Optimizing 3D UNet Parameters for Cranial Defect Reconstruction

Abstract

Cranial reconstruction is a critical task in computer-assisted surgery, requiring both high geometric accuracy and computational efficiency for patient-specific implant design. While recent deep learning approaches, particularly 3D UNet-based models, have demonstrated promising performance, most studies primarily focus on architectural modifications, with limited attention to the systematic impact of data preparation and training strategies on reconstruction quality. In this study, we present a comprehensive data-centric investigation of key factors influencing the performance of a baseline 3D UNet for cranial defect reconstruction. Specifically, we analyze the effects of data preprocessing (denoising), dataset organization (ordered versus randomized training), defect morphology diversity, convolutional kernel size, and loss function design under controlled experimental conditions. Experiments were conducted on 250 complete skulls (NRRD format) from the MUG500+ dataset, with synthetically generated defects across multiple anatomical regions. From these volumes, a total of 3750 training samples were generated, including: (i) 1250 noisy samples with diverse defect morphologies, (ii) 1250 denoised samples with ellipsoidal defects, and (iii) 1250 denoised samples with multiple defect types. The results demonstrate that data-centric and training-related factors have a substantial impact on model performance, in several cases exceeding the influence of architectural design. In particular, denoising significantly improves boundary stability and reduces geometric error, while incorporating diverse defect morphologies enhances generalization to unseen shapes. Additionally, ordered training contributes to more stable convergence, and an optimal kernel size of (3 × 3 × 3) achieves the best trade-off between accuracy and computational efficiency. A hybrid Dice and boundary loss further improves boundary precision compared to conventional Dice loss. The optimized configuration achieves a Dice Similarity Coefficient of 0.94 and a Hausdorff Distance of 3.8 mm, with an average inference time of 0.004 s per case. These results demonstrate that data-centric optimization can be as influential as, or even more impactful than, architectural design in cranial defect reconstruction. The findings provide practical and reproducible guidelines for developing efficient, robust, and clinically applicable deep learning-based systems for patient-specific cranial implant design.

1. Introduction

Cranial defects can arise from a variety of causes, most commonly including traumatic brain injury due to accidents, surgical resection of brain tumors, and severe neurological or craniofacial diseases [1]. In many cases, patients must undergo decompressive craniectomy to alleviate elevated intracranial pressure and preserve life, which inevitably results in partial loss of the cranial bone structure [2]. Such defects not only lead to aesthetic deformities but also compromise the protective function of the skull, alter cranial biomechanics, and negatively affect patients’ quality of life. Consequently, cranioplasty plays a critical role in restoring cranial integrity and supporting patient survival and neurological recovery [2].

When cranial defects are present, meticulous preoperative planning is required to enable effective cranial reconstruction [3]. Currently, two principal approaches are employed for cranial defect repair: reconstruction using autologous bone and reconstruction using artificial bone substitutes [4]. Although autologous bone is widely regarded as the gold standard due to its excellent biocompatibility and resistance to immune rejection, its clinical application is often limited. In cases of traumatic injury or bone-related pathologies such as osseous tumors, the original bone flap may be unsuitable for reuse. Furthermore, long-term bone resorption following reimplantation can result in secondary deformities and additional complications, thereby reducing aesthetic outcomes and patient satisfaction [4,5].

With the advancement of biomaterials, the use of artificial bone substitutes has emerged as a promising opportunity for patients with cranial defects. Artificial bone materials are required to exhibit excellent biocompatibility with the human body and, importantly, must be suitable for fabrication with appropriate geometric conformity and mechanical compatibility. Among the most commonly used biomaterials at present are polyetheretherketone (PEEK), titanium, and polymethyl methacrylate (PMMA). In terms of geometric and mechanical compatibility, the implant design stage plays a critical role in ensuring accurate geometric dimensions, aesthetically consistent curvature, and appropriate implant thickness [5,6,7,8,9].

Currently, there are two main approaches for cranial implant design. The first approach relies on commercial software tools, such as Mimics 2024, Slicer 5.9.0, SOLIDWORKS 2024 SP5, and MITK v2024.12, while the second approach employs deep learning-based methods for automated implant generation [10,11].

Regarding the first approach, several studies have reported limitations associated with the use of commercial software. For example, Nguyen Huu Long et al. [12] reported that the design process using commercial software is relatively time-consuming, requiring approximately 2–3 h per implant. Mamta et al. [13] demonstrated that even for skilled technicians who are proficient in using such software, the design time typically ranges from 40 to 45 min per implant. In contrast, the study by J. Zubizarreta-Oteiza et al. [14] showed that the application of algorithm-based methods can significantly reduce the design time from approximately 2 h to only 1–3 min. Furthermore, Marek Wodzinski et al. [15] pointed out that commercial software-based design workflows are associated with prolonged design time, high technical complexity, and limited accuracy, which may delay the treatment process and hinder timely clinical intervention, particularly when treatment time is considered a critical or “golden” window for patient outcomes.

With the rapid advancement of deep learning technologies in modern society, the application of deep learning to cranial defect implant reconstruction has become increasingly necessary. Deep learning-based approaches enable faster implant design processes while simultaneously improving geometric accuracy and morphological consistency of the reconstructed implants.

2. Previous Work

Recent advances in deep learning have demonstrated the effectiveness of multi-scale feature extraction, multi-level feature fusion, attention mechanisms, and multimodal learning in diverse image analysis tasks [16,17]. Although many of these approaches have been explored in detection and recognition problems, their underlying principles provide valuable inspiration for volumetric medical image reconstruction. In particular, hierarchical feature representation and feature fusion concepts are closely related to encoder–decoder architectures such as 3D UNet, which motivate their relevance to cranial defect reconstruction.

As summarized in

Table 1. Summary of deep learning approaches for cranial implant/skull defect reconstruction (2020–2025).

