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Instance Segmentation, which seeks to obtain both class and instance labels for each pixel in the input image, is a challenging task in computer vision. State-of-the-art algorithms often employ two separate stages, the first one generating…

Weakly Supervised Semantic Segmentation (WSSS) using only image-level labels has gained significant attention due to cost-effectiveness. Recently, Vision Transformer (ViT) based methods without class activation map (CAM) have shown greater…

This work tackles the problem of semi-supervised learning of image classifiers. Our main insight is that the field of semi-supervised learning can benefit from the quickly advancing field of self-supervised visual representation learning.…

Object detection and instance segmentation are dominated by region-based methods such as Mask RCNN. However, there is a growing interest in reducing these problems to pixel labeling tasks, as the latter could be more efficient, could be…

Deep Convolutional Neural Networks have proven effective in solving the task of semantic segmentation. However, their efficiency heavily relies on the pixel-level annotations that are expensive to get and often require domain expertise,…

We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces $ \mathbb{H}_{d}$ for $d \geq 2$. In contrast to the Euclidean setting, a limiting nontrivial ideal tessellation $ \mathcal{V}_{d}$ appears as the…

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…

When a sequence of numbers is slowly converging, it can be transformed into a new sequence which, under some assumptions, could converge faster to the same limit. One of the most well--known sequence transformation is Shanks transformation…

In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical…

The support vector machine (SVM) is a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…

In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…

Learning semantic segmentation models under image-level supervision is far more challenging than under fully supervised setting. Without knowing the exact pixel-label correspondence, most weakly-supervised methods rely on external models to…

The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges of these cells is ruled by a Markovian branching mechanism…

A hex sphere is a singular Euclidean sphere with four cones points whose cone angles are (integer) multiples of 2*pi/3 but less than 2*pi. Given a hex sphere M, we consider its Voronoi decomposition centered at the two cone points with…

Weakly supervised semantic segmentation is a challenging task as it only takes image-level information as supervision for training but produces pixel-level predictions for testing. To address such a challenging task, most recent…

The data-driven nature of deep learning (DL) models for semantic segmentation requires a large number of pixel-level annotations. However, large-scale and fully labeled medical datasets are often unavailable for practical tasks. Recently,…

This paper presents an algorithm to generate a new kind of polygonal mesh obtained from triangulations. Each polygon is built from a terminal-edge region surrounded by edges that are not the longest-edge of any of the two triangles that…