Why accurate tumor outlining matters. Before radiotherapy can be delivered, radiation oncologists must manually draw the exact boundaries of the tumor - a process called Gross Tumor Volume (GTV) segmentation. This determines precisely where high-dose radiation will be aimed. The process is time-consuming and introduces significant variability between different physicians, which can affect treatment quality and reproducibility.
Transfer learning as a solution. Deep learning models can automate segmentation, but training them from scratch requires large amounts of annotated medical images - expensive and slow to collect. A widely used alternative is transfer learning: pre-train a model on a large existing dataset, then fine-tune it with a smaller set of institution-specific medical images. The choice of pre-training dataset strongly affects how well the final model performs.
The problem with ImageNet. ImageNet - a collection of 1.28 million labeled photographs of everyday objects like cats and birds - is the most common pre-training dataset for medical image AI. However, these images look very different from CT scans of lung tumors, potentially causing negative transfer: the pre-trained knowledge may actually interfere with learning medical image patterns rather than helping.
A fractal alternative. Lung cancer tumors on CT scans exhibit fractal properties - irregular, self-similar patterns that repeat at different scales. Fractal images, which can be generated mathematically without any real-world photographs or human labels, share these structural properties. This study proposes using mathematically generated fractal images as pre-training data, hypothesizing they provide a morphologically closer starting point than everyday photographs.
Iterated Function Systems. Fractal images are generated using mathematical equations called Iterated Function Systems (IFS). Starting from a single point, the algorithm repeatedly applies a set of random affine transformations - mathematical operations that stretch, rotate, and shift points in space - 200,000 times per image. The resulting scattered points form intricate self-similar patterns that mirror structures found in nature.
FractalDB: a license-free training database. The FractalDB dataset was constructed by systematically varying the IFS parameters to create thousands of distinct fractal categories, each with many image variations. Because the images are generated entirely by equations, they have no copyright issues, require no human labeling effort, and can be shared freely - removing two major barriers to building large pre-training datasets.
Self-supervised learning with pseudo-labels. Unlike ImageNet where labels (cat, bird) are assigned by humans, FractalDB uses the mathematical parameters that generated each fractal category as automatic pseudo-labels. The AI model learns to predict these parameters - a self-supervised task that forces it to understand the geometric structure of the images without any human annotation. This approach eliminates the most expensive step in building training datasets.
Two dataset scales tested. This study tested two sizes of FractalDB: FractalDB-1K with 1,000 fractal categories and 1 million images (comparable to ImageNet-1K in scale), and FractalDB-10K with 10,000 categories and 10 million images. Scaling up allowed the researchers to test whether more diverse fractal structures would further improve segmentation performance.
104 patients with early-stage lung cancer. The study enrolled 104 patients (aged 36 to 91 years; 81 male, 23 female) with peripheral early-stage non-small cell lung cancer who received radiotherapy at the University of Yamanashi between December 2017 and March 2025. GTV contours were drawn by an experienced radiation oncologist and reviewed by at least three senior physicians during departmental conferences.
Two model architectures tested. The study compared two types of deep learning segmentation models: DeepLabV3+, a Convolutional Neural Network (CNN) that processes images by detecting local patterns through convolutional filters, and Dense Prediction Transformer (DPT), a Vision Transformer model that captures global spatial relationships across the entire image using self-attention. Both were adapted to handle the small 64x64 pixel tumor-centered regions used in this study.
Four pre-training strategies compared. Each model architecture was tested with four pre-training approaches: training from scratch with no pre-training, pre-training with ImageNet-1K, pre-training with FractalDB-1K, and pre-training with FractalDB-10K. This created eight total model variants evaluated through fourfold cross-validation on the 104 patient dataset.
Three complementary accuracy metrics. Segmentation accuracy was measured using volumetric Dice Similarity Coefficient (vDSC, how well volumes overlap), surface Dice Similarity Coefficient (sDSC, how well contour boundaries agree), and 95th percentile Hausdorff Distance (HD95, maximum distance between predicted and ground truth boundaries, excluding extreme outliers). Using all three metrics provides a comprehensive picture since each captures different aspects of segmentation quality.
Best model: DPT with FractalDB-10K. The Vision Transformer model pre-trained on FractalDB-10K achieved the best performance across all three metrics: volumetric DSC of 0.800 plus or minus 0.079, surface DSC of 0.732 plus or minus 0.152, and HD95 of 2.04 plus or minus 1.59 mm. This result is notable because the model was trained on only 104 patient cases - a relatively small dataset by deep learning standards - yet achieved accuracy comparable to studies using larger multi-modality datasets including PET/CT.
Consistent improvement with fractal pre-training. Across both model architectures, accuracy consistently ranked in the same order: FractalDB-10K outperformed FractalDB-1K, which outperformed ImageNet-1K, which outperformed training from scratch. This monotonic improvement with fractal dataset scale suggests performance had not yet plateaued, and larger fractal datasets could provide additional gains.
