Image inpainting based on coherence transport with adapted distance functions

We discuss an extension of our method Image Inpainting Based on Coherence Transport. For the latter method the pixels of the inpainting domain have to be serialized into an ordered list. Up till now, to induce the serialization we have used the distance to boundary map. But there are inpainting problems where the distance to boundary serialization causes unsatisfactory inpainting results. In the present work we demonstrate cases where we can resolve the difficulties by employing other distance functions which better suit the problem at hand

A well-posedness framework for inpainting based on coherence transport

Image inpainting is the process of touching-up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März [J. Math. Imaging Vis. , 28 (2007), pp. 259– 278] introduced a very efficient method called Image Inpainting Based on Coherence Transport which fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary towards the interior of the hole. The mathematical model behind this method is a first-order functional advection PDE posed on a compact domain with all inflow boundary. We show that this problem is well-posed under certain conditions

Calculus on surfaces with general closest point functions

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs

Self-monitoring accuracy does not increase throughout undergraduate medical education

Context: Accurate self-assessment of one's performace on a moment-by-moment basis (ie, accurate self-monitoring) is vital for the self-regulation of practising physicians and indeed for the effective regulation of self-directed learning during medical education. However, little is currently known about the functioning of self-monitoring and its co-development with medical knowledge across medical education. This study is the first to simultaneously investigate a number of relevant aspects and measures that have so far been studied separately: different measures of self-monitoring for a broad area of medical knowledge across 10 different performance levels. Methods: This study assessed the self-monitoring accuracy of medical students (n = 3145) across 10 semesters. Data collected during the administration of the formative Berlin Progress Test Medicine (PTM) were analysed. The PTM comprises 200 multiple-choice questions covering all major medical disciplines and organ systems. A self-report indicator (ie, confidence) and two behavioural indicators of self-monitoring accuracy (ie, response time and the likelihood of changing an initial answer to a correct rather than an incorrect item) were examined for their development over semesters. Results: Analyses of more than 390 000 observations (of approximately 250 students per semester) showed that confidence was higher for correctly than for incorrectly answered items and that 86% of items answered with high confidence were indeed correct. Response time and the likelihood of the initial answer being changed were higher when the initial answer was incorrect than when it was correct. Contrary to expectations, no differences in self-monitoring accuracy were observed across semesters. Conclusions: Convergent evidence from different measures of self-monitoring suggests that medical students self-monitor their knowledge on a question-by-question basis well, although not perfectly, and to the same degree as has been found in studies outside medicine. Despite large differences in performance, no variations in self-monitoring across semesters (with the exception of the first semester) were observed