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The round-trip distance function on a geographic network (such as a road network, flight network, or utility distribution grid) defines the "distance" from a single vertex to a pair of vertices as the minimum length tour visiting all three…
The primary issue in inverse halftoning is removing noisy dots on flat areas and restoring image structures (e.g., lines, patterns) on textured areas. Hence, a new structure-aware deep convolutional neural network that incorporates two…
Coronary arteries and their branches supply blood to myocardium. The obstruction of coronary arteries results in significant loss of myocardium, called acute myocardial infarction, and the number one cause of death globally. Hence,…
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one…
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…
Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs.…
Hourglass networks such as the U-Net and V-Net are popular neural architectures for medical image segmentation and counting problems. Typical instances of hourglass networks contain shortcut connections between mirroring layers. These…
We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
Background: In medical imaging, images are usually treated as deterministic, while their uncertainties are largely underexplored. Purpose: This work aims at using deep learning to efficiently estimate posterior distributions of imaging…
Image segmentation is a fundamental and challenging problem in computer vision with applications spanning multiple areas, such as medical imaging, remote sensing, and autonomous vehicles. Recently, convolutional neural networks (CNNs) have…
Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often…
Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
We investigate the problem of image retrieval based on visual queries when the latter comprise arbitrary regions-of-interest (ROI) rather than entire images. Our proposal is a compact image descriptor that combines the state-of-the-art in…
Multi-view image generation holds significant application value in computer vision, particularly in domains like 3D reconstruction, virtual reality, and augmented reality. Most existing methods, which rely on extending single images, face…
We consider problem of constructing purely Voronoi mesh where the union of uncut Voronoi cells approximates the planar computational domain with piecewise-smooth boundary. Smooth boundary fragments are approximated by the Voronoi edges and…
Image segmentation is pivotal in medical image analysis, facilitating clinical diagnosis, treatment planning, and disease evaluation. Deep learning has significantly advanced automatic segmentation methodologies by providing superior…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
The recently introduced Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a…