Related papers: Verifying an algorithm computing Discrete Vector F…
We propose digital-analog quantum kernels for enhancing the detection of complex features in the classification of images. We consider multipartite-entangled analog blocks, stemming from native Ising interactions in neutral-atom quantum…
We construct the space of vector fields on quantum groups . Its elements are products of the known left invariant vector fields with the elements of the quantum group itself. We also study the duality between vector fields and 1-forms. The…
In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Several Liouville--Arnold-type theorems and a \( q…
Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…
Precise calibration is a must for high reliance 3D computer vision algorithms. A challenging case is when the camera is behind a protective glass or transparent object: due to refraction, the image is heavily distorted; the pinhole camera…
In this paper, we introduce discrete approximate circle bundles, a class of objects designed to serve as the data science analog of circle bundles from algebraic topology. We show that, under appropriate conditions, one can meaningfully and…
Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Diffractive optical elements (DOEs) are widely applied as compact solutions for desired light manipulations via wavefront shaping. Recent advanced chip applications further require their feature sizes to move down to the subwavelength,…
Feature extraction in noisy image datasets presents many challenges in model reliability. In this paper, we use the discrete Fourier transform in conjunction with persistent homology analysis to extract specific frequencies that correspond…
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by…
This paper proposes quantum image reconstruction. Input-triggered selection of an image among many stored ones, and its reconstruction if the input is occluded or noisy, has been simulated by a computer program implementable in a real…
Geometric camera calibration is often required for applications that understand the perspective of the image. We propose perspective fields as a representation that models the local perspective properties of an image. Perspective Fields…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
We introduce algorithms to visualize feature spaces used by object detectors. The tools in this paper allow a human to put on `HOG goggles' and perceive the visual world as a HOG based object detector sees it. We found that these…
Computational content encoded into constructive type theory proofs can be used to make computing experiments over concrete data structures. In this paper, we explore this possibility when working in Coq with chain complexes of infinite type…
A theorem on subwavelength imaging with arrays of discrete sources is formulated. This theorem is analogous to the Kotelnikov (also named Nyquist-Shannon) sampling theorem as it represents the field at an arbitrary point of space in terms…
A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields.
Vector quantization (VQ) is a technique to deterministically learn features with discrete codebook representations. It is commonly performed with a variational autoencoding model, VQ-VAE, which can be further extended to hierarchical…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…