Gaussian-product subdivision surfaces

Reinhold Preiner,Tamy Boubekeur,Michael Wimmer

doi:10.1145/3306346.3323026

Abstract

Probabilistic distribution models like Gaussian mixtures have shown great potential for improving both the quality and speed of several geometric operators. This is largely due to their ability to model large fuzzy data using only a reduced set of atomic distributions, allowing for large compression rates at minimal information loss. We introduce a new surface model that utilizes these qualities of Gaussian mixtures for the definition and control of a parametric smooth surface. Our approach is based on an enriched mesh data structure, which describes the probability distribution of spatial surface locations around each vertex via a Gaussian covariance matrix. By incorporating this additional covariance information, we show how to define a smooth surface via a nonlinear probabilistic subdivision operator based on products of Gaussians, which is able to capture rich details at fixed control mesh resolution. This entails new applications in surface reconstruction, modeling, and geometric compression.

Highlights

For the efficient processing of fuzzy geometric data like noisy point sets, probabilistic distribution models such as Gaussian mixtures have recently shown great potential for tasks like registration, filtering or resampling
Despite representing a nonlinear subdivision scheme, the proposed subdivision operation based on Gaussians can be shown to be dual to traditional linear ones: We introduce a smooth map between covariance meshes and ordinary meshes in a dual space, such that all findings and tools developed for linear subdivision can be applied to our proposed Gaussian-product subdivision through these maps
We introduce a family of nonlinear subdivision schemes that uses the covariance information for a refinement based on the product of vertex Gaussians, leading to a continuous limit contour that closely approximates the ridge of their associated

Summary

Introduction

For the efficient processing of fuzzy geometric data like noisy point sets, probabilistic distribution models such as Gaussian mixtures have recently shown great potential for tasks like registration, filtering or resampling This is largely due to their ability to model large fuzzy data using only a reduced set of atomic distributions, allowing for large compression rates at minimal information loss. Due to this compactness, it is desirable to be able to define a surface directly on such a sparse model, and avoid the need to expand to larger representations (e.g., meshes or point clouds) for further processing and rendering.

Objectives

Methods

Discussion

Conclusion