In this chapter, we bring several contributions.
We first demonstrate in section 6.2 that the warps based on tensor-product B-splines (hereinafter abbreviated *BS-Warp*) corresponds to affine imaging condition, in the sense that it models the affine projection of some 3D surface.
We then propose our most important contribution in section 6.3: a novel parametric warp we call *NURBS-Warp*, that extends the classical BS-Warp to perspective projection.
This warp has a simple analytical form: it is obtained as the two-way tensor-product of bivalued Non-Uniform Rational B-Splines (NURBS).
Finally, we give in section 6.4 algorithms for the feature-based estimation of our NURBS-Warp.
More precisely, we consider that a set
of point correspondences between the two images is known, and show how the parameters that minimize the classical *transfer error* can be found, by solving:

where represents the warp and is the squared euclidean distance between the points and . We finally report experimental results in section 6.5 and conclude this section.

Contributions to Parametric Image Registration and 3D Surface Reconstruction (Ph.D. dissertation, November 2010) - Florent Brunet

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