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Matchbox manifolds ${\mathfrak M}$ are a special class of foliated spaces, which includes as special examples exceptional minimal sets of foliations, weak solenoids, suspensions of odometer and Toeplitz actions, and tiling spaces associated…

Weakly-supervised instance segmentation aims to detect and segment object instances precisely, given imagelevel labels only. Unlike previous methods which are composed of multiple offline stages, we propose Sequential Label Propagation and…

Pixel and superpixel classifiers have become essential tools for EM segmentation algorithms. Training these classifiers remains a major bottleneck primarily due to the requirement of completely annotating the dataset which is tedious,…

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…

Optimized spatial partitioning algorithms are the corner stone of many successful experimental designs and statistical methods. Of these algorithms, the Centroidal Voronoi Tessellation (CVT) is the most widely utilized. CVT based methods…

Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract…

Due to the costliness of labelled data in real-world applications, semi-supervised object detectors, underpinned by pseudo labelling, are appealing. However, handling confusing samples is nontrivial: discarding valuable confusing samples…

The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are…

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions with respect to a given probability measure. CVT…

There has been an increasing interest in semi-supervised learning in the recent years because of the great number of datasets with a large number of unlabeled data but only a few labeled samples. Semi-supervised learning algorithms can work…

Zooplankton images, like many other real world data types, have intrinsic properties that make the design of effective classification systems difficult. For instance, the number of classes encountered in practical settings is potentially…

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…

Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…

In this paper, we present new optimization models for Support Vector Machine (SVM), with the aim of separating data points in two or more classes. The classification task is handled by means of nonlinear classifiers induced by kernel…

The rapid development of deep learning has made a great progress in image segmentation, one of the fundamental tasks of computer vision. However, the current segmentation algorithms mostly rely on the availability of pixel-level…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…

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…

The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…

We study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms. On the positive side, we show for strictly convex and smooth norms that the geometry of Voronoi cells of lattices in any dimension is similar…

Recent leading approaches to semantic segmentation rely on deep convolutional networks trained with human-annotated, pixel-level segmentation masks. Such pixel-accurate supervision demands expensive labeling effort and limits the…