Template-based Monocular 3D Shape Recovery using Laplacian Meshes

TL;DR

This paper introduces a Laplacian mesh-based method for monocular 3D shape recovery that simplifies the problem into a linear least squares solution, enabling real-time surface reconstruction.

Contribution

It extends Laplacian formalism to improve the robustness and efficiency of monocular 3D shape reconstruction for deformable surfaces.

Findings

Linear least squares effectively eliminates outliers

Initial shape estimates have accurate 2D projections

Method enables real-time surface reconstruction

Abstract

We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a reference image into a much better-posed problem. This allows us to quickly and reliably eliminate outliers by simply solving a linear least squares problem. This yields an initial 3D shape estimate, which is not necessarily accurate, but whose 2D projections are. The initial shape is then refined by a constrained optimization problem to output the final surface reconstruction. Our approach allows us to reduce the dimensionality of the surface reconstruction problem without sacrificing accuracy, thus allowing for real-time implementations.