Related papers: Minimal and Canonical Images
A method for finding an optimum $n$-dimensional commutative group code of a given order $M$ is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of…
Evolutionary algorithms have recently been used to create a wide range of artistic work. In this paper, we propose a new approach for the composition of new images from existing ones, that retain some salient features of the original…
It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define…
It is shown how the canonical symmetry is used to look for the hierarchy of the Hamiltonian operators relevant to the system under consideration. It appears that only the invariance condition can be used to solve the problem.
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques.…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…
Following the footprints of what have been done with the algorithm Stacksort, we investigate the preimages of the map associated with a slightly less well known algorithm, called Queuesort. After having described an equivalent version of…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited to studying local properties of general finite groups. We…
This work addresses approximate nearest neighbor search applied in the domain of large-scale image retrieval. Within the group testing framework we propose an efficient off-line construction of the search structures. The linear-time…
The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their…
In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that…
In biological and medical research, scientists now routinely acquire microscopy images of hundreds of morphologically heterogeneous organoids and are then faced with the task of finding patterns in the image collection, i.e., subsets of…
Given a real objective function defined over the symmetric group, a direct local-search algorithm is proposed, and its complexity is estimated. In particular for an $n$-dimensional unit vector we are interested in the permutation isometry…
In many practical applications, signals and environments are time- varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…