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In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each…

Numerical Analysis · Mathematics 2025-01-28 Tianhao Hu , Bangti Jin , Fengru Wang

We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…

Computational Geometry · Computer Science 2025-01-03 Vítor Gomes Chagas , Elisa Dell'Arriva , Flávio Keidi Miyazawa

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple…

Computational Geometry · Computer Science 2022-03-23 Shunji Umetani , Shohei Murakami

Fast and robust pupil detection is an essential prerequisite for video-based eye-tracking in real-world settings. Several algorithms for image-based pupil detection have been proposed, their applicability is mostly limited to laboratory…

Computer Vision and Pattern Recognition · Computer Science 2015-11-24 Wolfgang Fuhl , Thiago C. Santini , Thomas Kuebler , Enkelejda Kasneci

Oriented object detection is a challenging task in aerial images since the objects in aerial images are displayed in arbitrary directions and are frequently densely packed. The mainstream detectors describe rotating objects using a…

Computer Vision and Pattern Recognition · Computer Science 2021-11-09 Xinyi Yu , Mi Lin , Jiangping Lu , Linlin Ou

The proposed system outlined in this paper is a solution to a use case that requires the autonomous picking of cuboidal objects from an organized or unorganized pile with high precision. This paper presents an efficient method for precise…

Computer Vision and Pattern Recognition · Computer Science 2025-05-09 Utsav Rai , Hardik Mehta , Vismay Vakharia , Aditya Choudhary , Amit Parmar , Rolif Lima , Kaushik Das

Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…

Numerical Analysis · Mathematics 2014-10-28 Yujia Chen , Colin B. Macdonald

We propose a precise ellipsometric method for the investigation of coherent light with a small ellipticity. The main feature of this method is the use of compensators with phase delays providing the maximum accuracy of measurements for the…

Instrumentation and Detectors · Physics 2017-06-21 Nazar Al-wassiti , Evelina Bibikova , Nataliya Kundikova

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact…

Numerical Analysis · Mathematics 2019-02-14 Yiqiu Dong , Per Christian Hansen , Michiel E. Hochstenbach , Nicolai Andre Brogaard Riis

Shape recognition is the main challenging problem in computer vision. Different approaches and tools are used to solve this problem. Most existing approaches to object recognition are based on pixels. Pixel-based methods are dependent on…

Computer Vision and Pattern Recognition · Computer Science 2019-09-10 Narges Mirehi , Maryam Tahmasbi , Alireza Tavakoli Targhi

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…

Optimization and Control · Mathematics 2026-02-24 Antonio M. Sudoso

This work presents a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers, which has many applications for shape modeling across diverse fields. Unlike prior approaches that either exclusively…

Computer Vision and Pattern Recognition · Computer Science 2026-05-19 Mingyang Zhao , Sipu Ruan , Xiaohong Jia

In this paper, we present a novel method for solving multiobjective linear programming problems (MOLPP) that overcomes the need to calculate the optimal value of each objective function. This method is a follow-up to our previous work on…

Optimization and Control · Mathematics 2024-07-02 Mustapha Kaci , Sonia Radjef

This paper presents a novel and effective technique for extracting multiple ellipses from an image. The approach employs an evolutionary algorithm to mimic the way animals behave collectively assuming the overall detection process as a…

Computer Vision and Pattern Recognition · Computer Science 2014-05-21 Erik Cuevas , Maurici Gonzalez , Daniel Zaldivar , Marco Perez

The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…

Optimization and Control · Mathematics 2013-05-09 Steven Thomas Smith

Accurate and reliable nuclei identification is an essential part of quantification in microscopy. A range of mathematical and machine learning approaches are used but all methods have limitations. Such limitations include sensitivity to…

Quantitative Methods · Quantitative Biology 2019-04-11 Carl J. Nelson , Philip T. G. Jackson , Boguslaw Obara

Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…

Computational Geometry · Computer Science 2025-03-11 Andrew Cinar , Yue Zhao , Forrest Laine

Intrinsic isometric shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency, i.e., the metric structure of the whole manifold…

Computer Vision and Pattern Recognition · Computer Science 2014-01-14 Alan Brunton , Michael Wand , Stefanie Wuhrer , Hans-Peter Seidel , Tino Weinkauf

Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-22 Amitpal Tagore , Charles Keeton