Year	Author	Dataset	Network	Methodology	Merits	Demerits
2020	Jianning Li et al. [18]	200 skulls (CQ500)	CNN	Two-stage direct implant prediction: (1) coarse implant estimation from downsampled skulls; (2) fine prediction on cropped defect regions.	Practical design suitable for limited GPU resources; direct implant prediction without geometric subtraction.	Limited generalization to unseen defect patterns; inferior performance compared with later shape-completion-based methods.
2020	Franco Matzkin et al. [19]	200 skulls (CQ500)	DE-UNet	Self-supervised learning via virtual craniectomy; direct implant estimation enhanced with atlas-based shape priors.	High accuracy; improved robustness for out-of-distribution cases; no need for real implant ground truth.	Strong dependence on atlas registration; shape priors may reduce average accuracy on in-distribution data.
2022	Marek Wodzinski et al. [20]	AutoImplant 2021	3D Residual UNet	Extensive data augmentation using cross-case (imperfect) image registration and VAE-based data synthesis.	Excellent generalization to real clinical cases; demonstrates the critical role of data augmentation over network design.	No novel reconstruction architecture; requires large datasets; limited performance for very large or highly asymmetric defects.
2022	Chieh-Tsai Wu et al. [21]	73 clinical CT scans	UNet/V-Net	Supervised learning with paired intact skulls and synthetically generated defects (virtual craniectomy).	Lightweight architecture; minimal post-processing required.	Low spatial resolution; strong dependence on simple synthetic defect shapes.
2023	Stefano Mazzocchetti et al. [22]	SkullFix, SkullBreak	3D UNet	Two-step pipeline: (1) full skull reconstruction from defective skulls; (2) implant generation via geometric subtraction.	Simple and stable pipeline; no requirement for real implant data.	Strong reliance on synthetic defects; lack of explicit geometric or anatomical constraints.
2023	Chieh-Tsai Wu et al. [23]	SkullFix, SkullBreak	3D UNet	Two-stage reconstruction with high-resolution refinement; implant obtained via Boolean subtraction.	High-resolution implants; stable performance; effective for large defects.	More complex two-stage pipeline; sutures are not reconstructed; reduced accuracy for highly irregular defects.
2024	Marek Wodzinski et al. [15]	SkullFix, SkullBreak	Deep Deformable Masked Autoencoder (3D UNet backbone)	Self-supervised masked autoencoding with deformable transformations for skull completion.	No need for ground-truth labels; superior generalization, especially on SkullBreak; fast inference; effective global shape modeling.	Long training time; requires sufficiently diverse healthy skull datasets.
2024	Marek Wodzinski et al. [24]	SkullFix, SkullBreak	3D Residual UNet	Large-scale data preparation using VAE, VQVAE, IntroVAE, SoftIntroVAE, WGAN-GP, and latent diffusion models.	Strong evidence that data preparation and augmentation dominate architectural changes; good performance on clinical data.	Extremely high computational cost; no new reconstruction architecture proposed.
2024	Resmi S. et al. [25]	AutoImplant 2021	3D UNet, 3D UNet + Transformer	Shape completion followed by implant generation via skull subtraction; Transformer used to model global context.	Improved global context modeling; simple and interpretable architecture.	Very low spatial resolution; overall performance remains limited; weak generalization.
2025	Marek Wodzinski et al. [26]	SkullFix, SkullBreak	ResNet, Vision Transformer	Learnable symmetry enforcement with two-stage reconstruction and symmetry refinement.	Significant accuracy improvement; reduced dependence on heavy data augmentation; robust for large, bilateral, and out-of-distribution defects.	Does not directly generate final implants; not integrated with generative models for extremely large defects.
2025	Mamta Juneja et al. [13]	MUG500+	CRIGNet	Supervised learning with synthetically generated defects using virtual craniectomy.	Simple and interpretable pipeline; effective for small-to-moderate defects.	Lack of geometric constraints; limited generalization to large or asymmetric defects.
2025	Thathapatt Kesornsri et al. [27]	CQ500	CraNeXt	Skull categorization prior to reconstruction; separate models trained for different skull shape categories.	Improved accuracy compared with a single global model; more stable learning for heterogeneous data.	Sensitive to categorization errors; scalability issues as the number of categories increases.

, recent deep learning approaches for cranial defect reconstruction exhibit several distinct methodological trends, primarily differing in reconstruction strategy, data usage, and network design. These three groups fundamentally differ in how geometric information is modeled: direct estimation relies mainly on local feature mapping, shape completion leverages global anatomical context, while data-driven approaches focus on improving representation through training strategies rather than architectural changes.

A first group of methods adopts direct implant estimation strategies, where the network predicts the implant geometry directly from defective skull inputs. For instance, Li et al. [18] proposed a two-stage prediction framework that performs coarse estimation followed by local refinement. Similarly, Matzkin et al. [19] introduced a DE-UNet model with atlas-based shape priors. These approaches are computationally efficient and suitable for limited hardware resources, as they avoid full-volume reconstruction. However, as indicated in Table 1, they tend to suffer from limited generalization to unseen or irregular defect patterns, and their performance is often inferior to later methods that incorporate global structural information. In practice, such methods are more suitable for real-time applications or scenarios with constrained computational resources.

A second group focuses on full skull reconstruction followed by implant extraction, typically based on UNet or 3D UNet architectures [20,21,22,23]. These methods first reconstruct the complete skull and then obtain the implant via geometric subtraction. As shown in Table 1, such approaches generally achieve better robustness and higher reconstruction accuracy, especially for large defects, due to their ability to capture global anatomical context. For example, high-resolution refinement strategies [23] improve spatial detail and stability. Nevertheless, these methods often involve more complex pipelines, including multi-stage processing and post-processing steps, and may struggle with fine anatomical structures such as sutures or highly irregular defect boundaries. These approaches are typically preferred in applications where reconstruction accuracy is prioritized over computational efficiency.

