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We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…

In this work, we examine the effectiveness of an uncertainty quantification framework known as Evidential Deep Learning applied in the context of biomedical image segmentation. This class of models involves assigning Dirichlet distributions…

Efficient and accurate joint representation of a collection of images, that belong to the same class, is a major research challenge for practical image set classification. Existing methods either make prior assumptions about the data…

The accurate segmentation of organs-at-risk (OARs) in head and neck CT images is a critical step for radiation therapy of head and neck cancer patients. However, manual delineation for numerous OARs is time-consuming and laborious, even for…

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…

Automatic security inspection using computer vision technology is a challenging task in real-world scenarios due to various factors, including intra-class variance, class imbalance, and occlusion. Most of the previous methods rarely solve…

The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…

Ultrasound localization microscopy has enabled super-resolution vascular imaging through precise localization of individual ultrasound contrast agents (microbubbles) across numerous imaging frames. However, analysis of high-density regions…

Speckle patterns produced by coherent X-ray have a close relationship with the internal structure of materials but quantitative inversion of the relationship to determine structure from speckle patterns is challenging. Here, we investigate…

In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

Autonomous vehicles that navigate in open-world environments may encounter previously unseen object classes. However, most existing LiDAR panoptic segmentation models rely on closed-set assumptions, failing to detect unknown object…

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…

We prove the following variant of Levi's Enlargement Lemma: for an arbitrary arrangement $\mathcal{A}$ of $x$-monotone pseudosegments in the plane and a pair of points $a,b$ with distinct $x$-coordinates and not on the same pseudosegment,…

Deep anomaly detection models using a supervised mode of learning usually work under a closed set assumption and suffer from overfitting to previously seen rare anomalies at training, which hinders their applicability in a real scenario. In…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…

Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…

In this article we investigate the efficiency of deep learning algorithms in solving the task of detecting anatomical reference points on radiological images of the head in lateral projection using a fully convolutional neural network and a…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…