Related papers: Image to Icosahedral Projection for $\mathrm{SO}(3…

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in…

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.…

6D pose estimation of rigid objects from RGB-D images is crucial for object grasping and manipulation in robotics. Although RGB channels and the depth (D) channel are often complementary, providing respectively the appearance and geometry…

Category-level object pose estimation aims to find 6D object poses of previously unseen object instances from known categories without access to object CAD models. To reduce the huge amount of pose annotations needed for category-level…

Estimating 3D from 2D is one of the central tasks in computer vision. In this work, we consider the monocular setting, i.e. single-view input, for 3D human pose estimation (HPE). Here, the task is to predict a 3D point set of human skeletal…

Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations. As panoramas are defined on the sphere, they naturally transform under the action of $SO(3)$, rendering conventional planar representations…

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the…

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…

Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…

Representation learning has become increasingly important, especially as powerful models have shifted towards learning latent representations before fine-tuning for downstream tasks. This approach is particularly valuable in leveraging the…

Image processing problems in general, and in particular in the field of single-particle cryo-electron microscopy, often require considering images up to their rotations and translations. Such problems were tackled successfully when…

Many robot manipulation tasks can be framed as geometric reasoning tasks, where an agent must be able to precisely manipulate an object into a position that satisfies the task from a set of initial conditions. Often, task success is defined…

This paper analyzes the robustness of recent 3D shape descriptors to SO(3) rotations, something that is fundamental to shape modeling. Specifically, we formulate the task of rotated 3D object instance detection. To do so, we consider a…

3D object detection from monocular images has proven to be an enormously challenging task, with the performance of leading systems not yet achieving even 10\% of that of LiDAR-based counterparts. One explanation for this performance gap is…

3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…

Incorporating inductive bias by embedding geometric entities (such as rays) as input has proven successful in multi-view learning. However, the methods adopting this technique typically lack equivariance, which is crucial for effective 3D…

Extending the translation equivariance property of convolutional neural networks to larger symmetry groups has been shown to reduce sample complexity and enable more discriminative feature learning. Further, exploiting additional symmetries…

Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…

Learning to predict reliable characteristic orientations of 3D point clouds is an important yet challenging problem, as different point clouds of the same class may have largely varying appearances. In this work, we introduce a novel method…