A third trend emphasizes data-driven enhancement and training strategies rather than introducing fundamentally new architectures. As reported by Wodzinski et al. [24], extensive data augmentation using techniques such as VAE, GAN, and latent diffusion significantly improves model generalization, highlighting the dominant role of data preparation over architectural changes. Similarly, self-supervised learning approaches [15] eliminate the need for ground-truth implants, while transformer-based models [25] enhance global context modeling. In addition, symmetry-based methods [26] improve reconstruction accuracy for large or bilateral defects by incorporating anatomical priors. Despite these advantages, such approaches typically require large datasets, longer training times, and higher computational cost, which may limit their practical applicability. These findings strongly suggest that, in cranial defect reconstruction, data quality and training strategy may play a role as critical as-if not more important than network architecture design. Another important observation from Table 1 is the strong dependence on synthetic defect generation in most studies [21,22,25]. While synthetic data enables large-scale training, it may not fully capture the complexity of real clinical defects, leading to reduced performance when applied to highly irregular or out-of-distribution cases. Furthermore, several methods exhibit trade-offs between model complexity and reconstruction accuracy, where more advanced architectures improve performance but reduce efficiency and reproducibility.

Overall, Table 1 indicates that while significant progress has been made, existing studies primarily focus on architectural design and data augmentation. In contrast, the systematic impact of data quality, dataset organization, and training configuration on reconstruction performance remains insufficiently investigated in a controlled and systematic manner, particularly under consistent experimental settings.

Therefore, instead of proposing a new architectural variant, this study aims to systematically quantify the impact of key data-centric and training-related factors, including preprocessing, dataset organization, and loss design, under controlled conditions. This approach provides reproducible insights for optimizing 3D UNet-based cranial reconstruction systems.

3. Materials and Methods

3.1. Research Pipeline

This study presents an end-to-end experimental framework for cranial defect reconstruction, designed not only for model training but also for systematic evaluation of data-related factors. The pipeline takes cranial CT data as input, performs standardized preprocessing, generates controlled synthetic defects, and applies a 3D UNet model for reconstruction, followed by quantitative evaluation, as illustrated in Figure 1.

Specifically, the workflow consists of three main stages: dataset preprocessing, defect generation, and model training and evaluation. In the preprocessing stage, CT data are spatially standardized and divided into two parallel branches (with and without denoising) to enable direct assessment of noise influence. In the defect generation stage, cranial defects are synthetically created under controlled conditions with respect to anatomical location, geometric shape, and data organization strategy, allowing isolation of individual factors during evaluation. Finally, a consistent 3D UNet architecture with fixed hyperparameters is employed across all experiments, where only specific variables (e.g., kernel size and loss function) are altered. This design ensures a fair comparison and enables clear analysis of how each factor affects reconstruction performance and generalization capability.

3.2. Data Preprocessing

A comprehensive and structured preprocessing pipeline was implemented to ensure high-quality input data for model training. This pipeline comprises several sequential steps, including volume cropping, intensity normalization, noise processing, and data organization for subsequent experimentation. An overview of the preprocessing workflow is illustrated in Figure 1.

3.2.1. Cropping

Due to variability in acquisition range and anatomical coverage within the MUG 500+ dataset (e.g., inclusion of cervical vertebrae and portions of the thoracic region), an automated cropping strategy was proposed to standardize the input volumes. Specifically, for each scan, the highest slice along the superior–inferior axis containing cranial voxels (voxel value of 1) was first identified to exclude slices consisting solely of background or air. From this reference point, a fixed number of subsequent slices (approximately 100 voxels) were retained in the inferior direction, corresponding to the cranial region. Empirical evaluation demonstrates that this approach effectively normalizes the half-skull region across samples while preserving essential anatomical structures required for model training.

3.2.2. Resampling

Following the cropping stage, the volumes with an initial resolution of 512 × 512 × 100 were downsampled to 64 × 64 × 96 to reduce spatial resolution and improve computational efficiency during training. The resampling process was performed using linear interpolation. Specifically, the scaling factors were computed independently along each spatial dimension (x, y, z) based on the ratio between the original and target resolutions, and subsequently applied to resample the volumetric data. In addition, the metadata in the file header were updated to reflect the new volume dimensions and voxel spacing. The spatial orientation matrix (space directions) was adjusted to a diagonal form consistent with the updated voxel spacing, thereby ensuring geometric consistency of the resampled data.

3.2.3. Noise Processing

CT cranial data often contain various types of noise and artifacts that adversely affect the accuracy of cranial defect reconstruction. One common source of noise arises from calcification deposits in soft tissues, including brain tissue, which exhibit Hounsfield Unit (HU) values similar to bone [28]. Another type of interference originates from external head pads or fixation devices, which also share comparable HU ranges with cranial bone structures [29]. To address these artifacts, we retained only the largest connected voxel component, corresponding to the actual cranial region. In contrast, soft tissues, blood, and muscle, which have significantly lower HU values than bone, were easily removed using a threshold-based HU segmentation [30]. Eliminating these artifacts substantially reduces the preprocessing burden and enhances both the training stability and convergence speed of deep learning models [30,31]. To assess the effect of noise in CT data on reconstruction performance, a controlled experiment was conducted under two conditions: raw (noise) data and denoised data. Cranial defects were simulated on both datasets using exactly the same generation procedure and strictly identical shape distributions. The resulting datasets were then split into training, validation, and testing sets using the same ratios, while maintaining one-to-one correspondence between samples to eliminate potential sample mismatch and distribution bias introduced during data partitioning.

3.3. Defect Generation

3.3.1. Defect Morphology Simulation

Prior to defect morphology simulation, each skull from the MUG500 dataset was represented as a discretized binary volumetric complete skull model, where bone voxels were assigned a value of 1 and background voxels a value of 0. Artificial cranial defects were generated using predefined defect masks (cylindrical, ellipsoidal, cuboid, and boundary-perturbed shapes) positioned at specific anatomical locations (Figure 2), followed by Boolean subtraction:

Defective skull = Complete skull − Defect mask

Through this voxel-based discretization process, voxels within the defect region were removed while the remaining cranial structure was preserved unchanged. The removed missing segment was retained as implant ground truth for training and evaluation.

Based on a standard cranial atlas, the skull is anatomically partitioned into five primary regions: frontal, parietal, left temporal, right temporal, and occipital. To enhance dataset diversity, cranial defects were systematically generated across these five anatomical locations.

In addition to spatial variability, defect morphology was carefully designed to reflect clinically relevant patterns observed in cranial pathologies.

