$K$-NeAS: Scalable Multi-Material CT Reconstruction Using Neural SDFs

Computed Tomography (CT) carries significant ionizing radiation risks, driving the need for sparse-view reconstruction. Implicit scene representations (ISRs) address this by recovering continuous volumetric attenuation fields directly from sparse projections, and recent geometry-aware extensions jointly model surface geometry alongside attenuation to improve fidelity and enable clean tissue segmentation without manual thresholding. However, these methods remain limited by manually tuned attenuation bounds and rigid two-material constraints. This paper proposes $K$-NeAS, a unified and scalable architecture for automated, multi-material surface reconstruction. We replace independent material networks with a shared latent backbone and introduce a fully differentiable $K$-material sequential soft selector to model an arbitrary number of overlapping tissues. To eliminate manual tuning, we automate attenuation bounding using a Gaussian Mixture Model (GMM) and implement a scheduled auxiliary floater loss to mitigate geometric hallucinations common under extreme sparsity. Evaluated across four clinical Cone-Beam CT (CBCT) datasets, $K$-NeAS successfully scales to arbitrary material counts, achieving superior 3D volumetric fidelity at $K=3$ materials on complex multi-tissue regions such as the Abdomen ($33.28\text{ dB}$ 3D PSNR vs. $31.40\text{ dB}$ single-material NeAS baseline, a $+1.88\text{ dB}$ improvement). Furthermore, our model exhibits enhanced robustness under sparse-sampling conditions, outperforming baseline 3D PSNR by up to $1.17\text{ dB}$ under 5- and 10-view constraints.