Related papers: Rotation-Invariant Vectorized Shape Representation…

In this paper, we propose a fixed-size object encoding method (FOE-VRD) to improve performance of visual relationship detection tasks. Comparing with previous methods, FOE-VRD has an important feature, i.e., it uses one fixed-size vector to…

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…

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…

Convolution is conventionally defined as a linear operation on functions of one or more variables which commutes with shifts. Group convolution generalizes the concept to linear operations on functions of group elements representing more…

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…

Heterogeneous object modelling is an emerging area where geometric shapes are considered in concert with their internal physically-based attributes. This paper describes a novel theoretical and practical framework for modelling volumetric…

This paper details an application which yields significant improvements to the adeptness of place recognition with Frequency-Modulated Continuous-Wave radar - a commercially promising sensor poised for exploitation in mobile autonomy. We…

A stationary rotating surface is a compact surface in Euclidean space whose mean curvature $H$ at each point $x$ satisfies $2H(x)=a r^2+b$, where $r$ is the distance from $x$ to a fixed straight-line $L$, and $a$ and $b$ are constants.…

In this paper, we propose a novel 3D graph convolution based pipeline for category-level 6D pose and size estimation from monocular RGB-D images. The proposed method leverages an efficient 3D data augmentation and a novel vector-based…

With the field of rigid-body robotics having matured in the last fifty years, routing, planning, and manipulation of deformable objects have recently emerged as a more untouched research area in many fields ranging from surgical robotics to…

Rotary Position Embedding (RoPE) is widely adopted in large language models, but when applied to vision-language models (VLMs) it couples text and image position indices and can introduce spurious cross-modal relative-position bias. We…

Embodied AI models often employ off the shelf vision backbones like CLIP to encode their visual observations. Although such general purpose representations encode rich syntactic and semantic information about the scene, much of this…

Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to…

Our aim is to study invariant hypersurfaces immersed in the Euclidean space $\mathbb{R}^{n+1}$, whose mean curvature is given as a linear function in the unit sphere $\mathbb{S}^n$ depending on its Gauss map. These hypersurfaces are closely…

Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on…

In this paper, we propose a simple yet effective method to endow deep 3D models with rotation invariance by expressing the coordinates in an intrinsic frame determined by the object shape itself. Key to our approach is to find such an…

$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…

We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…

Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topological transforms to be defined…

In this paper, we focus on recognizing 3D shapes from arbitrary views, i.e., arbitrary numbers and positions of viewpoints. It is a challenging and realistic setting for view-based 3D shape recognition. We propose a canonical view…