Specifically, circular and cylindrical defects were used to approximate bone loss caused by tumor-related lesions.

Square-shaped defects were introduced to simulate craniectomy procedures, such as decompressive surgery.

Elliptical and irregular (noise-perturbed circular) defects were generated to mimic the complex and heterogeneous geometries typically associated with traumatic brain injuries.

This design enables the model to learn from a wide spectrum of defect shapes, thereby improving its generalization capability in realistic clinical scenarios.

As shown in Figure 2, five types of defect masks were generated to simulate various cranial defect geometries for model training.

• Cylindrical defect: A circular cylinder with a radius of $r=45$ voxels and height $h=80$ voxels.
• Ellipsoidal defect: An ellipsoid with semi-axes $(a,b,c)=(50,60,45)$ voxels.
• Cuboidal defect: A rectangular box with an edge length of 80 voxels.
• Noisy cylindrical defect: A cylindrical mask with boundary perturbations introduced by noisy_mask().
• Noisy ellipsoidal defect: An ellipsoidal mask with stochastic boundary deformations.

3.3.2. Noisy Defective Skull

As part of the experimental protocol, the defective skull volumes generated according to the five defect types and five anatomical locations described in Section 3.3.1 were retained in their original (non-denoised) form. These samples were consolidated into a dedicated dataset, referred to as the Noisy defective skulls. This dataset serves as one of the inputs for subsequent experimental evaluation.

3.3.3. Denoised Defective Skull

At this stage, noise artifacts were removed to construct a refined dataset for subsequent experiments. The preprocessing and dataset construction were further organized into the following components:

Ellipsoidal mask: A single defect was generated using an ellipsoidal mask at five distinct anatomical locations corresponding to the primary cranial regions. The resulting samples were stored as a separate dataset for subsequent evaluation.

Multi-mask dataset: Defects were generated according to the strategy described in Section 3.3.1, incorporating multiple shapes and locations. This dataset was subsequently used for training under different data organization schemes.

One of the key challenges in deep learning is overfitting, which occurs when a model memorizes training samples rather than learning generalizable features. A major contributing factor is insufficient data diversity, where samples fail to capture the full variability of real-world conditions. As reported by Yu et al. [32], increasing structural and morphological diversity can significantly improve generalization performance, even when the dataset size remains unchanged. These findings highlight that, beyond dataset size, diversity plays a critical role in enhancing model robustness and reliability.

To further investigate the impact of data organization, two training strategies were designed:

Random ordering: According to Mamta Juneja et al. [33], dividing the dataset into five anatomical regions enhances data diversity and improves model performance. However, their study did not address the effect of organizing and training data based on distinct regional groups.

Based on previously reported standard deviation measurements of cranial vault thickness [34], regional variations across anatomical sites can be observed. Specifically, the temporal and parietal regions exhibit lower standard deviations, indicating relatively high structural homogeneity. In contrast, the frontal region, and particularly the occipital region, show higher standard deviations, reflecting greater variability in thickness and increased geometric heterogeneity.

These observations suggest that cranial regions can be organized according to increasing levels of variability, ranging from more stable regions to those with higher structural complexity. In this study, the degree of variability (quantified by standard deviation) is adopted as a proxy indicator of the geometric complexity of each region.

Furthermore, prior studies have demonstrated that organizing training data in a curriculum from easier to more complex samples can improve both the stability and performance of deep learning models [35].

Motivated by these findings, we propose a region-based training strategy in which the input data are progressively ordered according to increasing variability: parietal, temporal, frontal, and occipital regions. In parallel, a control dataset is constructed by randomly shuffling the training samples.

To ensure a fair comparison, all other factors between the two configurations are kept identical, including the same initial dataset and identical training/validation/testing split, the same 3D UNet architecture, identical loss function, and consistent training hyperparameters. Additionally, both models are evaluated on the same test set.

As shown in

Table 2. Examples of simulated cranial defect morphologies used for model training.

Defective Morphology	Rectangular	Circular Cylinder	Circular Cylinder with Boundary Disturbance	Elliptical Cylinder	Elliptical Cylinder with Boundary Disturbance
Defective
Implant
Mask

, five defect morphologies were generated for training. The cuboidal, ellipsoidal, and cylindrical shapes represent regular defect geometries, analogous to those commonly observed in decompressive craniectomy. In contrast, the noisy ellipsoidal and noisy cylindrical shapes introduce irregular and complex boundaries, mimicking defect morphologies typically associated with traumatic injuries.

3.4. 3D UNet

3.4.1. 3D UNet Architecture

A 3D UNet architecture was implemented with symmetric encoder–decoder blocks and skip connections, as shown in Figure 3. The network uses varying kernel sizes (2 × 2 × 2), (3 × 3 × 3), and (4 × 4 × 4), hybrid Dice and boundary loss, and a sigmoid activation function was used for binary segmentation.

The skull reconstruction task was performed using a 3D UNet architecture with four encoder and four decoder blocks, symmetrically connected by skip connections to preserve spatial features.

Network Architecture and Training Setup

Encoder: Each encoder block consists of a sequence of Conv3D → BatchNorm3D → LeakyReLU → MaxPooling3D operations. To investigate the influence of receptive field size on spatial feature learning, convolutional kernels of (2 × 2 × 2), (3 × 3 × 3), and (4 × 4 × 4) were systematically tested. Downsampling progressively reduces spatial resolution while increasing the number of feature channels from 48 → 96 → 192 → 384, allowing the network to capture multi-scale contextual information.

Bottleneck Layer: The bottleneck comprises two convolutional layers with a (3 × 3 × 3) kernel and stride $=1$, designed to extract global contextual representations. A dropout rate of 0.3 was applied to prevent overfitting and enhance model generalization.

Decoder: The decoder mirrors the encoder through ConvTranspose3D upsampling layers, each concatenated with its corresponding encoder feature map via skip connections. This design facilitates the recovery of fine-grained anatomical details in the reconstructed output and preserves spatial consistency across feature levels.

