Gaussian Curvature Filter on 3D Meshes

Curvature flow is a principled framework for mesh smoothing: by iteratively moving vertices in the direction of curvature, noise is removed and surfaces become fairer. The dominant variant, mean curvature flow, has a well-known drawback—it shrinks meshes toward zero volume and erases sharp features such as ridges and corners. This paper explores Gaussian curvature as an alternative foundation for mesh filtering. Gaussian curvature, unlike mean curvature, is intrinsic: it depends only on the distances within the surface itself and is invariant to isometric deformations such as bending. Preserving Gaussian curvature during filtering therefore naturally prevents volume collapse and protects topologically significant features. The proposed filter formulates vertex updates as minimising the deviation of the filtered mesh Gaussian curvature from the input, solved iteratively with a simple local update rule. No sharp feature detection or special boundary treatment is required. The filter is fast, easy to implement, and controlled by a single smoothing-strength parameter. Experiments on standard noisy mesh benchmarks (arXiv:2003.09178) show feature retention and volume preservation superior to mean curvature flow and competitive with dedicated feature-preserving methods, at lower implementation complexity.

Problem setting

Mesh denoising based on curvature flow is a classical approach to surface smoothing, but mean curvature flow shrinks volumes and blurs sharp features. This paper proposes a Gaussian curvature filter that iteratively updates vertex positions to match a target Gaussian curvature distribution, minimising changes to the intrinsic geometry of the surface. Gaussian curvature is an intrinsic quantity invariant to bending, so its preservation naturally avoids volume collapse and respects geometric features such as saddle points and convex corners.

In the broader publication record, this work appears in arXiv:2003.09178. The visual notes below pair the paper’s original figures with a concise reading of the method, experimental setup, and reported results.

Method and visual evidence

The method operates on discrete geometry and is designed to preserve meaningful shape structure while filtering noise, estimating features, or improving downstream geometric processing.

The extracted figures below show the geometry-processing pipeline, representative shapes, and visual or numerical comparisons.

Method overview. This image is extracted from an embedded PDF image object on page 1, then recomposed for web display.

Representation and setup. This image is extracted from an embedded PDF image object on page 4, then recomposed for web display.

Experimental evidence. This image is extracted from an embedded PDF image object on page 4, then recomposed for web display.

Result comparison. This image is extracted from an embedded PDF image object on page 5, then recomposed for web display.

Additional visual result. This image is extracted from an embedded PDF image object on page 5, then recomposed for web display.

Results and impact

The evaluation reported in arXiv:2003.09178 uses the extracted figures above to show the method’s measurement, reconstruction, segmentation, matching, or diagnostic behavior on representative experiments. These visuals are paired with the paper’s quantitative or qualitative analysis to make the workflow easier to inspect from the homepage.

Source handling

I extracted 164 candidate image objects from paper.pdf and generated the compressed WebP figures used on this page.