Monocular Template-Based 3D Surface Reconstruction: Convex Inextensible and Nonconvex Isometric Methods
Florent Brunet, Adrien Bartoli, Richard Hartley
Computer Vision and Image Understanding, April 2014
Abstract
We study the 3D reconstruction of an isometric surface from point
correspondences between a template and a single input image. The
template shows the surface flat and fronto-parallel. We propose
three new methods. The first two use a convex relaxation of
isometry to inextensibility. They are formulated as Second Order
Cone Programs (SOCP). The first proposed method is point-wise
(it reconstructs only the input point correspondences) while the
second proposed method uses a smooth and continuous surface model,
based on Free-Form Deformations (FFD). The third proposed method
uses the ‘true’ nonconvex isometric constraint and the same
continuous surface model. It is formulated with Nonlinear
Least-Squares and can thus be solved with the efficient
Levenberg-Marquardt minimization method. The proposed approaches
may be combined in a single pipeline whereby one of the convex
approximations is used to initialize the nonconvex method. Our
contributions solve two important limitations of current state of
the art: our convex methods are the first ones to handle noise in
both the template and image points, and our nonconvex method is the
first one to use ‘true’ isometric constraints. Our experimental
results on simulated and real data show that our convex point-wise
method and our nonconvex method outperform respectively current
initialization and refinement methods in 3D reconstructed surface
accuracy.