scholarly journals Euclidean Distance Geometry and Applications

SIAM Review ◽  
2014 ◽  
Vol 56 (1) ◽  
pp. 3-69 ◽  
Author(s):  
Leo Liberti ◽  
Carlile Lavor ◽  
Nelson Maculan ◽  
Antonio Mucherino
Keyword(s):  
Euclidean Distance ◽  
Distance Geometry ◽  
Euclidean Distance Geometry

scholarly journals Homology Initialization for Protein Structure Determination via Distance Geometry

2020 ◽  
Author(s):  
Abiy Tasissa ◽  
Rongjie Lai ◽  
Chunyu Wang
Keyword(s):  
Protein Structure ◽  
Structure Determination ◽  
Numerical Experiments ◽  
Euclidean Distance ◽  
Partial Information ◽  
Distance Geometry ◽  
Protein Structure Determination ◽  
Geometry Problem ◽  
Distance Geometry Problem ◽  
Euclidean Distance Geometry

AbstractThe problem of finding the configuration of points given partial information on pairwise inter-point distances, the Euclidean distance geometry problem, appears in multiple applications. In this paper, we propose an approach that integrates homology modeling and a nonconvex distance geometry algorithm for the protein structure determination problem. Preliminary numerical experiments show promising results.

scholarly journals Microphone array positioning technique with Euclidean distance geometry

2020 ◽  
Vol 167 ◽  
pp. 107377
Author(s):  
Simon Bouley ◽  
Charles Vanwynsberghe ◽  
Thibaut Le Magueresse ◽  
Jérôme Antoni ◽  
Allan Outrequin
Keyword(s):  
Euclidean Distance ◽  
Microphone Array ◽  
Distance Geometry ◽  
Positioning Technique ◽  
Euclidean Distance Geometry

scholarly journals A maximal Gross-Stadje number in the Euclidean plane

2000 ◽  
Vol 61 (1) ◽  
pp. 109-119
Author(s):  
F. Pillichshammer
Keyword(s):  
Continuous Function ◽  
Positive Integer ◽  
Real Number ◽  
Upper Bound ◽  
Euclidean Distance ◽  
Hausdorff Space ◽  
Euclidean Plane ◽  
Distance Geometry ◽  
Open Question ◽  
Squared Euclidean Distance

Let X be a compact, connected Hausdorff space and f a real valued, symmetric, continuous function on X × X. Then the Gross-Stadje number r (X, f) is the unique real number with the property that for each positive integer n and for all (not necessarily distinct) x1,…,xn in X, there exists some x in X such that . This paper solves the following open question in distance geometry: What is the least upper bound g2(R2) of r (X, d2), where X ranges over all compact, connected subsets of the Euclidean plane with diameter one and where d2 denotes the squared, Euclidean distance. We show: .

The Earth Mover’s Distance as a Metric for the Space of Inorganic Compositions

2020 ◽  
Author(s):  
Cameron Hargreaves ◽  
Matthew Dyer ◽  
Michael Gaultois ◽  
Vitaliy Kurlin ◽  
Matthew J Rosseinsky
Keyword(s):  
Euclidean Distance ◽  
Nearest Neighbor ◽  
Nearest Neighbor Search ◽  
Inorganic Crystal Structure Database ◽  
Earth Mover’S Distance ◽  
Chemical Similarity ◽  
Earth Mover's Distance ◽  
Neighbor Search ◽  
The Earth ◽  
Binary Compounds

