Related papers: Rotation-Invariant Spherical Watermarking via Thir…
Spherical convolutional networks have been introduced recently as tools to learn powerful feature representations of 3D shapes. Spherical CNNs are equivariant to 3D rotations making them ideally suited to applications where 3D data may be…
Second-order conic optimization (SOCO) can be considered as a special case of semidefinite optimization (SDO). In the literature it has been advised that a SOCO problem can be embedded in an SDO problem using the arrow-head matrix…
Features that are equivariant to a larger group of symmetries have been shown to be more discriminative and powerful in recent studies. However, higher-order equivariant features often come with an exponentially-growing computational cost.…
Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…
We develop an in-depth analysis of the $SO(4)$ Landau models on $S^3$ in the $SU(2)$ monopole background and their associated matrix geometry. The Schwinger and Dirac gauges for the $SU(2)$ monopole are introduced to provide a concrete…
We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical…
In this paper, we present the implicit equations for one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation, we construct the rotationally invariant measure of deviation from the…
When doing representation learning on data that lives on a known non-trivial manifold embedded in high dimensional space, it is natural to desire the encoder to be homeomorphic when restricted to the manifold, so that it is bijective and…
3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity.…
No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding.…
This paper focuses on visual motion-based invariants that result in a representation of 3D points in which the stationary environment remains invariant, ensuring shape constancy. This is achieved even as the images undergo constant change…
When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness…
This paper proposes a correspondence-free method for point cloud rotational registration. We learn an embedding for each point cloud in a feature space that preserves the SO(3)-equivariance property, enabled by recent developments in…
This article proposes a mortar type finite element formulation for consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into 3D solid volumes. A consistent 1D-3D coupling scheme for this problem type is proposed, which…
Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…
This paper proposes a convolution structure for learning SE(3)-equivariant features from 3D point clouds. It can be viewed as an equivariant version of kernel point convolutions (KPConv), a widely used convolution form to process point…
Data augmentation in feature space is effective to increase data diversity. Previous methods assume that different classes have the same covariance in their feature distributions. Thus, feature transform between different classes is…
Intraoperative 2D/3D registration aligns preoperative 3D volumes with real-time 2D radiographs, enabling accurate localization of instruments and implants. A recent fully differentiable similarity learning framework approximates geodesic…
The dictionary learning problem can be viewed as a data-driven process to learn a suitable transformation so that data is sparsely represented directly from example data. In this paper, we examine the problem of learning a dictionary that…
The $\mathrm{SE}(3)$ invariants of a pose include its rotation angle and screw translation. In this paper, we present a complete comprehensive study of the relative pose estimation problem for a calibrated camera constrained by known…