Activation and Output: A sigmoid activation function was applied to the final output layer to generate voxel-wise probabilities for distinguishing defect and non-defect regions. The total loss function combines Dice Loss and Boundary Loss to jointly optimize volumetric overlap and boundary accuracy. This formulation encourages both global shape consistency and precise delineation of defect boundaries.

Training Configuration: The model optimization was performed using the Adam optimizer with a learning rate of $1\times {10}^{-4}$ and parameters ${\beta }_1=0.9$, ${\beta }_2=0.999$. Training was conducted for 200 epochs with a batch size of 2, employing a cosine annealing learning rate scheduler for gradual decay. Mixed-precision training (float16) was enabled to improve computational efficiency.

The best model checkpoint was selected based on a composite validation criterion that maximized Dice Similarity Coefficient (${\mathrm{DSC}}_{\mathrm{val}}$) and minimized Hausdorff Distance (${\mathrm{HD}}_{\mathrm{val}}$), ensuring both volumetric and geometric accuracy in the reconstructed results.

3.4.2. Kernel Size

According to [33], cranial bone thickness in adults varies between 2–12 mm depending on anatomical location (parietal, frontal, and temporal regions). Therefore, a kernel size of (2 × 2 × 2) provides insufficient spatial context for learning features across thin cranial regions. Moreover, even-sized kernels can introduce asymmetric padding and one-voxel output shifts, which may affect spatial alignment during convolution. To address this, kernel configurations of (2 × 2 × 2), (3 × 3 × 3), and (4 × 4 × 4) were investigated to evaluate their impact on spatial representation and reconstruction accuracy.

3.4.3. Dice Loss and Hybrid Combinations of Dice Loss and Boundary Loss

Loss functions commonly used for convolutional neural network (CNN)-based segmentation include Dice and Cross-Entropy losses. Dice Loss focuses on maximizing volumetric overlap between predicted and ground-truth regions; however, small boundary discrepancies, which are crucial for anatomically accurate reconstruction are not explicitly penalized during optimization. Consequently, reconstructed implants tend to appear overly smoothed or to lack fine boundary details, especially when the defect region is much smaller than the overall 3D volume.

Boundary loss, designed to emphasize distance discrepancies along predicted and reference boundaries, directly addresses this limitation and enhances geometric accuracy without introducing significant computational overhead.

According to Kervadec et al. (2019) [36], combining Boundary Loss with region-based losses such as Dice leads to substantial improvements in boundary accuracy, with up to 8% higher Dice scores and approximately 10% lower Hausdorff distances.

A hybrid loss function combining Dice and Boundary loss was employed to enhance both regional consistency and boundary accuracy during model training. In medical image segmentation tasks, particularly in cranial defect reconstruction, the defective region typically occupies only a small fraction of the entire cranial volume. Under such class imbalance conditions, relying solely on Dice loss primarily optimizes volumetric overlap between the predicted and ground-truth masks but provides limited sensitivity to geometric precision along boundaries. This often leads to over-smoothed or blurred edges, especially in complex or discontinuous defect regions.

To overcome this limitation, the present study employs a hybrid loss function that combines Dice loss with a boundary loss component. The boundary loss penalizes discrepancies along the morphological boundary between the predicted and reference masks. It is computed using the distance transform of the ground-truth boundary, enabling the network to learn sharper and anatomically consistent edges.

To evaluate the impact of loss formulation on reconstruction performance, a controlled experiment was conducted using two loss configurations: Dice Loss and a hybrid Dice + boundary loss. All other factors were kept identical, including the same training, validation, and test sets, network architecture, kernel size (fixed at (3 × 3 × 3)), and training hyperparameters, ensuring that performance differences can be attributed solely to the loss function. Model performance was evaluated using the Dice Similarity Coefficient (DSC) and Hausdorff Distance (HD) [37,38].

Similarity Coefficient (DSC)

$$DSC={\displaystyle \frac{2|P\cap G|}{\left|P\right|+\left|G\right|}}$$

(1)

where P and G denote the predicted and ground-truth implant voxels, respectively. DSC quantifies volumetric overlap between reconstructed and reference implant regions, with higher values indicating better overlap agreement.

Hausdorff Distance (HD)

$$HD(P,G)=max\left\{\underset{p\in P}{sup}\underset{g\in G}{inf}d(p,g),\underset{g\in G}{sup}\underset{p\in P}{inf}d(g,p)\right\}$$

(2)

where $d(·,·)$ denotes the Euclidean distance. HD evaluates boundary accuracy by measuring the maximum geometric deviation between reconstructed and reference boundaries, where lower values indicate better boundary agreement.

3.4.4. Three Data-Centric Training Configurations

To systematically evaluate the impact of data characteristics and training strategies on model performance, the dataset was organized into three distinct groups under controlled conditions.

Experiments were conducted on 250 complete skull volumes (NRRD format) from the MUG500+ dataset. Synthetic cranial defects were generated across five anatomical regions: frontal, parietal, left temporal, right temporal, and occipital.

The dataset was divided into three groups:

• Noisy samples with diverse defect morphologies: This group includes 1250 samples generated from non-denoised data, incorporating five defect types across the five anatomical regions (250 samples per region).
• Denoised samples with ellipsoidal defects: This group consists of 1250 samples generated from denoised data, where a single ellipsoidal defect is applied at each anatomical region (250 samples per region).
• Denoised samples with multiple defect morphologies: This group includes 1250 samples generated from denoised data, incorporating multiple defect types across the five anatomical regions (250 samples per region).

In total, 3750 training samples were generated across the three dataset groups.

For each dataset group, an independent model was trained using the same network architecture, hyperparameters, and training configuration to ensure a fair comparison. The samples were split into training, validation, and testing sets using a ratio of 80%, 10%, and 10%, respectively, and the same data split strategy was applied consistently across all experiments.

This three-stage training strategy enables a controlled and interpretable evaluation of how noise, defect morphology, and data diversity influence model convergence and reconstruction performance.

3.4.5. Experimental Setup

All experiments were conducted on a workstation equipped with a single NVIDIA GeForce RTX 5060 Ti GPU with 16 GB of GPU memory. Each training run was performed using a single GPU. Inference and evaluation were also carried out on the same RTX 5060 Ti GPU. The training time for each experiment did not exceed 8 h on a single GPU.

