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Hyperspectral images often have hundreds of spectral bands of different wavelengths captured by aircraft or satellites that record land coverage. Identifying detailed classes of pixels becomes feasible due to the enhancement in spectral and…
Current methods for developing foundation models in medical image segmentation rely on two primary assumptions: a fixed set of classes and the immediate availability of a substantial and diverse training dataset. However, this can be…
In this article we propose a novel nonstationary iterated Tikhonov (NIT) type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical…
Foundation models have recently emerged as powerful feature extractors in computational pathology, yet they typically omit mechanisms for leveraging the global spatial structure of tissues and the local contextual relationships among…
We present a differentiable simulation architecture for articulated rigid-body dynamics that enables the augmentation of analytical models with neural networks at any point of the computation. Through gradient-based optimization,…
Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
The target of human pose estimation is to determine body part or joint locations of each person from an image. This is a challenging problems with wide applications. To address this issue, this paper proposes an augmented parallel-pyramid…
Several imaging applications (vessels, retina, plant roots, road networks from satellites) require the accurate segmentation of thin structures for subsequent analysis. Discontinuities (gaps) in the extracted foreground may hinder…
The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology today. We sought to develop a mathematical approach to this problem using, as a test case, one of…
For many robotic manipulation and contact tasks, it is crucial to accurately estimate uncertain object poses, for which certain geometry and sensor information are fused in some optimal fashion. Previous results for this problem primarily…
Accurate representations of 3D faces are of paramount importance in various computer vision and graphics applications. However, the challenges persist due to the limitations imposed by data discretization and model linearity, which hinder…
We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values…
We develop a Lagrange multiplier theory for nonconvex set-valued optimization problems under Lipschitz-type regularity conditions. Instead of classical continuous linear functionals, we introduce closed convex processes -- set-valued…
The current series of two papers focus on a 3-dimensional Lotka-Volterra competition model of differential equations with seasonal succession, which exhibits that populations experience an external periodically forced environment. We are…
introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph $G,$ $k$…
The Volterra series is a powerful tool in modelling a broad range of nonlinear dynamic systems. However, due to its nonparametric nature, the number of parameters in the series increases rapidly with memory length and series order, with the…
Multicuts enable to conveniently represent discrete graphical models for unsupervised and supervised image segmentation, in the case of local energy functions that exhibit symmetries. The basic Potts model and natural extensions thereof to…
In this paper we analyze recent work \cite{Hone1} by Hone, Roberts and Vanhaecke, where the so-called Volterra map was introduced via the Lax equation that looks similar to the Lax representation for the Mumford's system \cite{Vanhaecke}.…
Deep neural networks have shown remarkable performance in image classification. However, their performance significantly deteriorates with corrupted input data. Domain generalization methods have been proposed to train robust models against…