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We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…
The paper is devoted to a detailed analysis of nonlocal error bounds for nonconvex piecewise affine functions. We both improve some existing results on error bounds for such functions and present completely new necessary and/or sufficient…
Image segmentation is the foundation of several computer vision tasks, where pixel-wise knowledge is a prerequisite for achieving the desired target. Deep learning has shown promising performance in supervised image segmentation. However,…
We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…
Images can be segmented by first using a classifier to predict an affinity graph that reflects the degree to which image pixels must be grouped together and then partitioning the graph to yield a segmentation. Machine learning has been…
PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information…
The framework of Partial Information Decomposition (PID) unveils complex nonlinear interactions in network systems by dissecting the mutual information (MI) between a target variable and several source variables. While PID measures have…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
Image segmentation is a challenging task influenced by multiple sources of uncertainty, such as the data labeling process or the sampling of training data. In this paper we focus on binary segmentation and address these challenges using…
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…
Artificial Neural Networks (ANNs) are prevalent machine learning models that are applied across various real-world classification tasks. However, training ANNs is time-consuming and the resulting models take a lot of memory to deploy. In…
We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
Multi-modal medical image segmentation plays an essential role in clinical diagnosis. It remains challenging as the input modalities are often not well-aligned spatially. Existing learning-based methods mainly consider sharing trainable…
$\textit{Implicit neural representations}$ (INRs) aim to learn a $\textit{continuous function}$ (i.e., a neural network) to represent an image, where the input and output of the function are pixel coordinates and RGB/Gray values,…