Coarse Tumor Synthesis Process

• Coarse tumor synthesis is the initial phase in artificial tumor generation that establishes tumor geometry, location, and context in 3D medical images.
• It employs both modeling-based methods, like cellular automata and geometric warps, and learning-based approaches, including GANs and diffusion models, to simulate realistic tumor structures.
• The process creates a scaffold for subsequent fine texture refinement and enables effective data augmentation for segmentation, detection, and classification in medical imaging.

Coarse tumor synthesis is the initial, geometry- and context-determining phase of artificial tumor generation in medical images. This process generates control over tumor shape, location, and overall “first draft” appearance in 3D volumes, providing a scaffold upon which detailed textural refinement can subsequently be built. Coarse synthesis is central to most modern tumor generation frameworks, encompassing both modeling-based cellular automata, radiomics- or mask-conditioned GANs, and mask- or bounding-box–guided diffusion models. It aims to efficiently sample anatomically plausible, diverse, and quantitatively controllable tumor insertions that can be used for data augmentation in segmentation, detection, and classification tasks. The following sections organize and synthesize technical details of coarse tumor synthesis across leading approaches.

1. Core Methodological Taxonomy

Current coarse tumor synthesis methods are broadly divided into modeling-based and learning-based paradigms (Chen et al., 9 Sep 2024):

• Modeling-based methods: Rely on hand-crafted rules (cellular automata, geometric models, pathomimetic progression) for tumor growth and invasion. Key representatives: Pixel2Cancer (Lai et al., 11 Mar 2024), explicit ellipsoid-plus-elastic models (Li et al., 2023).
• Learning-based methods: Use machine learning to sample masks or initial tumor impressions, typically conditioning generative models (GANs, diffusion, VAE) on shape, radiomics, or anatomical priors. Approaches include radiomics-guided GANs (Kim et al., 29 Sep 2025, Na et al., 2023), mask-conditioned diffusion (Chen et al., 29 Feb 2024, Yang et al., 3 Sep 2025), multi-stage mask/image GAN pipelines (Wu et al., 23 Feb 2025, Wu et al., 3 Jun 2024), and pseudo-mask with rectified flow matching (Liu et al., 30 May 2025).

These coarse stages uniformly precede secondary refinement, where fine-scale texture and intensity characteristics are imposed.

2. Pipeline Structure and Key Algorithms

Modeling-Based: Cellular Automata and Geometric Warps

Cellular automata (CA) models (Lai et al., 11 Mar 2024) proceed via:

• State variable assignment: Assign each voxel a discrete tumor cell population $s_i(t)\in\{-1,0,\dots,10\}$.
• Rule-based dynamics: Iterative neighborhood progression—proliferation with probability $p_g$, invasion into neighbors depending on tissue quantization and crowding ($L_j$, $c_i$), and necrosis with probability $p_d$ in overcrowded regions.
• Spatial constraints: Tissue awareness by HU-based quantization, tissue-dependence of growth/invasion probabilities.
• Intensity mapping: Synthetic image intensity at voxel $i$ is

$$H_i^{\rm syn} = (1-\alpha_i)\,H_i^{\rm orig} + \alpha_i\,H_{\rm tum} + \varepsilon_i,$$

where $\alpha_i = \mathrm{clamp}(s_i/S_{\max},0,1)$.

Geometric methods, e.g., in pancreatic cancer (Li et al., 2023), sample ellipsoid axes according to empirical or parametric distributions and apply elastic warping to the mask to increase realism, then blend with local intensity regression and texture sampling for the coarse tumor region.

