Stochastic Geometric Iterative Method for Loop Subdivision Surface Fitting

TL;DR

This paper introduces a stochastic iterative approach for fitting high-resolution 3D models with Loop subdivision surfaces, improving speed and accuracy over existing methods.

Contribution

The paper presents a novel stochastic geometric iterative method for efficient and precise fitting of Loop subdivision surfaces to 3D models, with proven convergence.

Findings

Faster fitting speed compared to existing methods

Higher fitting precision achieved

Method convergence is theoretically proven

Abstract

In this paper, we propose a stochastic geometric iterative method to approximate the high-resolution 3D models by finite Loop subdivision surfaces. Given an input mesh as the fitting target, the initial control mesh is generated using the mesh simplification algorithm. Then, our method adjusts the control mesh iteratively to make its finite Loop subdivision surface approximates the input mesh. In each geometric iteration, we randomly select part of points on the subdivision surface to calculate the difference vectors and distribute the vectors to the control points. Finally, the control points are updated by adding the weighted average of these difference vectors. We prove the convergence of our method and verify it by demonstrating error curves in the experiment. In addition, compared with an existing geometric iterative method, our method has a faster fitting speed and higher fitting precision.