HR-IDF: Hessian-Regularized Implicit Displacement Fields for high precision industrial assembly representation

Representing high-precision industrial assemblies characterized by complex structural features remains challenging. In this paper, we propose Hessian-Regularized Implicit Displacement Fields (HR-IDF), a framework that integrates a two-scale neural implicit representation with Hessian-based regularization. In a coarse-to-fine manner, our method generates a smooth base surface from mesh-sampled points and then refines it with a high-frequency displacement field to capture fine geometric details. Moreover, we introduce a relaxed off-surface loss that helps preserve a more consistent gradient in the generated SDF field, while suppressing ghost geometry and improving representation stability and fidelity. Extensive experiments on complex industrial assemblies and 3D models demonstrate that HR-IDF achieves a reliable solution for high-precision industrial applications. • Two-scale implicit model with Hessian regularization suppresses ghost surfaces. • Relaxed off-surface loss stabilizes signed distance gradients, reducing artifacts. • Coarse-to-fine design gives compact high-fidelity assembly representation. • Compact model matches baseline size, trains faster, and preserves detail. • State-of-the-art accuracy on complex industrial assemblies and raw Sketchfab models.