The hit-or-miss transform (HMT) is a fundamental operation on binary images, widely used since forty years. As it is not increasing, its extension to grey-level images is not straightforward, and very few authors have considered it. Moreover, despite its potential usefulness, very few applications of the grey-level HMT have been proposed until now. Part I of this paper, developed hereafter, is devoted to the description of a theory leading to a unification of the main definitions of the grey-level HMT, mainly proposed by Ronse and Soille, respectively (part II will deal with the applicative potential of the grey-level HMT, which will be illustrated by its use for vessel segmentation from 3D angiographic data). In this first part, we review the previous approaches to the grey-level HMT, especially the supremal one of Ronse, and the integral one of Soille; the latter was defined only for flat structuring elements, but it can be generalized to non-flat ones. We present a unified theory of the grey-level HMT, which is decomposed into two steps. First a fitting associates to each point the set of grey-levels for which the structuring elements can be fitted to the image; as in Soille's approach, this fitting step can be constrained. Next, a valuation associates a final grey-level value to each point; we propose three valuations: supremal (as in Ronse), integral (as in Soille) and binary.

Deep learning has been shown to produce state of the art results in many tasks in biomedical imaging, especially in segmentation. Moreover, segmentation of the cerebrovascular structure from magnetic resonance angiography is a challenging problem because its complex geometry and topology have a large inter-patient variability. Therefore, in this work, we present a convolutional neural network approach for this problem. Particularly, a new network topology inspired by the U-net 3D and by the Inception modules, entitled Uception. In addition, a discussion about the best objective function for sparse data also guided most choices during the project. State of the art models are also implemented for a comparison purpose and final results show that the proposed architecture has the best performance in this particular context.

Background:We systematically reviewed the literature on definitions and outcomes of large-forsize (LFS) syndrome in orthotopic liver transplantation (LT).Methods: This systematic review was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The Cochrane library, PUBMED, and Embase were searched (January 1990-January 2019) for studies reporting LFS in LT. Primary outcomes were definitions and mortality of LFS LT.Results: Eleven studies reporting patients with LFS LT were identified. Four different formulas (Graft-recipient weight ratio (GRWR), Body surface area index (BSAi), Donor standardized total liver volume (sTLV)-recipient sTLV ratio, and Graft-weight/Right anteroposterior distance (RAP) ratio) with their critical thresholds were found. There were 81 patients (54% women) with a median weight and height of 62.5 kg (range, 40-105 kg) and 165 cm (range, 145-180 cm). The median graft weight was 1772 g (range, 1290-2400 g), and the median GWRW was 2.77% (range, 2. 1-4.00%). Graft venous outflow obstruction was described in seven patients(8.6%). At the time of LT, fascial closure was not achieved in 24 patients (29.6%) and the graft size was reduced by a liver resection in three patients(3.7%). Thirteen deaths (16%) were reported in the first 90 postoperative days with two patients undergoing re-transplant.Conclusions: LFS LT remains heterogeneously defined but characterized by high mortality rates despite the use of tailored surgical solutions (graft reduction and open abdomen). A composite definition is proposed in order to better describe LFS clinical syndrome.