Discrete analytical curve reconstruction without patches

Discrete analytical curve reconstruction without patches

Invertible Euclidean reconstruction methods without patches for 2D and 3D discrete curves are proposed. From a discrete 4-connected curve in 2D, or 6-connected curve in 3D, the proposed algorithms compute a polygonal line which digitization with the standard model is equal to all the pixels or voxels of the curve. The framework of this method is the discrete analytical geometry and parameter sp...

Discrete Coons patches

We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles. We show that no single blend of variational principles can produce...

Curve Reconstruction

Discrete Jordan Curve Theorems

There has been recent interest in combinatorial versions of classical theorems in topology. In particular, Stahl [S] and Little [3] have proved discrete versions of the Jordan Curve Theorem. The classical theorem states that a simple closed curve y separates the 2-sphere into two connected components of which y is their common boundary. The statements and proofs of the combinatorial versions in...

Hierarchical Curve Reconstruction

Conventional edge linking methods perform poorly when multiple responses to the same edge, bifurcations and nearby edges are present. We propose a scheme for curve inference where divergent bifur-cations are initially suppressed so that the smooth parts of the curves can be computed more reliably. Recovery of curve singularities and gaps is deferred to a later stage, when more contextual inform...