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We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are…

Optimization and Control · Mathematics 2013-05-22 Clemens Kirisits , Lukas F. Lang , Otmar Scherzer

We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…

Numerical Analysis · Mathematics 2023-01-18 Jan-F. Pietschmann , Matthias Schlottbom

In spite of the utility of 3-D electron back-scattered diffraction (EBSD) microscopy, the data collection process can be time-consuming with serial-sectioning. Hence, it is natural to look at other modalities, such as polarized light (PL)…

Image and Video Processing · Electrical Eng. & Systems 2026-04-27 Harry Dong , Timofey Efimov , Megna Shah , Jeff Simmons , Sean Donegan , Marc De Graef , Yuejie Chi

Temporally consistent dense video annotations are scarce and hard to collect. In contrast, image segmentation datasets (and pre-trained models) are ubiquitous, and easier to label for any novel task. In this paper, we introduce a method to…

Computer Vision and Pattern Recognition · Computer Science 2022-03-18 Aharon Azulay , Tavi Halperin , Orestis Vantzos , Nadav Borenstein , Ofir Bibi

Optical imaging plays a crucial role in advancing science and technology, enabling applications in fields ranging from biomedicine to astronomy. However, imaging through scattering media such as biological tissues, fog, or turbulent…

We address unsupervised optical flow estimation for ego-centric motion. We argue that optical flow can be cast as a geometrical warping between two successive video frames and devise a deep architecture to estimate such transformation in…

Computer Vision and Pattern Recognition · Computer Science 2017-10-31 Stefano Alletto , Davide Abati , Simone Calderara , Rita Cucchiara , Luca Rigazio

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…

Numerical Analysis · Mathematics 2018-12-10 Miroslav Bačák , Ronny Bergmann , Gabriele Steidl , Andreas Weinmann

Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…

Computer Vision and Pattern Recognition · Computer Science 2016-04-12 Laura Sevilla-Lara , Deqing Sun , Varun Jampani , Michael J. Black

The paper addresses the generalization of the half-quadratic minimization method for the restoration of images having values in a complete Riemannian manifold. We recall the half-quadratic minimization method using the notation of the…

Numerical Analysis · Mathematics 2018-12-10 Ronny Bergmann , Raymond H. Chan , Ralf Hielscher , Johannes Persch , Gabriele Steidl

We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion…

Optimization and Control · Mathematics 2014-06-26 Clemens Kirisits , Lukas F. Lang , Otmar Scherzer

Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition.…

Signal Processing · Electrical Eng. & Systems 2024-01-15 Muhammad Wasim Nawaz , Abdesselam Bouzerdoum , Muhammad Mahboob Ur Rahman , Ghulam Abbas , Faizan Rashid

The aim of this paper is to discuss and evaluate total variation based regularization methods for motion estimation, with particular focus on optical flow models. In addition to standard $L^2$ and $L^1$ data fidelities we give an overview…

Numerical Analysis · Mathematics 2015-12-02 Martin Burger , Hendrik Dirks , Lena Frerking

Reconstructing high-quality images from undersampled dynamic MRI data is a challenging task and important for the success of this imaging modality. To remedy the naturally occurring artifacts due to measurement undersampling, one can…

Optimization and Control · Mathematics 2025-04-29 Matthias J. Ehrhardt , Marco Mauritz

Conditional diffusion inversion provides a powerful framework for unpaired image-to-image translation. However, we demonstrate through an extensive analysis that standard deterministic inversion (e.g. DDIM) fails when the source domain is…

Computer Vision and Pattern Recognition · Computer Science 2026-02-17 Nicolas Bourriez , Alexandre Verine , Auguste Genovesio

We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. The synchrosqueezed transform is applied to extract initial…

Materials Science · Physics 2016-04-20 Jianfeng Lu , Benedikt Wirth , Haizhao Yang

This study explores the use of photometric techniques (shape-from-shading and uncalibrated photometric stereo) for upsampling the low-resolution depth map from an RGB-D sensor to the higher resolution of the companion RGB image. A…

Computer Vision and Pattern Recognition · Computer Science 2019-06-26 Bjoern Haefner , Songyou Peng , Alok Verma , Yvain Quéau , Daniel Cremers

X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…

Computer Vision and Pattern Recognition · Computer Science 2022-08-22 Arpit Bansal , Eitan Borgnia , Hong-Min Chu , Jie S. Li , Hamid Kazemi , Furong Huang , Micah Goldblum , Jonas Geiping , Tom Goldstein

Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…

Computer Vision and Pattern Recognition · Computer Science 2018-06-05 Jérémy Anger , Mauricio Delbracio , Gabriele Facciolo

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