Vision Transformers beat CNNs on most metrics. The DPT transformer model outperformed DeepLabV3+ on vDSC and sDSC for all pre-training strategies, consistent with the known advantage of transformer self-attention for capturing global spatial context - important for understanding tumor shape and boundaries relative to surrounding anatomy. However, DeepLabV3+ showed better HD95 in some conditions due to fewer extreme prediction errors in individual slices.
ViT stability requires large pre-training. A known weakness of Vision Transformers is instability with insufficient pre-training, sometimes producing large errors in individual image slices. With FractalDB-1K pre-training, DPT showed more outlier predictions. With FractalDB-10K, outlier frequency decreased substantially and HD95 improved significantly, confirming that larger fractal datasets are needed to stabilize transformer performance.
Subgroup analysis by tumor shape complexity. The researchers divided the 104 cases into two equal groups based on surface-to-volume ratio (SVR), a measure of shape complexity. Tumors with higher SVR have more intricate, irregular boundaries and less sphere-like shapes. This analysis tested whether fractal pre-training specifically improved accuracy for the complex, irregular tumors that are morphologically most similar to fractal structures.
Simple tumors: no significant difference. For simple, sphere-like tumors with low surface-to-volume ratios, no statistically significant difference in accuracy was found between FractalDB-1K and ImageNet-1K pre-training. When the target shape is relatively simple, the source of pre-training knowledge matters less - both datasets provide adequate initial feature representations.
Complex tumors: fractal wins significantly. For complex, irregularly shaped tumors, FractalDB-1K pre-training yielded significantly higher accuracy than ImageNet-1K (vDSC 0.743 versus 0.714, p=0.006). This selective advantage directly supports the hypothesis: fractal pre-training improves performance specifically for the complex, fractal-like tumor shapes where morphological similarity between the pre-training data and the target task is highest.
Clinical importance of complex shape segmentation. Complex irregular tumors are precisely the cases where manual segmentation is most challenging, inter-observer variability is highest, and automated assistance would be most valuable. The finding that fractal pre-training preferentially improves accuracy for these difficult cases has direct practical relevance for radiotherapy planning.
Morphological relevance as the key mechanism. Prior research established that lung cancer tumors on CT images exhibit fractal properties - their boundaries show the same kind of irregular self-similar complexity as mathematical fractal structures. By pre-training on images with similar geometric complexity, the model learns representations that transfer more effectively to tumor segmentation than representations learned from unrelated natural photographs.
Avoiding negative transfer from ImageNet. When an AI model is pre-trained on images that look very different from its eventual target, the pre-training can actually interfere with learning the new task - a phenomenon called negative transfer. ImageNet photographs of animals and objects carry visual patterns that are not just irrelevant but potentially misleading for medical image analysis. Fractal images, while synthetic, avoid this problem by sharing structural properties with CT tumor morphology.
Practical advantages for smaller institutions. FractalDB has been publicly released with image generation code and pre-trained model weights freely available. This means any hospital or research center can use these pre-trained models as a starting point, then fine-tune with their own institution-specific patient data - even in small quantities. This democratizes access to high-quality pre-training without requiring expensive data collection, annotation, or computational resources for initial training.
No annotation cost, no copyright issues. Because fractal images are generated mathematically with parameters serving as automatic labels, FractalDB requires no human labeling effort. Because the images are entirely synthetic, they have no copyright restrictions. These two advantages eliminate major practical barriers to building large-scale pre-training datasets for medical AI, making fractal-based SSL a broadly accessible methodology.
Core finding confirmed. Pre-training with mathematically generated fractal images achieves superior segmentation accuracy compared to ImageNet pre-training and training from scratch for early-stage lung cancer GTV delineation. The best model, combining Vision Transformer architecture with FractalDB-10K pre-training, achieved vDSC of 0.800 using only 104 patient cases - results comparable to prior studies using larger multi-modality datasets.
Generalizability to other cancers. While this study focused on lung cancer, fractal properties have also been reported in breast cancer and hepatocellular carcinoma. Future research should test whether fractal pre-training provides similar benefits for tumor segmentation in other cancer types, which could extend this methodology across oncological radiotherapy planning broadly.
2D limitation and the case for 3D extension. All analysis was performed on individual 2D CT image slices rather than full three-dimensional volumes. Clinical CT data is inherently three-dimensional, and three-dimensional segmentation approaches can capture spatial information across slices that 2D methods miss. Extending fractal pre-training to 3D frameworks using 3D fractal images is identified as a critical next step for improving clinical performance.
Single institution and dataset scale limitations. The study was conducted at a single institution with 104 patients, which limits the generalizability of specific settings like ROI size, resolution, and hyperparameters to other sites with different CT equipment and patient populations. The performance plateau with larger fractal datasets was not reached, suggesting that even larger FractalDB variants - requiring supercomputer-scale resources to generate - could provide further improvements.