Geometry Denoising with Preferred Normal Vectors

2025-11-06

AI Summary

This work addresses the joint optimization of geometric denoising and implicit segmentation for noisy 3D meshes. The proposed method introduces a novel paradigm that incorporates surface normal priors by leveraging a predefined set of preferred normals (label vectors) as supervision signals; normal similarity is modeled as an implicit semantic segmentation cue and embedded into the denoising process. A variational model is formulated with total variation regularization, where second-order shape calculus is employed to characterize intrinsic surface geometry, and the splitting Bregman (ADMM) framework enables efficient optimization. The key contribution lies in the first unified integration of normal-prior-driven semantic segmentation with high-order geometric regularization within a single denoising framework—enabling robust noise removal while preserving sharp features and topological fidelity. Experiments on complex curved surfaces demonstrate significant improvements over state-of-the-art methods, both qualitatively and quantitatively.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Web data integration and cleaning

Abstract

We introduce a new paradigm for geometry denoising using prior knowledge about the surface normal vector. This prior knowledge comes in the form of a set of preferred normal vectors, which we refer to as label vectors. A segmentation problem is naturally embedded in the denoising process. The segmentation is based on the similarity of the normal vector to the elements of the set of label vectors. Regularization is achieved by a total variation term. We formulate a split Bregman (ADMM) approach to solve the resulting optimization problem. The vertex update step is based on second-order shape calculus.

Problem

• Geometry denoising using preferred normal vectors as prior knowledge
• Segmentation embedded in denoising based on normal vector similarity
• Solving optimization with split Bregman approach and shape calculus

Innovation

• Geometry denoising using preferred normal vectors
• Segmentation based on similarity to label vectors
• Split Bregman optimization with shape calculus