Learning-Based: GANs, Diffusion, and Hybrid Approaches

• Random Mask Sampling and Mask-Augmentation: Many approaches begin by generating a binary mask $M$ of plausible tumor shape and location, either via random ellipsoidal sampling (Wu et al., 23 Feb 2025, Wu et al., 3 Jun 2024), spatial box expansion (Liu et al., 30 May 2025), augmentation of real masks (Dong et al., 23 Nov 2025), GAN-generated masks conditioned on radiomics (Kim et al., 29 Sep 2025), or via radiomics-guided latent injection (Na et al., 2023).
• Image Synthesis in Masked Regions: The mask defines the region to be replaced or altered. Subsequent operations include:
  • Blurring and linear intensity remapping (Dong et al., 23 Nov 2025).
  • Inpainting using gated or dilated convolutional generators (e.g., RicherDG in (Jin et al., 2021), DeepFillv2 variant in (Na et al., 2023)).
  • Conditioning a latent diffusion model to “paint” tumors in the latent space of a VQ-VAE/3D-VQGAN (Chen et al., 29 Feb 2024, Yang et al., 3 Sep 2025, Biller et al., 10 Oct 2025).
  • Rectified flow matching to sample both latent features and mask in a single forward ODE process (Liu et al., 30 May 2025).
• Objective Functions:
  • Adversarial losses—discriminator-based realism checks (Wu et al., 23 Feb 2025, Jin et al., 2021, Na et al., 2023).
  • Segmentation-driven losses—requiring a pre-trained segmenter to recognize synthetic tumor regions as real (Wu et al., 3 Jun 2024, Wu et al., 23 Feb 2025).
  • Perceptual, feature-space, and mask similarity losses—e.g., L1/L2 distance in pretrained CNN feature spaces (Dong et al., 23 Nov 2025), radiomics feature consistency (Kim et al., 29 Sep 2025, Na et al., 2023).
• Filtering and Quality Assurance: Many methods filter coarse syntheses by requiring a threshold proportion of voxels in the mask to be identified as tumor by a segmenter (Wu et al., 23 Feb 2025, Wu et al., 3 Jun 2024).

3. Mathematical Formulations

Example: Mask-Augmentation and Blending

From (Dong et al., 23 Nov 2025), the coarse image transformation is:

• Mask augmentation: $$m_s = \mathrm{Combine}_{j \in J}\left[T_{s,t}(m_r^j)\right]$$
• Blur operator: $$B(x_h, m_s) = x_h \odot (1-m_s) + (G_{\sigma=2} * x_h) \odot m_s$$
• Intensity remapping:

$$I(x, m_s) = x \odot (1-m_s) + \sum_{k=1}^{C_t} (a_k x + b_k) \odot 1_{[m_s = k]}$$

with $a_k, b_k$ regressed to match UNet feature-space embeddings of real tumors.

Example: GAN-based Shape Generation

From (Kim et al., 29 Sep 2025):

• Generator $$G: (z, r_{sh}) \to M \in \{0,1\}^{H \times W \times D}$$.
• Losses:

  $$\mathcal{L}_G = \mathcal{L}_G^{\rm adv} + \lambda_{\rm shape}\,\mathcal{L}_{\rm shape}$$

with shape-consistency

$$\mathcal{L}_{\rm shape} = \mathbb{E}_{z, r_{sh}}\|F_{\rm shape}(G(z, r_{sh})) - r_{sh}\|_1$$

cross-attended through generator blocks.

Example: Diffusion- and Flow-Based Coarse Synthesis

In mask-conditioned latent diffusion (e.g., (Chen et al., 29 Feb 2024, Yang et al., 3 Sep 2025, Biller et al., 10 Oct 2025)), Denoising Diffusion Probabilistic Models (DDPMs) or Rectified Flow Matching (RFM) are applied in the latent space:

• Forward diffusion: $$q(z_t|z_{t-1}) = \mathcal{N}(z_t; \sqrt{1 - \beta_t}z_{t-1}, \beta_t I)$$
• Reverse sampling (LDM): $$z_{t-1} = 1/\sqrt{1-\beta_t}(z_t - \beta_t/\sqrt{1-\bar{\alpha}_t}\epsilon_\theta( \cdot)) + \sqrt{ \beta_t } \eta$$.

In RFM (Liu et al., 30 May 2025):

• ODE-like path: $x_t = (1-t)\epsilon + t x_1$; vector field $v_\theta(x_t, z^m, t) \approx x_1 - \epsilon$
• Losses enforce both coarse box constraint and fine mask accuracy via SSIM.

4. Parameterization and Control

Parameter	Role in Coarse Synthesis	Typical Effects
Shape parameters	Ellipsoid, sphericity, surface, etc.	Control tumor size, roundness, elongation
Position sampling	Mask center/random sampling	Uniform tumor insertion across organ
Deformation/noise	Elastic warps, noise, smoothing	Local boundary variability, non-circularity
Intensity mapping	Linear regression, mean/variance, blur	Set global contrast, suppress high-freq texture
Conditioning vector	Radiomics, tissue maps, segmentation	Enforce global statistics, anatomy-aware
Filtering threshold	Min fraction of mask detected as tumor	Discard unrecognizable or implausible masks

These parameters are often manipulated to generate diversity and maintain anatomical validity.