The proposed 3D UNet was implemented in Python 3.11.9 using PyTorch 2.10.0+cu128 as the deep learning framework. Volumetric data preprocessing and NRRD handling were performed using NumPy 2.1, SciPy 1.14, and pynrrd 1.1.1, while visualization and qualitative verification of defect morphology were conducted using Slicer 5.9.0. This software environment supported all stages of data preparation, model training, and reconstruction evaluation.

4. Results and Discussion

4.1. Effect of Denoising on Model Stability

Two conditions were compared: non-denoised data vs. denoised data.

As shown in Figure 4 and

Table 3. Comparative Analysis of Denoised and Non-Denoised Reconstruction based on (a) DSC and (b) HD.

Condition	DSC	HD (mm)	Epoch Time (s)	Observation
Raw data (no filtering)	0.85	7.76	71.9	Slight boundary noise
Denoised data	0.92	4.46	71.8	More stable mask boundary

, the impact of denoising on reconstruction performance is both quantitatively and qualitatively significant. When trained on raw data without preprocessing, the model achieved a Dice Similarity Coefficient (DSC) of 0.85 and a Hausdorff Distance (HD) of 7.76 mm. In contrast, training on denoised data improved the DSC to 0.92 and reduced the HD to 4.46 mm, corresponding to an increase of approximately 8% in volumetric overlap and a reduction of 3.3 mm in boundary error.

This improvement highlights the critical role of noise removal in stabilizing model learning. In raw CT data, noise sources such as calcification artifacts and external structures introduce intensity ambiguities that are difficult to distinguish from true bone tissue. As a result, the model may incorrectly learn irrelevant voxel patterns, leading to unstable boundary predictions and increased geometric error. After denoising, these artifacts are removed, allowing the network to focus on meaningful bone–air transitions, which are essential for accurate skull reconstruction.

From a geometric perspective, the reduction in HD is particularly important, as it indicates improved boundary precision of the reconstructed implant. While DSC reflects overall volumetric overlap, HD is more sensitive to local boundary deviations, which directly affect implant fitting and clinical usability. The substantial decrease in HD therefore suggests that denoising not only improves segmentation accuracy but also enhances the anatomical plausibility of reconstructed implants.

Importantly, the computational cost remained nearly unchanged, with epoch time showing negligible variation between the two conditions. This indicates that denoising provides a high-performance gain without introducing additional computational overhead, making it a practical and efficient preprocessing step.

Overall, these results demonstrate that data quality-specifically noise reduction-has a direct and significant impact on both model stability and reconstruction accuracy. This finding reinforces the importance of data-centric design in medical image reconstruction, supporting the hypothesis that preprocessing strategies can be as influential as network architecture in determining final performance.

4.2. Effect of Training Data Arrangement

In this experiment, the training data were organized under two configurations: randomized batching and ordered batching grouped by anatomical regions. As shown in Figure 5 and

Table 4. Data arrangement comparison.

Arrangement	DSC	HD (mm)	Observation
Random	0.91	5.11	Slower convergence, weaker boundaries
Ordered	0.92	4.58	Stable binary segmentation

, the ordered training configuration achieved a slightly higher DSC (0.92 vs. 0.91) and a lower HD (4.58 mm vs. 5.11 mm), indicating improved reconstruction accuracy and boundary consistency. Although the numerical difference appears moderate, the improvement in HD (approximately 0.5 mm) is meaningful in the context of cranial reconstruction, where boundary precision directly affects implant fitting. The observed performance gain can be attributed to reduced intra-batch variability in the ordered configuration. By grouping samples with similar anatomical characteristics, the model is exposed to more consistent geometric patterns within each training batch, facilitating more stable gradient updates and faster convergence. In contrast, randomized training introduces higher variability within each batch, which can improve generalization across diverse defect patterns but may also lead to fluctuations during optimization. This trade-off is reflected in the slightly lower DSC and higher HD values observed for the randomized configuration. From a learning perspective, ordered training encourages the model to capture region-specific morphological features, while randomized training promotes more global generalization. Overall, these results suggest that dataset organization plays a non-negligible role in training stability and reconstruction quality. While the impact is less pronounced than that of preprocessing, it highlights an important trade-off between convergence stability and generalization capability. In practice, hybrid strategies that combine structured grouping with controlled randomization may further improve performance.

4.3. Effect of Defect Morphology in Training

Evaluates the generalization capability of the proposed model under different training data configurations. Specifically, two models were trained: one using only ellipsoidal defects, and another using a combination of five distinct defect morphologies. Both models were then evaluated on previously unseen defect shapes.

This experiment evaluates the influence of defect morphology diversity on model generalization. Two training configurations were considered: one using a single defect type (ellipsoidal), and another using multiple defect geometries. As shown in Figure 6 and

Table 5. Defect morphology configuration comparison.

Configuration	DSC	HD (mm)	Observation
Single	0.86	6.86	Lower generalization; poor adaptation to unseen geometries
Multiple	0.92	6.83	Better generalization; stable boundary accuracy

, the model trained on diverse defect shapes achieved a significantly higher DSC (0.92 vs. 0.86), while the HD values remained nearly unchanged.

The substantial increase in DSC (approximately 6%) indicates that incorporating morphological diversity enables the model to better capture the global geometric variations of cranial defects. When trained on a single defect type, the model tends to overfit to specific geometric patterns, limiting its ability to generalize to unseen shapes, particularly irregular and complex geometries.

From a practical perspective, these findings highlight the importance of dataset diversity in medical image reconstruction. Cranial defects in real clinical scenarios exhibit high variability in both shape and location. Therefore, training with multiple defect morphologies is essential to ensure robust performance across different cases. This result reinforces the hypothesis that data diversity is a key factor in improving generalization, even when the total dataset size remains unchanged.

4.4. Influence of Kernel Size on Accuracy and Efficiency

A set of experiments was conducted with convolutional kernels of size (2 × 2 × 2), (3 × 3 × 3), and (4 × 4 × 4).

