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$\ell_1$ regularization is used to preserve edges or enforce sparsity in a solution to an inverse problem. We investigate the Split Bregman and the Majorization-Minimization iterative methods that turn this non-smooth minimization problem…

Numerical Analysis · Mathematics 2024-12-16 Brian Sweeney , Rosemary Renaut , Malena Español

Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutive images. This work introduces an efficient dual…

Optimization and Control · Mathematics 2021-10-05 Hongpeng Sun , Xue-Cheng Tai , Jing Yuan

This paper deals with a challenging, frequently encountered, yet not properly investigated problem in two-frame optical flow estimation. That is, the input frames are compounds of two imaging layers -- one desired background layer of the…

Computer Vision and Pattern Recognition · Computer Science 2016-05-09 Jiaolong Yang , Hongdong Li , Yuchao Dai , Robby T. Tan

Occlusions pose a significant challenge to optical flow algorithms that rely on local evidences. We consider an occluded point to be one that is imaged in the first frame but not in the next, a slight overloading of the standard definition…

Computer Vision and Pattern Recognition · Computer Science 2021-08-02 Shihao Jiang , Dylan Campbell , Yao Lu , Hongdong Li , Richard Hartley

Moving object detection and its associated background-foreground separation have been widely used in a lot of applications, including computer vision, transportation and surveillance. Due to the presence of the static background, a video…

Computer Vision and Pattern Recognition · Computer Science 2022-04-27 Jing Qin , Ruilong Shen , Ruihan Zhu , Biyun Xie

In this work we consider the problem of finding optimal regularization parameters for general-form Tikhonov regularization using training data. We formulate the general-form Tikhonov solution as a spectral filtered solution using the…

Numerical Analysis · Mathematics 2014-07-09 Julianne Chung , Malena I. Español , Tuan Nguyen

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

Optimization and Control · Mathematics 2021-11-15 Bennet Gebken , Katharina Bieker , Sebastian Peitz

A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization via the use of the total variation. On the other hand, sparse or noisy data often demands a…

Optimization and Control · Mathematics 2020-04-13 Oliver R. A. Dunbar , Matthew M. Dunlop , Charles M. Elliott , Viet Ha Hoang , Andrew M. Stuart

Video-based person re-identification matches video clips of people across non-overlapping cameras. Most existing methods tackle this problem by encoding each video frame in its entirety and computing an aggregate representation across all…

Computer Vision and Pattern Recognition · Computer Science 2018-03-28 Shuang Li , Slawomir Bak , Peter Carr , Xiaogang Wang

Image registration is an inherently ill-posed problem that lacks the constraints needed for a unique mapping between voxels of the two images being registered. As such, one must regularize the registration to achieve physically meaningful…

Numerical Analysis · Mathematics 2025-02-03 Keyur D. Shah , James A. Shackleford , Nagarajan Kandasamy , Gregory C. Sharp

Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…

Optimization and Control · Mathematics 2021-02-09 Yan-ran Li , Raymond H. F. Chan , Lixin Shen , Xiaosheng Zhuang

When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…

Image and Video Processing · Electrical Eng. & Systems 2023-07-03 Min Zhao , Nicolas Dobigeon , Jie Chen

In this paper, we proposed an unsupervised learning method for estimating the optical flow between video frames, especially to solve the occlusion problem. Occlusion is caused by the movement of an object or the movement of the camera,…

Computer Vision and Pattern Recognition · Computer Science 2020-03-05 Jianfeng Li , Junqiao Zhao , Tiantian Feng , Chen Ye , Lu Xiong

Motion detection has been widely used in many applications, such as surveillance and robotics. Due to the presence of the static background, a motion video can be decomposed into a low-rank background and a sparse foreground. Many…

Computer Vision and Pattern Recognition · Computer Science 2023-04-12 Jing Qin , Biyun Xie

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…

Optimization and Control · Mathematics 2022-05-09 Michael Hintermüller , Kostas Papafitsoros , Carlos N. Rautenberg , Hongpeng Sun

The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static…

Computer Vision and Pattern Recognition · Computer Science 2017-05-04 Jonas Wulff , Laura Sevilla-Lara , Michael J. Black

We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…

Optimization and Control · Mathematics 2025-02-13 Majid E. Abbasov , Anna I. Belenok

Knowing the 3D motions in a dynamic scene is essential to many vision applications. Recent progress is mainly focused on estimating the activity of some specific elements like humans. In this paper, we leverage a neural motion field for…

Computer Vision and Pattern Recognition · Computer Science 2023-04-07 Liangchen Song , Xuan Gong , Benjamin Planche , Meng Zheng , David Doermann , Junsong Yuan , Terrence Chen , Ziyan Wu

For the success of video deblurring, it is essential to utilize information from neighboring frames. Most state-of-the-art video deblurring methods adopt motion compensation between video frames to aggregate information from multiple frames…

Computer Vision and Pattern Recognition · Computer Science 2021-08-27 Hyeongseok Son , Junyong Lee , Jonghyeop Lee , Sunghyun Cho , Seungyong Lee

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The…

Machine Learning · Computer Science 2025-06-25 Carlos Stein Brito