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The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which…

数值分析 · 数学 2018-05-09 Neil K. Chada , Marco A. Iglesias , Lassi Roininen , Andrew M. Stuart

In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…

最优化与控制 · 数学 2025-06-16 Guozhi Dong , Michael Hintermüller , Clemens Sirotenko

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in…

Image matting is an important vision problem. The main stream methods for it combine sampling-based methods and propagation-based methods. In this paper, we deal with the combination with a normalized weighting parameter, which could well…

计算机视觉与模式识别 · 计算机科学 2017-10-30 Ping Li , Tingyan Duan , Yongfeng Cao

We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not…

We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

机器学习 · 计算机科学 2021-03-31 Allan Zhou , Tom Knowles , Chelsea Finn

This is a sequel to our paper `On the kernel learning problem'. We identify a canonical choice of Riemannian gradient flow, to find the stationary points in the kernel learning problem. In the presence of Gaussian noise variables, this flow…

最优化与控制 · 数学 2025-06-11 Yang Li , Feng Ruan

The task of image segmentation is to classify each pixel in the image based on the appropriate label. Various deep learning approaches have been proposed for image segmentation that offers high accuracy and deep architecture. However, the…

图像与视频处理 · 电气工程与系统科学 2022-12-29 Lukman Hakim , Takio Kurita

This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in…

最优化与控制 · 数学 2024-09-04 Dmitrij Sitenko , Bastian Boll , Christoph Schnörr

We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…

机器学习 · 统计学 2025-01-15 Bastian Boll , Daniel Gonzalez-Alvarado , Stefania Petra , Christoph Schnörr

Computer vision research has long aimed to build systems that are robust to spatial transformations found in natural data. Traditionally, this is done using data augmentation or hard-coding invariances into the architecture. However, too…

计算机视觉与模式识别 · 计算机科学 2024-02-19 Utkarsh Singhal , Carlos Esteves , Ameesh Makadia , Stella X. Yu

3D LiDAR sensors are indispensable for the robust vision of autonomous mobile robots. However, deploying LiDAR-based perception algorithms often fails due to a domain gap from the training environment, such as inconsistent angular…

计算机视觉与模式识别 · 计算机科学 2022-10-24 Kazuto Nakashima , Yumi Iwashita , Ryo Kurazume

Automatic and accurate detection of anatomical landmarks is an essential operation in medical image analysis with a multitude of applications. Recent deep learning methods have improved results by directly encoding the appearance of the…

计算机视觉与模式识别 · 计算机科学 2021-05-20 Guang-Quan Zhou , Juzheng Miao , Xin Yang , Rui Li , En-Ze Huo , Wenlong Shi , Yuhao Huang , Jikuan Qian , Chaoyu Chen , Dong Ni

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…

机器学习 · 计算机科学 2023-07-13 Tony Bonnaire , Aurélien Decelle , Nabila Aghanim

Practical networks for edge devices adopt shallow depth and small convolutional kernels to save memory and computational cost, which leads to a restricted receptive field. Conventional efficient learning methods focus on lightweight…

计算机视觉与模式识别 · 计算机科学 2023-01-25 Peijie Dong , Xin Niu , Zhiliang Tian , Lujun Li , Xiaodong Wang , Zimian Wei , Hengyue Pan , Dongsheng Li

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

无序系统与神经网络 · 物理学 2009-10-31 Magnus Rattray , David Saad

We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…

计算机视觉与模式识别 · 计算机科学 2017-05-10 Byung-Woo Hong , Ja-Keoung Koo , Martin Burger , Stefano Soatto

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…

最优化与控制 · 数学 2024-01-23 Matthias J. Ehrhardt , Silvia Gazzola , Sebastian J. Scott

In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…

机器学习 · 计算机科学 2019-02-04 Dimche Kostadinov , Behrooz Razdehi , Slava Voloshynovskiy