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Some biological mechanisms of early vision are comparatively well understood, but they have yet to be evaluated for their ability to accurately predict and explain human judgments of image similarity. From well-studied simple connectivity…
High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organization of the connectome at the macroscopic…
Self-organization of orientation-wheels observed in the visual cortex is discussed from the view point of topology. We argue in a generalized model of Kohonen's feature mappings that the existence of the orientation-wheels is a consequence…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
In this paper we consider the problem of reconstructing an image that is downsampled in the space of its $SE(2)$ wavelet transform, which is motivated by classical models of simple cells receptive fields and feature preference maps in…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of level curves to their curvature and to the gradient field of…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…
The paper aims to reveal the relationship between the geometrical features and linear and nonlinear optical properties of InAs quantum dots (QDs). This problem is justified by the extreme variety offered by the recent advances in growth…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
A recent body of work has demonstrated that Transformer embeddings can be linearly decomposed into well-defined sums of factors, that can in turn be related to specific network inputs or components. There is however still a dearth of work…
Despite the centrality of the notion of representation in neuroscience, the field lacks a unified framework for the concepts used to characterize representation, leading to disparate use of both terminology and measures associated with it.…
Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important.…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…
This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…