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Image reconstruction is likely the most predominant auxiliary task for image classification, but we would like to think twice about this convention. In this paper, we investigated "approximating the Fourier Transform of the input image" as…

Computer Vision and Pattern Recognition · Computer Science 2021-07-05 Chen Liu

Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…

Optimization and Control · Mathematics 2017-03-31 Mattias Fält , Pontus Giselsson

The utility of aerial imagery (Satellite, Drones) has become an invaluable information source for cross-disciplinary applications, especially for crisis management. Most of the mapping and tracking efforts are manual which is…

Computer Vision and Pattern Recognition · Computer Science 2020-04-28 Ruchit Rawal , Prabhu Pradhan

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic…

Classical Analysis and ODEs · Mathematics 2015-02-03 D. Karp , A. Savenkova , S. M. Sitnik

We mechanize the fundamental properties of a rounding error model for floating-point arithmetic based on relative precision, a measure of error proposed as a substitute for relative error in rounding error analysis. A key property of…

Numerical Analysis · Mathematics 2025-10-16 Max Fan , Ariel E. Kellison , Samuel D. Pollard

Localization in aerial imagery-based maps offers many advantages, such as global consistency, geo-referenced maps, and the availability of publicly accessible data. However, the landmarks that can be observed from both aerial imagery and…

Modern statistical analysis often encounters high-dimensional problems but with a limited sample size. It poses great challenges to traditional statistical estimation methods. In this work, we adopt auxiliary learning to solve the…

Statistics Theory · Mathematics 2025-01-08 Hanchao Yan , Feifei Wang , Chuanxin Xia , Hansheng Wang

Alpha matting aims to estimate the translucency of an object in a given image. The resulting alpha matte describes pixel-wise to what amount foreground and background colors contribute to the color of the composite image. While most methods…

Computer Vision and Pattern Recognition · Computer Science 2020-06-29 Thomas Germer , Tobias Uelwer , Stefan Conrad , Stefan Harmeling

The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…

Chemical Physics · Physics 2017-11-29 A. Bagci , P. E. Hoggan

When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…

Numerical Analysis · Mathematics 2018-08-23 Siyang Wang , Anna Nissen , Gunilla Kreiss

The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…

Computer Vision and Pattern Recognition · Computer Science 2014-09-12 Roberto Marazzato , Amelia Carolina Sparavigna

After the revelation that neural networks tend to produce overconfident predictions, the problem of calibration, which aims to align confidence with accuracy to enhance the reliability of predictions, has gained significant importance.…

Computer Vision and Pattern Recognition · Computer Science 2024-06-17 Gyusang Cho , Chan-Hyun Youn

This short article presents a mathematical formula required for metric corrections in image extraction and processing when using different length scale factors in three-dimensional space which is normally encountered in cryomicrotome image…

Quantitative Methods · Quantitative Biology 2012-09-05 Taha Sochi

Mask-guided matting networks have achieved significant improvements and have shown great potential in practical applications in recent years. However, simply learning matting representation from synthetic and lack-of-real-world-diversity…

Computer Vision and Pattern Recognition · Computer Science 2024-03-29 Weihao Jiang , Zhaozhi Xie , Yuxiang Lu , Longjie Qi , Jingyong Cai , Hiroyuki Uchiyama , Bin Chen , Yue Ding , Hongtao Lu

This paper presents the exact error analysis of point positioning equation used for airborne three-dimensional(3D) imaging sensor. With differential calculus and principles of precision analysis a mathematics formula on the point position…

Optics · Physics 2015-03-13 Yuesong Jiang , Xiaoxia Liu , Ruiqiang Chen , Yanling Wang

The auxiliary field method, defined through introducing an auxiliary (also called as the Hubbard-Stratonovich or the Mean-) field and utilizing a loop-expansion, gives an excellent result for a wide range of a coupling constant. The…

High Energy Physics - Theory · Physics 2009-10-31 Taro Kashiwa

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…

Discrete Mathematics · Computer Science 2025-10-20 Chengpu Wang

In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…

Numerical Analysis · Mathematics 2021-09-21 Carola Doerr , Michael Gnewuch , Magnus Wahlström

This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.

General Relativity and Quantum Cosmology · Physics 2007-05-23 S. Tertychniy

Improvement of the prediction accuracy of the Earth's rotation parameters (ERP) is one of the main problems of applied astrometry. In order to solve this problem, various approaches are used and in order to select the best one, comparison…

Geophysics · Physics 2023-04-11 Z. M. Malkin , V. M. Tissen