Related papers: Rotation-Invariant Vectorized Shape Representation…
This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…
Machine learning has become a promising approach for molecular modeling. Positional quantities, such as interatomic distances and bond angles, play a crucial role in molecule physics. The existing works rely on careful manual design of…
Robotics and computer vision problems commonly require handling rigid-body motions comprising translation and rotation - together referred to as pose. In some situations, a vectorial parameterization of pose can be useful, where elements of…
In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a…
The ability to automatically encircle boundaries with mobile robots is crucial for tasks such as border tracking and object enclosing. Previous research has primarily focused on regular boundaries, often assuming that their geometric…
There is a Rota-Baxter algebra structure on the field $A=\mathbf{k}((t))$ with $ P$ being the projection map $A=\mathbf{k}[[t]]\oplus t^{-1}\mathbf{k}[t^{-1}]$ onto $ \mathbf{k}[[ t]]$. We study the representation theory and…
Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…
Continuum robots possess high flexibility and redundancy, making them well suited for safe interaction in complex environments, yet their continuous deformation and nonlinear dynamics pose fundamental challenges to perception, modeling, and…
Many data representations are vectors of continuous values. In particular, deep learning embeddings are data-driven representations, typically either unconstrained in Euclidean space, or constrained to a hypersphere. These may also be…
The physical properties of matter are typically described by coefficient matrices governed by crystal symmetry. Applying spatial operations, such as rotation, inversion, and mirror, to these matrices provides an effective approach for…
3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do…
This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the…
Although the vectorization operation is known and well-defined, it is only defined for 2-D matrices, and its inverse isn't as well-popularized. This work proposes to generalize the vectorization to higher dimensions, and define…
Invariant integrals of functions and forms over $q$ - deformed Euclidean space and spheres in $N$ dimensions are defined and shown to be positive definite, compatible with the star - structure and to satisfy a cyclic property involving the…
In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions.…
The rotational dimension is a minor monotone graph invariant related to the dimension of an Euclidean space containing a spectral embedding corresponding to the first nonzero eigenvalue of the graph Laplacian, which is introduced by…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
Transformers have emerged as a universal backbone across 3D perception, video generation, and world models for autonomous driving and embodied AI, where understanding camera geometry is essential for grounding visual observations in…
Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…