Related papers: Morphology on categorical distributions
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
We examine a general framework for visualizing datasets of high (> 2) dimensionality, and demonstrate it using the morphology of galaxies at moderate redshifts. The distributions of various populations of such galaxies are examined in a…
The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a cube, with regions, surfaces, lines and vertices labelled by…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
Pooling is essentially an operation from the field of Mathematical Morphology, with max pooling as a limited special case. The more general setting of MorphPooling greatly extends the tool set for building neural networks. In addition to…
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability…
This work proposes a new type of classifier called Morphological Classifier (MC). MCs aggregate concepts from mathematical morphology and supervised learning. The outcomes of this aggregation are classifiers that may preserve shape…
Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques,…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
In recent years Artificial Intelligence has emerged as a fundamental tool in medical applications. Despite this rapid development, deep neural networks remain black boxes that are difficult to explain, and this represents a major limitation…
While many image colorization algorithms have recently shown the capability of producing plausible color versions from gray-scale photographs, they still suffer from the problems of context confusion and edge color bleeding. To address…
The identification and quantification of markers in medical images is critical for diagnosis, prognosis and management of patients in clinical practice. Supervised- or weakly supervised training enables the detection of findings that are…
Probabilistic convolutional neural networks, which predict distributions of predictions instead of point estimates, led to recent advances in many areas of computer vision, from image reconstruction to semantic segmentation. Besides state…
Understanding morphological types of galaxies is a key parameter for studying their formation and evolution. Neural networks that have been used previously for galaxy morphology classification have some disadvantages, such as not being…