Linear one-sided stability of MAT for weakly injective 3D domain

One-sided Stability of MAT and Its Applications

Although useful in many applications, the medial axis transform (MAT) has a few fit-falls, one of which is its extreme sensitivity to the boundary perturbation. In this paper, we first summarizes the previous attempts to get around this by bounding the one-sided Hausdorff distance of the MAT with respect to the boundary perturbation. We illustrate these results and their optimality with various...

On One-Sided Ideals of Rings of Linear Transformations

On weakly projective and weakly injective modules

The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...

One-Sided Unsupervised Domain Mapping

In unsupervised domain mapping, the learner is given two unmatched datasets A and B. The goal is to learn a mapping GAB that translates a sample in A to the analog sample in B. Recent approaches have shown that when learning simultaneously both GAB and the inverse mapping GBA, convincing mappings are obtained. In this work, we present a method of learning GAB without learning GBA. This is done ...

One-Sided Stability of Medial Axis Transform