Related papers: Fractal Interpolation on the Real Projective Plane
Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules.…
Linear Geometry describes geometric properties that depend on the fundamental notion of a line. In this paper we survey basic notions and results of Linear Geomery that depend on the flat hulls: flats, exchange, rank, regularity,…
This paper is a sharp and focussed exploration of the Fibonacci substitution and the mathematical entity it gives rise to, the Fibonacci word. Our investigations are both of an algebraic and a geometric nature. Indeed, it is the combination…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
Video Frame Interpolation synthesizes non-existent images between adjacent frames, with the aim of providing a smooth and consistent visual experience. Two approaches for solving this challenging task are optical flow based and kernel-based…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
We introduce a special subset of the graph of a homogeneous coupled cell network, called a projection block, and show that the network obtained from identifying this block to a single point can be used to understand the generic bifurcations…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown…
This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a $\mathcal{C}^2$-continuous spline for the trajectory naturally…
We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
The simplest way to obtain continuous interpolation between two points in high dimensional space is to draw a line between them. While previous works focused on the general connectivity between model parameters, we explored linear…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…