Patch-Grid: An Efficient and Feature-Preserving Neural Implicit Surface Representation

TL;DR

This work tackles neural implicit surface representations that struggle with sharp features, open boundaries, and efficiency. It proposes Patch-Grid, a patch-based representation with per-patch feature volumes and an adaptive merge grid to localize CSG operations, enabling robust modeling and fast training (around 5 seconds) plus interactive local updates (under 2 seconds). The approach achieves state-of-the-art reconstruction quality on shapes with intricate sharp features, open surfaces, and thin structures, while offering robust shape editing and open-distance querying via global blending. These capabilities promise practical impact for interactive CAD-style modeling and rapid shape editing with neural implicit surfaces.

Abstract

Neural implicit representations are widely used for 3D shape modeling due to their smoothness and compactness, but traditional MLP-based methods struggle with sharp features, such as edges and corners in CAD models, and require long training times. To address these limitations, we propose Patch-Grid, a unified neural implicit representation that efficiently fits complex shapes, preserves sharp features, and handles open boundaries and thin geometric structures. Patch-Grid learns a signed distance field (SDF) for each surface patch using a learnable patch feature volume. To represent sharp edges and corners, it merges the learned SDFs via constructive solid geometry (CSG) operations. A novel merge grid organizes patch feature volumes within a shared octree structure, localizing and simplifying CSG operations. This design ensures robust merging of SDFs and significantly reduces computational complexity, enabling training within seconds while maintaining high fidelity. Experimental results show that Patch-Grid achieves state-of-the-art reconstruction quality for shapes with intricate sharp features, open surfaces, and thin structures, offering superior robustness, efficiency, and accuracy.

Figures (30)

• Figure 1: Overview. (a) Input to Patch-Grid is a B-Rep model of a 3D shape $\mathcal{S}$; (b) Patch-Grid encloses each surface patch of the given shape with a patch volume. We assign a learnable feature vector to each grid point of the patch volume and convert this volume into a patch feature volume $FV$, which defines a continuous feature field $F(\mathbf{x})$ via trilinear interpolation within each cell. Then, a shared MLP decoder $f$ is used to map $F(\mathbf{x})$ to $\mathbb{R}$, representing the SDF of the target surface patch. As there exists an extended zero-level set beyond the fitting surface (called extraneous zero-level set in the following), patches are robustly trimmed off through CSG merging operations to derive a neural implicit field that reproduces the SDF of the given shape. To this end, we construct a merge grid$\mathcal{G}$ and enforce a merge loss within each merge grid cell. The merge grid confines the CSG operations required to merge multiple learned SDFs to localized regions. (c) We design two types of loss terms to enable accurate fitting of individual patches ($\mathcal{L}_{\mathrm{patch}}$) and model the relationship between connected patches ($\mathcal{L}_{\mathrm{merge}}$), respectively; (d) Finally, the individual neural surface patches are composed into the final surface shape that reconstructs the target shape. It takes on average 5 seconds to fit a 3D CAD model.
• Figure 2: Given a 3D shape (a), we show (b) a patch volume for the patch in orange and (c) the merge gird.
• Figure 3: (a) A challenging case with highly concave regions at the top and bottom of the cylindrical shell. (b) NH-Rep fails in this challenging case due to the difficulty in merging the learned implicit functions in a global manner. (c) Our Patch-Grid performs robustly due to the localized approach adopted.
• Figure 4: (a) The ground truth shape; (b) An ideal case of the extraneous zero-level set of curve $A$ learned by Patch-Grid; (c) A failure case caused by undesired interference between the zero-level sets of curves $A$ and $C$; (d) Applying the merge grid $\mathcal{G}$ converts the original CSG operations to localized regions (i.e., cell $C_{031}$). The first row depicts 2D illustrations of the curves. The second row shows the merged zero-level sets in black. The third row shows the CSG operations under different circumstances, and applying merge grid$\mathcal{G}$ simplifies the CSG operations in each cell and significantly reduces the burden for learning coordinated extraneous zero-level sets.
• Figure 5: Sharp geometric features in a 3D shape. (a) A 3D example; (b) The adjacency graph of an edge feature; (c) The adjacency graph of a corner feature.