It is a core problem in any field to reliably tell how close two objects are to being the same, and once this relation has been established we can use this information to precisely quantify potential relationships, both analytically and with machine learning (ML). For inorganic solids, the chemical composition is a fundamental descriptor, which can be represented by assigning the ratio of each element in the material to a vector. These vectors are a convenient mathematical data structure for measuring similarity, but unfortunately, the standard metric (the Euclidean distance) gives little to no variance in the resultant distances between chemically dissimilar compositions. We present the Earth Mover’s Distance (EMD) for inorganic compositions, a well-defined metric which enables the measure of chemical similarity in an explainable fashion. We compute the EMD between two compositions from the ratio of each of the elements and the absolute distance between the elements on the modified Pettifor scale. This simple metric shows clear strength at distinguishing compounds and is efficient to compute in practice. The resultant distances have greater alignment with chemical understanding than the Euclidean distance, which is demonstrated on the binary compositions of the Inorganic Crystal Structure Database (ICSD). The EMD is a reliable numeric measure of chemical similarity that can be incorporated into automated workflows for a range of ML techniques. We have found that with no supervision the use of this metric gives a distinct partitioning of binary compounds into clear trends and families of chemical property, with future applications for nearest neighbor search queries in chemical database retrieval systems and supervised ML techniques.

Level Set Method Optimized with the Euclidean Distance Transform

2019 ◽  
Author(s):  
Luis Fernando Segalla ◽  
Alexandre Zabot ◽  
Diogo Nardelli Siebert ◽  
Fabiano Wolf
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Euclidean Distance ◽  
Distance Transform ◽  
Euclidean Distance Transform

Improving the Computational Cost for Copied Region Detection in Forensic Images

2016 ◽  
Vol 2 (1) ◽  
pp. 55
Author(s):  
Tu Huynh-Kha ◽  
Thuong Le-Tien ◽  
Synh Ha ◽  
Khoa Huynh-Van
Keyword(s):  
Wavelet Transform ◽  
Euclidean Distance ◽  
Research Work ◽  
Computational Cost ◽  
Correlation Coefficients ◽  
Zernike Moments ◽  
Computational Time ◽  
Discrete Wavelet ◽  
Feature Vectors ◽  
Region Detection

This research work develops a new method to detect the forgery in image by combining the Wavelet transform and modified Zernike Moments (MZMs) in which the features are defined from more pixels than in traditional Zernike Moments. The tested image is firstly converted to grayscale and applied one level Discrete Wavelet Transform (DWT) to reduce the size of image by a half in both sides. The approximation sub-band (LL), which is used for processing, is then divided into overlapping blocks and modified Zernike moments are calculated in each block as feature vectors. More pixels are considered, more sufficient features are extracted. Lexicographical sorting and correlation coefficients computation on feature vectors are next steps to find the similar blocks. The purpose of applying DWT to reduce the dimension of the image before using Zernike moments with updated coefficients is to improve the computational time and increase exactness in detection. Copied or duplicated parts will be detected as traces of copy-move forgery manipulation based on a threshold of correlation coefficients and confirmed exactly from the constraint of Euclidean distance. Comparisons results between proposed method and related ones prove the feasibility and efficiency of the proposed algorithm.

IMPLEMENTASI METODE EUCLIDEAN DISTANCE UNTUK EKSTRAKSI FITUR JARAK PADA CITRA SKELETON

2019 ◽  
Vol 24 (2) ◽  
pp. 134-139
Author(s):  
Miftahul Jannah ◽  
Nurul Humaira
Keyword(s):  
Euclidean Distance

Gait adalah cara atau sikap berjalan kaki seseorang. Tiap orang memiliki cara berjalan yang berbeda, sehingga gerak jalan seseorang sulit untuk disembunyikan ataupun direkayasa. Analisis gait adalah ilmu pengetahuan yang mempelajari tentang kemampuan atau cara bergerak manusia. Dalam bidang kedokteran, analisis gait digunakan untuk menentukan penanganan dan terapi bagi pasien rehabilitasi medik. Dalam penelitian ini digunakan fitur jarak pada citra skeleton. Ekstraksi fitur jarak pada citra skeleton menggunakan metode euclidean distance terbagi dalam beberapa tahapan, dimulai dengan mengambil citra skeleton, konversi citra RGB menjadi citra Biner, proses menemukan titik koordinat dari titik akhir dan titik percabangan, dan ekstraksi fitur pada skeleton. Metode yang digunakan menghasilkan persentase tingkat keberhasilan sebesar 87.84%.

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