Template-based Monocular 3D Shape Recovery using Laplacian Meshes
This addresses the problem of real-time 3D shape recovery from single images for applications like computer vision and graphics, representing an incremental improvement by adapting existing regularization methods.
The paper tackles monocular 3D shape reconstruction of deformable surfaces by extending the Laplacian formalism to regularize meshes, turning it into a better-posed problem that allows outlier elimination via linear least squares and refinement through constrained optimization, achieving real-time implementations without sacrificing accuracy.
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.