Accelerating Neural Signed Distance Field Ray Marching via Idempotent Curvature Contraction and In-Situ Empty Space Culling

Abstract

Neural Signed Distance Fields (Neural SDFs) provide compact, continuous, and topologically flexible geometric representations for inverse rendering, generative 3D modeling, and scientific visualization. However, real-time ray casting through neural implicit volumes remains severely constrained by computational cost: unlike analytical primitives, every ray marching step incurs multiple spatial feature hash lookups and multi-layer perceptron (MLP) forward evaluations. Classical sphere tracing exhibits acute ray deceleration near grazing silhouettes due to conservative Lipschitz step sizing, while aggressive overstepping heuristics frequently cause tunneling and overshoot across thin boundaries. Furthermore, traversing unculled empty space between the camera frustum and active geometric boundaries squanders dozens of redundant neural evaluations per primary ray. In this paper, we introduce a unified, zero-heap neural ray marching architecture that couples in-situ empty space bounding volume culling with an analytical Jacobian directional curvature contractor and an idempotent zero-level-set manifold projection (Phit2 = Phit). By integrating exact analytical backpropagation through multi-resolution hash grids and TinyMLPs directly into AVX2 vector registers, our architecture computes directional curvature and analytical surface normals in a single evaluation with strictly zero auxiliary memory reads, eliminating numerical finite-difference stencil overhead. Through an extensive empirical ablation across three authentic real-world datasets spanning distinct geometric domains—the Stanford Bunny 3D range scan (35,947 vertices), authentic human cortical geometry featuring dense sulcal folds, and an ASME B16.5 industrial CAD flange—we isolate the distinct contributions of geometric bounding volume culling and analytical curvature contraction. On the Stanford Bunny (512×512), IdemRender achieves 55.87 ms (4.69 MRays/s), delivering a 1.34× wall-clock speedup over classical sphere tracing (74.60 ± 3.91 ms, 3.51 MRays/s) and slashing iteration steps from 12.50 to 5.85 steps/ray, while delivering over 219 FPS at 1282 (4.56 ± 0.37 ms). Concurrently, in-situ culling and bounded exit clamping deliver up to 3.72× speedup on CAD (16.66 ± 0.10 ms, 15.73 MRays/s) and 3.34× on Cortex (22.57 ± 0.88 ms, 11.62 MRays/s). Furthermore, whereas relaxed sphere tracing catastrophically collapses (yielding hit rates of only 0.87% on Cortex and 2.92% on CAD due to overstepping tunneling), our adaptive formulation eliminates tunneling entirely, achieving >99.9% geometric hit agreement on continuous scan geometry (Stanford Bunny: 34.06% vs. 34.08%) and >99.2% on CAD (7.56% vs. 7.62%), while resolving step-limit stalls in narrow anatomical fissures on Human Cortex (2.60% vs. 2.00% on unculled classical tracing), with near-zero operator idempotency error (~10-3). The accompanying SIMD AVX2 C++ engine executes with strictly O(1) stack allocation (< 1.0 KB) and zero dynamic heap allocation, providing hard deterministic bounds for interactive neural graphics on compute-constrained edge platforms.