This paper presents a novel approach to represent spatiotemporal visual information. We introduce a surface-based shape model whose structure is invariant to surface variations over time to describe 3D dynamic surfaces (e.g., obtained from multiview video capture). The descriptor is defined as a graph lying on object surfaces and anchored to invariant local features (e.g., extremal points). Geo...

We derive a complete set of invariants for a formal Bishop surface near a point of complex tangent with a vanishing Bishop invariant under the action of formal transformations. We prove that the modular space of Bishop surfaces with a vanishing Bishop invariant and with a fixed Moser invariant s < ∞ is of infinite dimension. We also prove that the equivalence class of the germ of a generic real...

We study the polynomial functions on tensor states in (Cn)⊗k which are invariant under SU(n). We describe the space of invariant polynomials in terms of symmetric group representations. For k even, the smallest degree for invariant polynomials is n and in degree n we find a natural generalization of the determinant. For n, d fixed, we describe the asymptotic behavior of the dimension of the spa...

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynomial and skein theory. Some examples of the invariant are computed. An unlinked embedded graph is one that contains only trivial knots or links. Examples show that the invariant is sufficiently powerful to distinguish some different unlinked embeddings of the ...

The modified Randić index of a graph G is a graph invariant closely related to the classical Randić index, defined as

Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have achieved only limited success in the classification of images that undergo geometric transformations. In this work we present a novel Transformation Invariant Gra...