Title :
Shape-from-Template in Flatland
Author :
Mathias Gallardo;Daniel Pizarro;Adrien Bartoli;Toby Collins
Author_Institution :
ALCoV-ISIT, Univ. d´Auvergne, Clermont-Ferrand, France
fDate :
6/1/2015 12:00:00 AM
Abstract :
Shape-from-Template (SfT) is the problem of inferring the shape of a deformable object as observed in an image using a shape template. We call 2DSfT the `usual´ instance of SfT where the shape is a surface embedded in 3D and the image a 2D projection. We introduce 1DSfT, a novel instance of SfT where the shape is a curve embedded in 2D and the image a 1D projection. We focus on isometric deformations, for which 2DSfT is a well-posed problem, and admits an analytical local solution which may be used to initialize nonconvex refinement. Through a complete theoretical study of 1DSfT with perspective projection, we show that it is related to 2DSfT, but may have very different properties: (i) 1DSfT cannot be exactly solved locally and (ii) 1DSfT cannot be solved uniquely, as it has a discrete amount of at least two solutions. We then propose two convex initialization algorithms, a local analytical one based on infinitesimal planarity and a global one based on inextensibility. We show how nonconvex refinement can be implemented where, contrarily to current 2DSfT methods, one may enforce isometry exactly using a novel angle-based parameterization. Finally, our method is tested with simulated and real data.
Keywords :
"Mathematical model","Deformable models","Shape","Approximation methods","Three-dimensional displays","Surface reconstruction","Image reconstruction"
Conference_Titel :
Computer Vision and Pattern Recognition (CVPR), 2015 IEEE Conference on
Electronic_ISBN :
1063-6919
DOI :
10.1109/CVPR.2015.7298902