The choice of a reference image typically influences the results of deformable image registration, thereby making it asymmetric. This is a consequence of a spatially non-uniform weighting in the cost function integral that leads to general registration inaccuracy. The inhomogeneous integral measure--which is the local volume change in the transformation, thus varying through the course of the r...

We first prove a version of Tietze-Urysohn's theorem for proper functions taking values in non-negative real numbers defined on $\sigma$-compact locally compact Hausdorff spaces. As its application, we an extension metrics, which states that if $X$ is space, $A$ closed subset $X$, and $d$ metric generates the same topology $A$, then there exists such $D$ $D|_{A^{2}}=d$. Moreover, retraction, ca...

In this work the main objective is to extend the theory of Hausdorff measures in general metric spaces. Throughout the thesis Hausdorff measures are defined using premeasures. A condition on premeasures of ‘finite order’ is introduced which enables the use of a Vitali type covering theorem. Weighted Hausdorff measures are shown to be an important tool when working with Hausdorff measures define...

We consider the BDDC preconditioner for Reissner-Mindlin plate problems, discretized with the MITC element, introduced and analyzed in [11]. In that contribution the authors prove that the condition number of the ensuing linear system is independent of the plate thickness and scalable with respect to the mesh. We here prove, in addition, that the BDDC preconditioner of [11] is also quasi-optima...

In the present work we show that the linear operations in the space of Hausdorff continuous functions are generated by an extension property of these functions. We show that the supremum norm can be defined for Hausdorff continuous functions in a similar manner as for real functions, and that the space of all bounded Hausdorff continuous functions on an open set is a normed linear space. Some i...

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...

I t1 1 ⊗ · · · ⊗ tn n γ. This problem will be called the weak multilinear Hausdorff problem of moments for μk. Comparison with classical results will allow us to relate the weak multilinear Hausdorff problem with the multivariate Hausdorff problem. A solution to the strong multilinear Hausdorff problem of moments will be provided by exhibiting necessary and sufficient conditions for the existen...

1. Definitions. The general reference for definitions is [3]. Throughout the paper (X, T, ir) will denote a transformation group for which X is a compact Hausdorff space. Whenever it is stated that X is a uniform space, it will be implicitly assumed that the (Hausdorff) topology of X is the one induced by the uniformity. It is further assumed that T is abelian. P and Q will be used to denote re...

OBJECTIVE To evaluate surgery results, we established a novel method to digitize nasal morphology with the use of Hausdorff distance and analyzed nose morphology after cheiloplasty. STUDY DESIGN We evaluated the naris after primary cheiloplasty of 30 unilateral cleft lip and palate patients. Similarity between left and right sides was assessed by visual evaluation, area ratio, perimeter ratio...