Related papers: The Depth Poset under Transpositions in the Filter
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
This research presents a novel depth estimation algorithm based on a Transformer-encoder architecture, tailored for the NYU and KITTI Depth Dataset. This research adopts a transformer model, initially renowned for its success in natural…
We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large…
In the past years, numerous methods have been introduced to reliably detect digital face image manipulations. Lately, the generalizability of these schemes has been questioned in particular with respect to image post-processing. Image…
Depth completion starts from a sparse set of known depth values and estimates the unknown depths for the remaining image pixels. Most methods model this as depth interpolation and erroneously interpolate depth pixels into the empty space…
Continuous diffusion models have demonstrated their effectiveness in addressing the inherent uncertainty and indeterminacy in monocular 3D human pose estimation (HPE). Despite their strengths, the need for large search spaces and the…
Denoising Diffusion models are gaining increasing popularity in the field of generative modeling for several reasons, including the simple and stable training, the excellent generative quality, and the solid probabilistic foundation. In…
Accurate 6D object pose estimation is an important task for a variety of robotic applications such as grasping or localization. It is a challenging task due to object symmetries, clutter and occlusion, but it becomes more challenging when…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
Morphogen profiles allow cells to determine their position within a developing organism, but the mechanisms behind the formation of these profiles are still not well agreed upon. Here we derive fundamental limits to the precision of…
The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with \v{C}ech filtration. A persistence diagram is a graphical descriptor of a topological and algebraic structure of geometric objects. We…
In this note, we investigate the relation between double points and complex points of immersed surfaces in almost-complex 4-manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number…
Transformer models systematically favor certain token positions, yet the architectural origins of this position bias remain poorly understood. This bias is closely connected to the Lost-in-the-Middle phenomenon, where models underutilize…
Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of…
Estimating the 6D object pose is an essential task in many applications. Due to the lack of depth information, existing RGB-based methods are sensitive to occlusion and illumination changes. How to extract and utilize the geometry features…
The Lefschetz number and fixed point index can be thought of as two different descriptions of the same invariant. The Lefschetz number is algebraic and defined using homology. The index is defined more directly from the topology and is a…
Deep learning is regarded as a promising solution for reversible steganography. There is an accelerating trend of representing a reversible steo-system by monolithic neural networks, which bypass intermediate operations in traditional…
High-precision localization is pivotal in underwater reinspection missions. Traditional localization methods like inertial navigation systems, Doppler velocity loggers, and acoustic positioning face significant challenges and are not…
This paper addresses the task of estimating the 6 degrees of freedom pose of a known 3D object from depth information represented by a point cloud. Deep features learned by convolutional neural networks from color information have been the…
The persistent homology transform (PHT) of a subset $M \subset \mathbb{R}^d$ is a map $\text{PHT}(M):\mathbb{S}^{d-1} \to \mathbf{Dgm}$ from the unit sphere to the space of persistence diagrams. This map assigns to each direction $v\in…