Shape-From-Template in Flatland

Mathias Gallardo, Daniel Pizarro, Adrien Bartoli, Toby Collins; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 2847-2854

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.

Related Material


[pdf]
[bibtex]
@InProceedings{Gallardo_2015_CVPR,
author = {Gallardo, Mathias and Pizarro, Daniel and Bartoli, Adrien and Collins, Toby},
title = {Shape-From-Template in Flatland},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2015}
}