To investigate the effect of receptive field size on reconstruction performance, convolutional kernels of size (2 × 2 × 2), (3 × 3 × 3), and (4 × 4 × 4) were evaluated. As shown in Figure 7 and

Table 6. Comparative Analysis of the Effect of Kernel Size on Reconstruction Performance based on (a) DSC, (b) HD, and Epoch Time.

Kernel Size	DSC	HD (mm)	Time (s/epochs)	Observation
(2 × 2 × 2)	0.86	5.39	50.8	Computationally efficient but less accurate
(3 × 3 × 3)	0.92	4.46	71.8	Optimal balance
(4 × 4 × 4)	0.92	4.34	135.2	Computationally expensive, marginal gain

, the kernel size of (3 × 3 × 3) achieved the best balance between accuracy and computational efficiency, with a DSC of 0.92 and an HD of 4.46 mm.

Smaller kernels (2 × 2 × 2) result in limited receptive fields, restricting the model’s ability to capture global anatomical context. This leads to lower reconstruction accuracy (DSC = 0.86) and higher boundary error (HD = 5.39 mm), as the model primarily relies on local features without sufficient spatial awareness. On the other hand, larger kernels (4 × 4 × 4) provide a wider receptive field but introduce excessive smoothing and increased computational cost. Although the HD is slightly reduced (4.34 mm), the marginal improvement does not justify the significant increase in training time.

The (3 × 3 × 3) kernel offers an optimal compromise by effectively capturing both local curvature and broader anatomical structures. This is particularly relevant for cranial reconstruction, where the bone thickness typically ranges from 2 to 12 mm. Given that CT data are often resampled to isotropic spacing (approximately 1 mm), a (3 × 3 × 3) kernel corresponds well to the physical scale of relevant anatomical features, enabling accurate modeling without over-smoothing.

From a computational standpoint, the results also demonstrate that increasing kernel size leads to a non-linear increase in training time, while accuracy gains quickly saturate. Therefore, selecting an appropriate kernel size is crucial not only for reconstruction performance but also for maintaining computational efficiency.

Overall, these findings confirm that kernel size is a critical factor in balancing spatial feature representation and computational cost. The results further support the importance of carefully tuning network parameters in conjunction with data-related factors to achieve optimal performance.

4.5. Loss Function Selection

Loss functions play a critical role in guiding the optimization process of convolutional neural networks, particularly in medical image segmentation tasks characterized by strong class imbalance and complex boundary structures. In cranial defect reconstruction, the defective region typically occupies only a small portion of the overall 3D volume, making accurate boundary prediction more challenging than volumetric overlap. As shown in Figure 8, the conventional Dice loss improves volumetric agreement between predicted and ground-truth regions by directly optimizing overlap. However, it does not explicitly penalize local boundary discrepancies. As a result, models trained with Dice loss alone tend to produce over-smoothed predictions, especially near defect edges, where precise geometric reconstruction is essential. To address this limitation, a hybrid loss function combining Dice loss and boundary loss was employed. The boundary loss component incorporates distance-based information by penalizing deviations along the contour between predicted and reference masks. This allows the model to focus not only on region-level accuracy but also on boundary precision, which is critical for ensuring anatomically consistent implant shapes. Experimental results demonstrate that the hybrid loss improves both DSC and HD simultaneously. Specifically, the DSC increased from approximately 0.92 to 0.94, while the HD decreased from about 4.46 mm to 3.8 mm. While the improvement in DSC appears moderate, the reduction in HD is more significant, indicating enhanced boundary alignment and reduced local geometric errors. From an optimization perspective, the combination of region-based and boundary-aware losses provides complementary learning signals. Dice loss stabilizes global convergence by ensuring volumetric consistency, whereas boundary loss refines local structures by emphasizing edge accuracy. This synergy leads to more stable training behavior, as evidenced by the reduced variance in HD across test samples. In the context of cranial reconstruction, boundary accuracy is particularly important, as even small deviations can affect implant fitting and postoperative outcomes. Therefore, the observed reduction in HD suggests that the hybrid loss function contributes directly to improved clinical applicability of the reconstructed implants. Overall, these results confirm that loss function design is a critical factor in balancing volumetric accuracy and geometric precision. The proposed hybrid Dice–boundary loss provides a more effective optimization objective for cranial defect reconstruction compared to conventional region-based losses.

4.6. Summary of Findings

As summarized in

Table 7. Comparison of DSC and HD values with representative studies.

Study	Dataset	Method	DSC	HD (mm)	Notes
This work	MUG500	3D UNet	0.94	3.8	Single-network architecture
Juneja et al. (2025) [13]	MUG500	CRIGNet	0.98	4.63	Synthetic defects with simple geometric shapes
G. Mainprize et al. (2020) [39]	AutoImplant 2020	UNet	0.87	6.72	Limited dataset size (<300 cases)
Li et al. (2020) [18]	AutoImplant 2020	Encoder-decoder	0.85	5.18	Two-stage multi-network architecture
G. Ellis et al. (2020) [40]	AutoImplant 2020	UNet	0.94	3.60	Limited dataset size (<100 cases)
Matzkin et al. (2020) [19]	CQ500	DE-UNet	0.90	4.47	Synthetic defect generation

, the proposed method achieves competitive reconstruction accuracy compared with representative studies reported in the literature, while maintaining a simple single-network architecture and moderate computational requirements. Although the results are obtained on different datasets and experimental protocols, the comparison indicates that the proposed approach provides a favorable balance between accuracy and practical applicability.

Denoising and isotropic resampling further stabilized training by reducing background artifacts, while a kernel size of (3 × 3 × 3) achieved the optimal trade-off between feature extraction and computational efficiency. Training with morphologically diverse defects significantly improved model generalization to unseen geometries, as reflected by a consistent increase in DSC and a reduction in variance across test samples.

Figure 9 provides a comprehensive overview of the performance trends across all experimental configurations, evaluated using the Dice Similarity Coefficient (DSC) and Hausdorff Distance (HD). Among the investigated settings, the optimal configuration-comprising denoised input data, a (3 × 3 × 3) convolutional kernel, a hybrid Dice–boundary loss, and a morphologically diverse training dataset-achieved the best overall performance, with a DSC of 0.94 and an HD of 3.8 mm.