5. Evaluation Strategies and Metrics

• Dice Similarity Coefficient (DSC) and Normalized Surface Dice (NSD) measure overlap and contour accuracy between synthetic (or synthetic-trained) segmentation and real ground-truth (Lai et al., 11 Mar 2024, Dong et al., 23 Nov 2025, Chen et al., 29 Feb 2024).
• Visual Turing Tests: Clinical radiologists distinguish real from synthetic. Coarse-tumor methods (Pixel2Cancer (Lai et al., 11 Mar 2024), FreeTumor (Wu et al., 23 Feb 2025), radiomics-based GANs (Kim et al., 29 Sep 2025)) often produce synthetic tumors that experts cannot reliably distinguish—specificity routinely under 60%.
• Fréchet Inception Distance (FID): Quantifies feature-space similarity of real and synthetic tumor patches (Wu et al., 23 Feb 2025).
• Feature-space or radiomics similarity: Pearson/Spearman correlations and cosine similarity in shape and texture features between synthesized and real tumors (Kim et al., 29 Sep 2025, Na et al., 2023).
• Downstream performance: Measuring segmentation or detection accuracy/Sensitivity using networks trained on synthetic-augmented datasets (Wu et al., 3 Jun 2024, Chen et al., 29 Feb 2024, Li et al., 2023).

6. Limitations, Trade-Offs, and Extensions

Common limitations of coarse tumor synthesis include:

• Inability to model micro-textural heterogeneity, micronecrosis, or infiltrative boundaries (especially in pure CA or geometric approaches) (Chen et al., 9 Sep 2024).
• Manual or semi-automatic parameter tuning is required for new organ sites (Li et al., 2023, Lai et al., 11 Mar 2024).
• Coarse GAN or mask-sampling approaches rely on subsequent refinement to achieve photorealism; coarse stages alone are optimized for geometric fidelity, not detailed intensity variation (Dong et al., 23 Nov 2025).
• Mask design (fixed, randomized, or radiomics-conditioned) can limit anatomical plausibility, though recent advances in radiomics-feature and spatial constraint learning (Kim et al., 29 Sep 2025, Liu et al., 30 May 2025) mitigate this.
• Severe artifacts may result unless filtered by segmentation or human review; filtering thresholds improve downstream model accuracy (Wu et al., 3 Jun 2024, Wu et al., 23 Feb 2025).

Potential improvements include finer-scale conditional texture synthesis, automated organ transfer via learned generalization (Chen et al., 29 Feb 2024), and biomechanical modeling for boundary realism.

7. Comparative Summary of Leading Frameworks

Method	Mask Generation	Conditioning	Synthesis Model	Filtering/QC	Noted Metrics / Outcomes
Pixel2Cancer	CA-rule, spherical	Tissue map	Rule-based CA	None	DSC/NSD: real ≈ synthetic (Lai et al., 11 Mar 2024)
DiffTumor	Manual or random	Mask, latent code	VQGAN+diffusion	Optionally via heuristics	DSC +10.7% vs. cross-organ (Chen et al., 29 Feb 2024)
FreeTumor	Random ellipsoid	Organ location	U-Net GAN	Segmentation threshold	Sensitivity ≈ real, FID: 23.5 (Wu et al., 23 Feb 2025, Wu et al., 3 Jun 2024)
TF-Aug	Augmented real masks	Feature extractor	Blur+linear layer	Feature-space loss only	+0.3% DSC gain pre-refinement (Dong et al., 23 Nov 2025)
TumorGen	Bounding box (box pm)	VAE latent+mask	Rectified flow	Mask refiner, ODE steps	FID ≈52 at 50 steps, fast (<0.25s)(Liu et al., 30 May 2025)
RadiomicsFill	Radiomics-driven	Radiomics features	DeepFillv2 GAN	Adversarial loss	>0.9 correlation mask-real shape (Na et al., 2023, Kim et al., 29 Sep 2025)
FRGAN	Free-form mask	Patch/shape mask	Gated/dilated GAN	Multi-mask/adv. loss	+1–3% Dice, sharp edges (Jin et al., 2021)

The coarse synthesis process, regardless of architectural choice, is both a generative modeling challenge (diversity, anatomical plausibility) and a pipeline design challenge (efficient sampling, filtering for downstream utility). Its product—a semantically valid, geometry-faithful tumor “draft”—is the essential prerequisite for further realistic refinement and data-driven medical image augmentation.