifolds and more meaningful downstream statistics (Xu et al., 10 Jul 2025).

At a larger spatial scale, atlas-space models encode normality as coherent anatomical positioning. BodyGPS learns a subject-to-atlas spatial correspondence function by mapping any query point to reference atlas coordinates, which can support matching, registration, segmentation, and abnormality detection via comparison with normal anatomy atlases (Yerebakan et al., 12 May 2025). For network anatomy, the attributes-informed brain connectivity model estimates group-level structural connectivity in a latent space while jointly incorporating node anatomy, yielding an interpretable latent representation of group-level connectivity and posterior uncertainty over the estimated architecture (Wang et al., 2023). This extends anatomical normality modeling beyond surfaces and morphometry to the organization of white-matter-supported brain networks.

6. Applications, misconceptions, and open problems

The practical scope of anatomical normality modeling is broad. Whole-body models such as BOSS learn skin, internal organs, and bones in a unified pose-normalized shape space and function as statistical priors for reconstruction, completion, and digital twins (Shetty et al., 2023). Organ-specific models such as the statistical 3D stomach shape model define a low-dimensional stomach manifold through $\beta$4 and $\beta$5, yielding compact plausible-shape spaces for surgical simulation and pre-operative planning (Posner et al., 8 Sep 2025). In medical vision-language pre-training, anatomical normality modeling has also been used to model the distribution of normal samples for each anatomy with VQ-VAE and reconstruct normal vision embeddings in latent space, so that abnormal signals are amplified by distribution shifts in abnormal samples (Cao et al., 1 Aug 2025).

A persistent misconception is that any shape generator or reconstruction network is already a normality model. This is not generally true. Deep Medial Voxels is a topology-aware reconstruction method, but it does not learn a probabilistic distribution of normal anatomy, perform anomaly scoring, or separate healthy from pathological variation (Pepe et al., 2024). The morphology-preserving autoregressive 3D brain generator learns the data distribution of both radiologically healthy and pathological brains; this suggests that it can support normative modeling if restricted to a healthy cohort, but the reported model is a morphology-faithful population generator rather than a strict healthy-only normality model (Tudosiu et al., 2022). Likewise, the stomach SSM is a model of plausible stomach anatomy but not a strict healthy-normal model because the refinement data include healthy and diseased cases (Posner et al., 8 Sep 2025).

Open problems therefore remain stable across the literature: the normality-defining cohort must be specified carefully; the learned space must be shown to be truly normative rather than merely plausible; explicit density or uncertainty models are often still missing; and many systems depend heavily on preprocessing quality, correspondence quality, or atlas choice (Zhang et al., 2024, Liu et al., 23 Jan 2025). Current work increasingly points toward hybrid solutions in which dense corresponded shape statistics, conditional generative references, topology-aware implicit representations, and anatomy-conditioned longitudinal predictors are combined rather than treated as competing paradigms.