Related papers: Functional Maps Representation on Product Manifold…

Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum…

In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…

Shape matching is a fundamental task in computer graphics and vision, with deep functional maps becoming a prominent paradigm. However, existing methods primarily focus on learning informative feature representations by constraining…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

In this paper, we define the notion of a mapping on soft classes and study several properties of images and inverse images of soft sets supported by examples and counterexamples. Finally, these notions have been applied to the problem of…

Implicit Neural Representations (INRs) employ neural networks to represent continuous functions by mapping coordinates to the corresponding values of the target function, with applications e.g., inverse graphics. However, INRs face a…

Neural fields have emerged as a new paradigm for representing signals, thanks to their ability to do it compactly while being easy to optimize. In most applications, however, neural fields are treated like black boxes, which precludes many…

Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the…

The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…

A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes in flat domains while preserving…

Class activation maps are widely used for explaining deep neural networks. Due to its ability to highlight regions of interest, it has evolved in recent years as a key step in weakly supervised learning. A major limitation to the…

Point clouds can be regarded as discrete samples of smooth manifolds and are typically analyzed via the eigenfunctions of the Laplace-Beltrami operator. This paper extends manifold spectral analysis to the fractional domain, enabling…

When representing a solid object there are alternatives to the use of traditional explicit (surface meshes) or implicit (zero crossing of implicit functions) methods. Skeletal representations encode shape information in a mixed fashion:…

Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…

Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that…

While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…

Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure,…

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…

This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.

We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal…