Related papers: The Distance Transform and its Computation
Classical machine learning approaches are sensitive to non-stationarity. Transfer learning can address non-stationarity by sharing knowledge from one system to another, however, in areas like machine prognostics and defense, data is…
An isometry is a geometric transformation that preserves distances between pairs of points. We present methods to classify isometries in the Euclidean plane, and extend these methods to spherical, single elliptical, and hyperbolic geometry.…
We present a new method for image feature-extraction which is based on representing an image by a finite-dimensional vector of distances that measure how different the image is from a set of image prototypes. We use the recently introduced…
Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…
The performance of modern object detectors drops when the test distribution differs from the training one. Most of the methods that address this focus on object appearance changes caused by, e.g., different illumination conditions, or gaps…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
Accurately measuring mechanical displacements is essential for a vast portion of current technologies. Several optical techniques accomplish this task, allowing for non-contact sensing even below the diffraction limit. Here we introduce an…
The difference in the transmission for left and right circularly polarised light though thin films on substrates in a magnetic field is used to obtain the magnetic circular dichroism of the film. However there are reflections at all the…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this note, we study modifications of the distance induced by a…
A scheme to a complex-valued acquisition of the Fourier transform imaging was proposed. The main idea is to project the real and the imaginary parts of a diffraction field to intensity distributions respectively. The whole procedure was…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
The purpose of this paper is to introduce an algorithm that can detect the most unusual part of a digital image in probabilistic setting. The most unusual part of a given shape is defined as a part of the image that has the maximal distance…
We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…