Florent Brunet

TL;DR: The idea is to say that the 2D-3D map must be everywhere a local isometry, which induces conditions on the Jacobian matrix of the map which are included in a least-squares minimization problem.

TL;DR: Experimental results on simulated and real data show that the convex point-wise method and the nonconvex method outperform respectively current initialization and refinement methods in 3D reconstructed surface accuracy.

TL;DR: A new method to estimate derivatives of digitized functions is presented, which is convergent and can be computed by using only the arithmetic operations, and a new notion which solves the problem of correspondence between the parametrization of a continuous curve and the pixels numbering of a discrete object is introduced.

Abstract: The direct registration problem for images of a deforming surface has been well studied. Parametric flexible warps based, for instance, on the Free-Form Deformation or a Radial Basis Function such as the Thin-Plate Spline, are often estimated using additive Gauss-Newton-like algorithms. The recently proposed compositional framework has been shown to be more efficient, but cannot be directly applied to such non-groupwise warps.Our main contribution in this paper is the Feature-Driven framework. It makes possible the use of compositional algorithms for most parametric warps such as those above mentioned. Two algorithms are proposed to demonstrate the relevance of our Feature-Driven framework: the Feature-Driven Inverse Compositional and the Feature-Driven Learning-based algorithms. As another contribution, a detailed derivation of the Feature-Driven warp parameterization is given for the Thin-Plate Spline and the Free-Form Deformation. We experimentally show that these two types of warps have a similar representational power. Experimental results show that our Feature-Driven registration algorithms are more efficient in terms of computational cost, without loss of accuracy, compared to existing methods.

TL;DR: Experimental results show that the Feature-Driven registration algorithms are more efficient in terms of computational cost, without loss of accuracy, compared to existing methods.