3D Estimation of Extensible Surfaces Through a Local Monocular Reconstruction Technique

Abstract

This paper deals with the monocular reconstruction of an extensible surface by proposing a novel approach for the determination of the 3D positions of a set of points on images of the deformed surface. Given a 3D template, this approach is applied to each image independently of the others. To proceed with the reconstruction, the surface is divided into small patches that overlap in chain-like form. We model these surface patches as being uniformly extensible. Using a linear mapping from the template onto a patch, the variation of the patch shape is split into a rigid body transformation and a pure deformation. To estimate the pure deformation, we use an optimization procedure that minimizes the reprojection error along with the error over a constraint associated with uniform expansion. Having estimated the pure deformation, the rigid body transformation can be determined by decomposing the essential matrix between the current image and the virtual image that results from projecting the 3D positions that correspond to pure deformation of the template. This enables complete estimation of the linear mapping, thereby obtaining the 3D positions of the surface patch up to scale. To define a common scale, the surface smoothness is enforced by considering that the overlapping points of the patches are the same. The experimental results show the feasibility of the approach and that the accuracy of the reconstruction is good.