A key observation from these results is that reconstruction performance is not governed by a single dominant factor, but rather emerges from the interaction of multiple data-centric and training-related components. Specifically, denoising contributes primarily to boundary stabilization, leading to significant reductions in HD, while defect morphology diversity enhances generalization capability, reflected in improved DSC values. Dataset organization further improves convergence stability, and kernel size determines the balance between local feature extraction and global contextual understanding.

Figure 10 illustrates the optimized configuration derived from this systematic analysis, highlighting how the coordinated selection of preprocessing, network parameters, and loss design leads to optimal performance. This demonstrates that substantial improvements can be achieved without increasing architectural complexity, emphasizing the effectiveness of a data-centric optimization strategy.

To further validate the proposed method, Table 7 compares its performance with representative studies in the literature. Despite differences in datasets and evaluation protocols, the proposed approach achieves competitive results while maintaining a relatively simple single-network architecture. Notably, some existing methods report high DSC values but relatively larger HD, indicating that volumetric overlap alone does not guarantee geometric accuracy. In contrast, the proposed method achieves a balanced improvement in both DSC and HD, which is critical for ensuring anatomically accurate implant reconstruction.

As shown in

Table 8. Reconstruction results for each cranial region.

Position	Frontal	Parietal	Right Temporal	Left Temporal	Occipital
Defective
Ground Truth Implant
Reconstructed Implant

, five representative morphologies corresponding to the five cranial regions (frontal, parietal, left and right temporal, and occipital) are illustrated. Visual inspection shows that the reconstructed implant closely matches the ground-truth implant geometry, preserving curvature and boundary continuity. These results verify that the optimized configuration enables robust and accurate cranial implant reconstruction across diverse morphological and positional variations.

Table 9. Deep learning-based defect reconstruction of complex cranial defects.

Case	Defective Skull	Reconstruction Result
1
2

illustrates reconstruction results for more complex defect geometries. In Case 1, a real patient case (from Hanoi Medical University Hospital) with a frontal defect of irregular shape was used. The reconstructed implant, after post-processing with a surface-smoothing operation, accurately restored the defect region. In Case 2, a complete skull from the MUG500 dataset was manually modified in 3D Slicer to create an irregular defect, which was then reconstructed by the proposed model (shown as Reconstructed implant). In both cases, the reconstruction time and geometric accuracy were comparable to those reported in Table 8, confirming the model’s robustness and adaptability to complex cranial geometries. Overall, the findings of this study strongly support the central hypothesis that data-centric optimization strategies, including preprocessing, dataset design, and loss function selection, can have an impact comparable to or greater than architectural complexity in cranial defect reconstruction. These results provide a practical and reproducible guideline for developing efficient and robust deep learning-based systems, emphasizing that performance gains can be achieved through systematic optimization of the training pipeline rather than relying solely on increasingly complex network architectures.

5. Conclusions and Future Works

This study presented a systematic and controlled investigation of data-centric and training-related factors affecting cranial defect reconstruction using a baseline 3D UNet architecture. Unlike many existing approaches that focus primarily on architectural modifications, this work emphasizes the role of data preprocessing, dataset organization, defect morphology diversity, convolutional kernel size, and loss function design in determining reconstruction performance.

Experimental results demonstrate that these factors have a substantial impact on both volumetric accuracy and geometric precision. In particular, denoising significantly improves boundary stability and reduces geometric error, as reflected by a notable decrease in Hausdorff Distance. Incorporating diverse defect morphologies enhances generalization capability to unseen shapes, while structured dataset organization contributes to more stable convergence. In addition, the selection of an appropriate kernel size enables an effective balance between local feature extraction and global anatomical context modeling. The proposed hybrid Dice–boundary loss further improves boundary accuracy by integrating complementary optimization objectives.

The optimized configuration achieved a Dice Similarity Coefficient of 0.94 and a Hausdorff Distance of 3.8 mm, with an average inference time of 0.004 s per case. These results fall within clinically acceptable tolerance for patient-specific cranial implant fabrication, demonstrating both high geometric fidelity and computational efficiency. Importantly, this performance is achieved using a relatively simple single-network architecture, highlighting that carefully designed data-centric strategies can yield results comparable to more complex deep learning models.

A key contribution of this work is the establishment of a reproducible optimization framework that isolates and quantifies the influence of individual factors under controlled experimental conditions. This provides practical guidelines for developing efficient and robust deep learning pipelines for medical image reconstruction, and suggests that data quality and training strategy can play a role as critical as, if not more important than, network architecture.

Despite these promising results, several limitations remain. The experiments were conducted primarily on synthetically generated defects, which may not fully capture the complexity of real clinical cases. Additionally, while the proposed framework demonstrates strong generalization across different defect morphologies, further validation on multi-center clinical datasets is necessary to ensure robustness in diverse real-world scenarios.

Future work will focus on extending this framework in three main directions. First, incorporating real patient-specific defect data will improve clinical relevance and enable more realistic evaluation. Second, integrating anatomical priors, such as symmetry constraints or statistical shape models, may further enhance reconstruction accuracy for highly irregular defects. Third, advanced architectures, including attention mechanisms and transformer-based models, can be explored on top of the optimized baseline to further improve performance while maintaining computational efficiency.

Overall, this study demonstrates that systematic optimization of data and training strategies provides a powerful and practical approach for improving cranial defect reconstruction. The findings contribute to bridging the gap between deep learning research and clinical application, offering a scalable and efficient solution for patient-specific implant design.

6. Contributions

The main contributions of this work are summarized as follows:

• The impact of kernel size and loss function design on reconstruction accuracy is quantitatively analyzed.
• A boundary-aware loss function is shown to significantly improve implant surface continuity.
• The proposed model achieves competitive performance, demonstrating its suitability for clinical applications.
• A controlled optimization framework is proposed, where five factors (denoising, data arrangement, morphology diversity, kernel size, loss function) are evaluated independently and jointly.