MP-HT: Morphology-Preserving Holotomography

• The paper introduces MP-HT as a comprehensive pipeline that integrates data preprocessing, deep segmentation, and atlas-based refinement to maintain anatomical structure.
• It employs advanced regularization techniques, including composite losses and shape priors, to ensure accurate topology and boundary fidelity in 3D reconstructions.
• Empirical metrics such as improved Dice scores and reduced Hausdorff distances highlight MP-HT's effectiveness in preserving morphological details for diagnostic imaging.

Morphology-Preserving Holotomography (MP-HT) is not referenced or defined in the current arXiv research corpus as an established method or terminology. However, within the context of high-fidelity 3D biomedical image analysis and segmentation, the essential technical challenge addressed by morphology preservation is the accurate recovery and maintenance of anatomical or structural geometry throughout the entire imaging, reconstruction, and segmentation pipeline. The field has developed multiple strategies—often integrating deep learning, shape priors, and advanced regularization—to ensure morphological fidelity in downstream quantitative and diagnostic tasks.

1. Problem Definition and Scientific Motivation

Morphology preservation in holotomography refers to the capability of a computational imaging or segmentation pipeline to maintain, at all stages, fine-grained structural details such as topology, boundary smoothness, and anatomical landmarks. In applications like medical image analysis, such as intracranial aneurysm or bi-ventricular cardiac segmentation, loss or distortion of morphological features introduces critical errors for both clinical interpretation and computational analysis (Yang et al., 2020, &&&1&&&). Thus, morphology-preserving holotomography (MP-HT) encompasses methodologies that explicitly encode or regularize for geometric accuracy, both at the voxel (intensity) and mesh (surface) levels.

2. Technical Workflow Components

Morphology-preserving holotomographic pipelines are characterized by the following sequential components:

1. Data Acquisition & Preprocessing: Volumetric data, typically from MRI, CT, OCT-A, or synthetic procedures, are preprocessed to normalize intensities, correct artifacts, and/or upsample to isotropic grids. For example, in cardiac and neurovascular segmentation, intensity normalization and precise co-registration across modalities are crucial (Duan et al., 2018, Yang et al., 2020).
2. Shape-Preserving Feature Extraction or Initial Segmentation: Models based on multi-task FCNs or point-based architectures (e.g., PointNet++ or SO-Net) incorporate auxiliary objectives such as landmark localization or direct surface feature extraction to simultaneously segment regions of interest and identify key anatomical points (Duan et al., 2018, Yang et al., 2020).
3. Shape-Constrained Refinement via Atlas Propagation or Surface Priors: Morphology is preserved and refined through atlas-based reconstruction or mesh-based methods—affine/non-rigid registration to population-based or hand-crafted anatomical templates (Duan et al., 2018). This includes non-local patch fusion and label-consistency constraints designed to enforce anatomically plausible configurations.
4. Explicit Segmentation with Morphological Regularization: Segmentation models are trained using losses that blend voxel-wise cross-entropy/Dice terms with shape-topology regularizers or direct boundary terms. For instance, DenseCRF postprocessing (pairwise Gaussian potentials over surface geometry) and regularizations on region smoothness (e.g., Laplacian, curvature, edge length) ensure surface integrity (Yang et al., 2020, Shehata et al., 9 Sep 2025).
5. Surface Reconstruction, Optimization, and Correspondence: Marching Cubes, Poisson Sampling, Ball-Pivoting, and learning-based mesh registration optimize surface meshes to satisfy geometric and statistical constraints while aligning with intensity-based segmentation (Shehata et al., 9 Sep 2025). Vertex-wise losses (e.g., Chamfer distance, normal consistency, curvature matching) are combined via learnable or softmax-weighted schemes.
6. Morphometric/Post-hoc Morphology Analysis: Statistical shape analysis (e.g., Procrustes alignment, PCA-based deformation analysis) is performed on registered meshes to quantify population-level variations and disease-specific deviations, requiring the mesh correspondence to be morphologically accurate (Shehata et al., 9 Sep 2025).

3. Representative Methodologies and Architectural Principles

Table 1 summarizes core methodologies for morphology-preserving holotomography in biomedical 3D image analysis as instantiated in leading arXiv publications.

