Related papers: Rotation-Invariant Spherical Watermarking via Thir…
Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study…
In many practical applications, 3D point cloud analysis requires rotation invariance. In this paper, we present a learnable descriptor invariant under 3D rotations and reflections, i.e., the O(3) actions, utilizing the recently introduced…
Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local…
In this thesis, we give a unification of the quantum WRT invariants. Given a rational homology 3-sphere M and a link L inside, we define the unified invariants, such that the evaluation of these invariants at a root of unity equals the…
In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial robot, this configuration space is $SE(3)=\mathbb{R}^3\times…
Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new…
We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…
We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are…
Attitude estimation using scalar measurements, corresponding to partial vectorial observations, arises naturally when inertial vectors are not fully observed but only measured along specific body-frame vectors. Such measurements arise in…
Establishing correspondences between 3D shapes is a fundamental task in 3D Computer Vision, typically addressed by matching local descriptors. Recently, a few attempts at applying the deep learning paradigm to the task have shown promising…
We address scaling in inhomogeneous and anisotropic turbulent flows by decomposing structure functions into their irreducible representation of the SO(3) symmetry group which are designated by $j,m$ indices. Employing simulations of channel…
360$^{\circ}$ panoramas are a rich medium, yet notoriously difficult to visualize in the 2D image plane. We explore how intelligent rotations of a spherical image may enable content-aware projection with fewer perceptible distortions.…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
We study the recovery of an unknown three-dimensional band-limited signal from multiple noisy observations that are randomly rotated by latent elements of SO(3), where the rotations are drawn from an unknown, non-uniform distribution.…
Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction.…
The rapid growth of transformer-based models increases the concerns about their integrity and ownership insurance. Watermarking addresses this issue by embedding a unique identifier into the model, while preserving its performance. However,…
We propose a local-to-global representation learning algorithm for 3D point cloud data, which is appropriate to handle various geometric transformations, especially rotation, without explicit data augmentation with respect to the…
We consider evolution equations for curves in the 3-dimensional sphere $S^3$ that are invariant under the group $SU(2,1)$ of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we…