With the advent of Neural Radiance Fields (NeRF), neural networks can now render novel
views of a 3D scene with quality that fools the human eye. Yet, generating these images is …

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes).
When a small number of convexes are used, such a decomposition can be thought of as …

This paper is devoted to the generalized Fermat equation x p + y q = z r , where p, q and r are
integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent …

We propose a self-supervised capsule architecture for 3D point clouds. We compute
capsule decompositions of objects through permutation-equivariant attention, and self-supervise …

Capsule networks aim to parse images into a hierarchy of objects, parts and relations. While
promising, they remain limited by an inability to learn effective low level part descriptions. To …

In this paper, we develop machinery to solve ternary Diophantine equations of the shape Axn
+ Byn = C z3 for various choices of coefficients (A, B, C). As a byproduct of this, we show, if …

We introduce a method for instance proposal generation for 3D point clouds. Existing techniques
typically directly regress proposals in a single feed-forward step, leading to inaccurate …

Neural fields have emerged as a powerful and broadly applicable method for representing
signals. However in contrast to classical discrete digital signal processing the portfolio of tools …

Implicit representations of geometry, such as occupancy fields or signed distance fields (SDF),
have recently re-gained popularity in encoding 3D solid shape in a functional form. In this …

The Fekete polynomials are defined as\[F_q (z):=\sum^{q-1} _ {k= 1}\left (\frac {k}{q}\right) z^
k\] where $\left (\frac {\cdot}{q}\right) $ is the Legendre symbol. These polynomials arise in a …