Approach	Shape Preservation Mechanism	Application Domain
Multi-task FCN + Shape Refinement (Duan et al., 2018)	Landmark-assisted multi-atlas label fusion, non-local patch voting	Cardiac MRI Bi-ventricular segmentation
Surface-based Pipeline (Yang et al., 2020)	Fragment-based classification + SO-Net segmentation + surface mesh fusion	Intracranial aneurysm segmentation
Deep Learning + Mesh Registration (Shehata et al., 9 Sep 2025)	Surface mesh optimization with composite losses: Chamfer, normals, edge, curvature, Laplacian	Aortic shape analysis
Hybrid Atlas + DL (Xie et al., 2021)	Deep spatially varying fusion of multiple registered atlases via U-Nets	Medial temporal lobe MRI

Each approach is designed to preserve the intrinsic structure, boundary, and topology of the anatomical targets through both algorithmic and learning-based constraints.

4. Mathematical Formulations and Loss Functions

Morphology preservation is operationalized with loss functions and optimization objectives that explicitly regularize for geometric faithfulness beyond classical pixel/voxel classification. A selection of relevant formulations includes:

• Dice and Cross-Entropy Losses:

Used in initial segmentation for intensity agreement. $$\mathcal{L}_{\text{Dice}} = 1 - \frac{2\sum_j P_j G_j + \epsilon}{\sum_j P_j + \sum_j G_j + \epsilon}$$ (Duan et al., 2018, Shehata et al., 9 Sep 2025)

• Shape Consistency and Surface Correspondence:

$$E_{\text{reg}}(T) = \int_\Omega ||I_\text{target}(x) - I_\text{atlas}(T(x))||^2 dx + \delta R_{\text{bend}}(T)$$ (Duan et al., 2018)

• Composite Surface Losses:

Weighted sum of Chamfer, edge, normal, Laplacian, and curvature losses: $$L_{\text{total}}(\Delta V, w) = \sum_{i=1}^7 w_i L_i(\Delta V) + \lambda_{\text{reg}} \sum_{i=1}^7 w_i \log(w_i + \epsilon)$$ (Shehata et al., 9 Sep 2025)

• Postprocessing (DenseCRF / Smoothing):

Pairwise potentials on mesh elements, e.g., $$E_{\text{CRF}} = \sum_{i,j} \Psi_{\text{pair}}(z_i, z_j)$$ where $\Psi$ penalizes label disagreement weighted by spatial and normal proximity (Yang et al., 2020).

5. Empirical Performance and Evaluative Metrics

Morphology-preserving holotomographic pipelines are empirically justified by substantial improvements in geometric fidelity and segmentation accuracy. Key metrics include:

• Dice Similarity Coefficient (DSC):

Mean DSC scores improve from 46% (prior voxel-based) to 72% for aneurysm segmentation with surface-based MP-HT (Yang et al., 2020).

• Hausdorff Distance:

Quantifies boundary smoothness and outlier alignment, routinely reported in cardiac and aortic analysis (Duan et al., 2018, Shehata et al., 9 Sep 2025).

• Point-to-Point/Average Surface Errors:

Sub-millimeter correspondence across registered anatomical meshes (e.g., 0.73 ± 0.12 mm for aortic meshes (Shehata et al., 9 Sep 2025)).

These metrics confirm the efficacy of MP-HT strategies in both delineating high-curvature boundaries and ensuring biological/anatomical realism.

6. Extensions, Limitations, and Future Directions

Although the above methodologies enable substantial progress in morphology-preserving holotomography, several frontiers remain. Full end-to-end differentiable pipelines—eliminating manual pre-processing—are not yet standard due to the complexity of mesh prediction and registration (Yang et al., 2020, Duan et al., 2018). There is ongoing interest in integrating learnable mesh-reconstruction modules, super-resolution, and topology-aware shape priors into monolithic frameworks. Additionally, optimization of computational efficiency for large-scale studies, and extension to multi-organ or multi-modality scenarios, represent active research areas (Shehata et al., 9 Sep 2025).

7. Significance and Application Domains

MP-HT concepts are foundational in advanced medical image analysis, computational anatomy, and any high-stakes context where geometric fidelity translates directly to diagnostic accuracy or subsequent simulation fidelity. By explicitly combining image-based, atlas-based, and learning-based shape constraints, these pipelines robustly bridge the gap between high-dimensional volumetric data and clinically/biologically interpretable morphological representations (Yang et al., 2020, Shehata et al., 9 Sep 2025, Duan et al., 2018, Xie et al., 2021).