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Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological…
Optimal matrices for problems involving the matrix numerical radius often have fields of values that are disks, a phenomenon associated with partial smoothness. Such matrices are highly structured: we experiment in particular with the…
How to measure the complexity of a finite set of vectors embedded in a multidimensional space? This is a non-trivial question which can be approached in many different ways. Here we suggest a set of data complexity measures using universal…
Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image…
Cold sets and freezing sets belong to the theory of (approximate) fixed points for continuous self-maps on digital images. We study some properties of cold sets for digital images in the digital plane, and we examine some relationships…
This paper proposes a new cubical space model for the representation of continuous objects and surfaces in the n-dimensional Euclidean space by discrete sets of points. The cubical space model concerns the process of converting a continuous…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…
Image segmentation has long been a basic problem in computer vision. Depth-wise Layering is a kind of segmentation that slices an image in a depth-wise sequence unlike the conventional image segmentation problems dealing with surface-wise…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
Synthesizing a densely sampled light field from a single image is highly beneficial for many applications. The conventional method reconstructs a depth map and relies on physical-based rendering and a secondary network to improve the…
Superpixel segmentation is becoming ubiquitous in computer vision. In practice, an object can either be represented by a number of segments in finer levels of detail or included in a surrounding region at coarser levels of detail, and thus…
Single-pixel imaging can collect images at the wavelengths outside the reach of conventional focal plane array detectors. However, the limited image quality and lengthy computational times for iterative reconstruction still impede the…
A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
In this work, the possibilities for segmentation of cells from their background and each other in digital image were tested, combined and improoved. Lot of images with young, adult and mixture cells were able to prove the quality of…
Superpixels are widely used in computer vision to simplify image representation and reduce computational complexity. While traditional methods rely on low-level features, deep learning-based approaches leverage high-level features but also…
For a simplicial complex $X$, the $d$-clique complex $\Delta_d(X)$ is the simplicial complex having all subsets of vertices whose $(d + 1)$-subsets are contained by $X$ as its faces. We prove that if $p = n^{\alpha}$, with $\alpha <…
The goal of this paper is to develop a machine learning model to analyze the main gravitational lens and detect dark substructure (subhalos) within simulated images of strongly lensed galaxies. Using the technique of image segmentation, we…
Due to the current lack of large-scale datasets at the million-scale level, tasks involving panoramic images predominantly rely on existing two-dimensional pre-trained image benchmark models as backbone networks. However, these networks are…
The new generation of deep photometric surveys requires unprecedentedly precise shape and photometry measurements of billions of galaxies to achieve their main science goals. At such depths, one major limiting factor is the blending of…