Title: SCOPE-MIA: Scale-Consistent Partial Differential Equation-Optimized Encoding in 3D Medical Imaging Analysis
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: 3D Medical Image Analysis, Partial Differential Equations, Deep Learning, 3D Convolutional Neural Networks, Radiomics

Abstract: Medical scans such as Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) are inherently 3D, capturing rich volumetric information about patient anatomy and pathology. Analyzing this data requires models sensitive to both large-scale anatomical structures and fine-grained textural details. While traditional handcrafted radiomics features often miss subtle multi-scale relationships, standard 3D Convolutional Neural Networks (CNNs) learn data-driven filters without explicit mechanisms to disentangle structural and textural information. This entanglement can limit model interpretability and robustness. We propose SCOPE-MIA, a 3D framework driven by Partial Differential Equations (PDEs) that explicitly decomposes learned features into distinct anatomical and textural components. By embedding tailored PDE constraints - such as structure-enhancing diffusion for anatomy and detail-preserving flows for texture - into a modern 3D CNN architecture, we promote the learning of robust, scale-explicit, and disentangled representations. Our system processes volumetric data in tractable subvolumes for efficient training, while a sliding window approach during inference recovers the full 3D context. We present a unified mathematical treatment connecting PDE theory to our dual-pathway architectural design and discuss the advantages of this decomposition for clinical applications. Extensive experimental validations demonstrate that our method significantly outperforms the clinical gold-standard radiomics pipeline in challenging cancer imaging tasks, showing its potential to advance tumor characterization and biomarker discovery.