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Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous…

Numerical Analysis · Mathematics 2025-01-23 Toluwani Okunola , Mirjeta Pasha , Misha Kilmer , Melina Freitag

In many robotics and VR/AR applications, fast camera motions lead to a high level of motion blur, causing existing camera pose estimation methods to fail. In this work, we propose a novel framework that leverages motion blur as a rich cue…

Computer Vision and Pattern Recognition · Computer Science 2025-11-27 Jerred Chen , Ronald Clark

This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…

Numerical Analysis · Mathematics 2025-07-08 Yohann De Castro , Vincent Duval , Romain Petit

In this paper, two simple principal component regression methods for estimating the optical flow between frames of video sequences according to a pel-recursive manner are introduced. These are easy alternatives to dealing with mixtures of…

Computer Vision and Pattern Recognition · Computer Science 2016-11-09 Felipe P. do Carmo , Vania Vieira Estrela , Joaquim Teixeira de Assis

In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of…

Computer Vision and Pattern Recognition · Computer Science 2008-09-29 Claire Jonchery , Françoise Dibos , Georges Koepfler

This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complex-steerable pyramid.…

Computer Vision and Pattern Recognition · Computer Science 2016-09-09 S. L. Pintea , J. C. van Gemert

We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. (2013) and Weickert et al. (2013) The minimization of the proposed…

Computer Vision and Pattern Recognition · Computer Science 2020-03-26 Simone Parisotto , Luca Calatroni , Aurélie Bugeau , Nicolas Papadakis , Carola-Bibiane Schönlieb

Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…

Analysis of PDEs · Mathematics 2019-10-15 Carlos M. Paniagua Mejia

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a…

Numerical Analysis · Mathematics 2013-08-09 Konstantinos Papafitsoros , Carola-Bibiane Schönlieb

The ability to amplify or reduce subtle image changes over time is useful in contexts such as video editing, medical video analysis, product quality control and sports. In these contexts there is often large motion present which severely…

Computer Vision and Pattern Recognition · Computer Science 2017-04-25 Yichao Zhang , Silvia L. Pintea , Jan C. van Gemert

The computation of 2-D optical flow by means of regularized pel-recursive algorithms raises a host of issues, which include the treatment of outliers, motion discontinuities and occlusion among other problems. We propose a new approach…

Computer Vision and Pattern Recognition · Computer Science 2016-11-07 Vania V. Estrela , Luis A. Rivera , Paulo C. Beggio , Ricardo T. Lopes

We propose a method to restore and to segment simultaneously images degraded by a known point spread function (PSF) and additive white noise. For this purpose, we propose a joint Bayesian estimation framework, where a family of…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Hacheme Ayasso , Ali Mohammad-Djafari

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

Computer Vision and Pattern Recognition · Computer Science 2015-12-03 Xiaowei Zhou , Menglong Zhu , Kostas Daniilidis

The space of images can be equipped with a Riemannian metric measuring both the cost of transport of image intensities and the variation of image intensities along motion lines. The resulting metamorphosis model was introduced and analyzed…

Numerical Analysis · Mathematics 2017-05-15 Alexander Effland , Martin Rumpf , Florian Schäfer

A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…

Optimization and Control · Mathematics 2018-12-10 Antonin Chambolle , Martin Holler Thomas Pock

Event cameras provide rich signals that are suitable for motion estimation since they respond to changes in the scene. As any visual changes in the scene produce event data, it is paramount to classify the data into different motions (i.e.,…

Computer Vision and Pattern Recognition · Computer Science 2025-04-28 Ryo Yamaki , Shintaro Shiba , Guillermo Gallego , Yoshimitsu Aoki

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the…

Optimization and Control · Mathematics 2016-10-03 Fang Li , Stanley Osher , Jing Qin , Ming Yan

Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…

Computer Vision and Pattern Recognition · Computer Science 2020-12-01 Riccardo Barbano , Željko Kereta , Chen Zhang , Andreas Hauptmann , Simon Arridge , Bangti Jin

We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic…

Numerical Analysis · Mathematics 2020-05-20 Andreas Bock , Colin Cotter

Image animation aims to animate a source image by using motion learned from a driving video. Current state-of-the-art methods typically use convolutional neural networks (CNNs) to predict motion information, such as motion keypoints and…

Computer Vision and Pattern Recognition · Computer Science 2022-09-29 Jiale Tao , Biao Wang , Tiezheng Ge , Yuning Jiang , Wen Li , Lixin Duan