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Borradaile et al. (2017) investigated orientations of an undirected graph in which the sequence of in-degrees of the nodes is lexicographically minimal, which we call decreasingly minimal (=dec-min). They proved that an orientation is…
Accurate retinal vessel segmentation is a challenging problem in color fundus image analysis. An automatic retinal vessel segmentation system can effectively facilitate clinical diagnosis and ophthalmological research. Technically, this…
Purpose: Eye morphology varies significantly across the population, especially for the orbit and optic nerve. These variations limit the feasibility and robustness of generalizing population-wise features of eye organs to an unbiased…
We prove that the set of directions of lines intersecting three disjoint balls in $R^3$ in a given order is a strictly convex subset of $S^2$. We then generalize this result to $n$ disjoint balls in $R^d$. As a consequence, we can improve…
The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and…
For compression fracture detection and evaluation, an automatic X-ray image segmentation technique that combines deep-learning and level-set methods is proposed. Automatic segmentation is much more difficult for X-ray images than for CT or…
This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…
The reliable segmentation of retinal vasculature can provide the means to diagnose and monitor the progression of a variety of diseases affecting the blood vessel network, including diabetes and hypertension. We leverage the power of…
We introduce the notion of strongly orthogonal set relative to an element in the sense of Birkhoff-James in a normed linear space to find a necessary and sufficient condition for an element $ x $ of the unit sphere $ S_{X}$ to be an exposed…
Automatic analysis of retinal blood images is of vital importance in diagnosis tasks of retinopathy. Segmenting vessels accurately is a fundamental step in analysing retinal images. However, it is usually difficult due to various imaging…
We propose a method for visualizing uncertain set systems, which differs from previous set visualization approaches that are based on certainty (an element either belongs to a set or not). Our method is inspired by storyline visualizations…
A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space $X$ has a resolving subset that can be written as an at most countably infinite…
This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…
The elements of a finite field of prime order canonically correspond to the integers in an interval. This induces an ordering on the elements of the field. Using this ordering, Kiss and Somlai recently proved interesting properties of the…
Applying machine learning technologies, especially deep learning, into medical image segmentation is being widely studied because of its state-of-the-art performance and results. It can be a key step to provide a reliable basis for clinical…
In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture…
We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based…
We propose new structures called almost o-minimal structures and $\mathfrak X$-structures. The former is a first-order expansion of a dense linear order without endpoints such that the intersection of a definable set with a bounded open…
It is well-known that lens maps are convex mappings defined in the unit disc to itself. In this brief note, we show that these mappings are convex of order $\alpha>0$, and starlike of order $\beta>0$, and establish the precise orders in…
Let $X$ be a projective variety, homogeneous under a linear algebraic group. We show that the diagonal of $X$ belongs to a unique irreducible component $H_X$ of the Hilbert scheme of $X\times X$. Moreover, $H_X$ is isomorphic to the…