相关论文: Incorporating Cyclic Group Equivariance into Deep …
Computed Tomography (CT) using synchrotron radiation is a powerful technique that, compared to lab-CT techniques, boosts high spatial and temporal resolution while also providing access to a range of contrast-formation mechanisms. The…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces. To mitigate strong inter-subject variability, recent work has emphasized manifold-based approaches operating on covariance…
Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant…
Rotational invariance is a popular inductive bias used by many fields in machine learning, such as computer vision and machine learning for quantum chemistry. Rotation-invariant machine learning methods set the state of the art for many…
Computed Tomography (CT) reconstruction is a fundamental component to a wide variety of applications ranging from security, to healthcare. The classical techniques require measuring projections, called sinograms, from a full 180$^\circ$…
Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts…
X-ray Computed Tomography (CT) is an important tool in medical imaging to obtain a direct visualization of patient anatomy. However, the x-ray radiation exposure leads to the concern of lifetime cancer risk. Low-dose CT scan can reduce the…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…
We present Roto-Translation Equivariant Spherical Deconvolution (RT-ESD), an $E(3)\times SO(3)$ equivariant framework for sparse deconvolution of volumes where each voxel contains a spherical signal. Such 6D data naturally arises in…
Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
We present a method for learning discriminative filters using a shallow Convolutional Neural Network (CNN). We encode rotation invariance directly in the model by tying the weights of groups of filters to several rotated versions of the…
Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…
Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying…
Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for…
Deformable image registration plays a fundamental role in medical image analysis by enabling spatial alignment of anatomical structures across subjects. While recent deep learning-based approaches have significantly improved computational…
Image co-segmentation is an active computer vision task that aims to segment the common objects from a set of images. Recently, researchers design various learning-based algorithms to undertake the co-segmentation task. The main difficulty…
CNNs exhibit inherent equivariance to image translation, leading to efficient parameter and data usage, faster learning, and improved robustness. The concept of translation equivariant networks has been successfully extended to rotation…