Related papers: An Analysis of SVD for Deep Rotation Estimation

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…

Many settings in machine learning require the selection of a rotation representation. However, choosing a suitable representation from the many available options is challenging. This paper acts as a survey and guide through rotation…

Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

Recently, various view synthesis distortion estimation models have been studied to better serve for 3-D video coding. However, they can hardly model the relationship quantitatively among different levels of depth changes, texture…

We introduce a new approach for robotic manipulation tasks in human settings that necessitates understanding the 3D geometric connections between a pair of objects. Conventional end-to-end training approaches, which convert pixel…

The attitude of a rigid-body in the three dimensional space has a unique and global definition on the Special Orthogonal Group SO (3). This paper gives an overview of the rotation matrix, attitude kinematics and parameterization. The four…

Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations.…

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…

Determining the 3D orientations of an object in an image, known as single-image pose estimation, is a crucial task in 3D vision applications. Existing methods typically learn 3D rotations parametrized in the spatial domain using Euler…

Deep Convolutional Neural Networks (DCNN) have been proven to be effective for various computer vision problems. In this work, we demonstrate its effectiveness on a continuous object orientation estimation task, which requires prediction of…

Inserting an SVD meta-layer into neural networks is prone to make the covariance ill-conditioned, which could harm the model in the training stability and generalization abilities. In this paper, we systematically study how to improve the…

We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion},…

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…

Orthonormality is the foundation of matrix decomposition. For example, Singular Value Decomposition (SVD) implements the compression by factoring a matrix with orthonormal parts and is pervasively utilized in various fields. Orthonormality,…

Any model order reduced dynamical system that evolves a modal decomposition to approximate the discretized solution of a stochastic PDE can be related to a vector field tangent to the manifold of fixed rank matrices. The Dynamically…

A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…

Virtual orthognathic surgical planning involves simulating surgical corrections of jaw deformities on 3D facial bony shape models. Due to the lack of necessary guidance, the planning procedure is highly experience-dependent and the planning…

Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a random embedding to compress a target matrix, and they perform…