Finding Surface Correspondences Using Symmetry Axis Curves

Finding Surface Correspondences Using Symmetry Axis Curves

In this paper, we propose an automatic algorithm for finding a correspondence map between two 3D surfaces. The key insight is that global reflective symmetry axes are stable, recognizable, semantic features of most real-world surfaces. Thus, it is possible to find a useful map between two surfaces by first extracting symmetry axis curves, aligning the extracted curves, and then extrapolating co...

Finding point correspondences using simulated annealing

-Identifying corresponding points between two recordings of a point set has always been an important problem in stereo vision applications. We describe this matching problem in terms of cost minimization and present an algorithm to approach the minimal cost mapping using simulated annealing. The algorithm calculates the costs to match all possible point pairs and tries to minimize the sum of th...

Correspondences on Hyperbolic Curves

We consider hyperbolic curves over an algebraically closed field k of characteristic zero. We call two such curves X, Y isogenous if there exists a nonempty scheme C , together with finite étale morphisms C → X, C → Y . (We refer to such a pair (C → X,C → Y ) as a correspondence from X to Y .) It is easy to see that the relation of isogeny is an equivalence relation on the set of isomorphism cl...

Elastic Medical Image Registration Using Surface Landmarks with Automatic Finding of Correspondences

Using Symmetry to Count Rational Curves

The recent “close encounter” between enumerative algebraic geometry and theoretical physics has resulted in many new applications and new techniques for counting algebraic curves on a complex projective manifold. For example, string theorists demonstrated that generating functions built from counting curves can have completely unexpected relationships with other geometric constructions, via mir...