Related papers: The Depth Poset under Transpositions in the Filter
Motivated by questions about simplification of topology, we take a discrete approach to the dependency of simplifying operations, using methods based on combinatorial gradient dynamics. We interpret the filter in persistent homology as a…
The interleaving distance, although originally developed for persistent homology, has been generalized to measure the distance between functors modeled on many posets or even small categories. Existing theories require that such a poset…
Persistent homology encodes the evolution of homological features of a multifiltered cell complex in the form of a multigraded module over a polynomial ring, called a multiparameter persistence module, and quantifies it through invariants…
A family of simplicial complexes, connected with simplicial maps and indexed by a poset $P$, is called a poset tower. The concept of poset towers subsumes classical objects of study in the persistence literature, as, for example,…
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology,…
The perverse filtration in cohomology and in cohomology with compact supports is interpreted in terms of kernels of restrictions maps to suitable subvarieties by using the Lefschetz hyperplane theorem and spectral objects. Various…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
Monocular depth predictors are typically trained on large-scale training sets which are naturally biased w.r.t the distribution of camera poses. As a result, trained predictors fail to make reliable depth predictions for testing examples…
This paper proposes a generalizable, end-to-end deep learning-based method for relative pose regression between two images. Given two images of the same scene captured from different viewpoints, our method predicts the relative rotation and…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
The configuration of latent representations plays a critical role in determining the performance of deep neural network classifiers. In particular, the emergence of well-separated class embeddings in the latent space has been shown to…
In this work we integrate ideas from surface-based modeling with neural synthesis: we propose a combination of surface-based pose estimation and deep generative models that allows us to perform accurate pose transfer, i.e. synthesize a new…
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persistence diagram defined as the M\"obius inversion of its…
We describe the perverse filtration in cohomology using the Lefschetz Hyperplane Theorem.
Process model quality has been an area of considerable research efforts. In this context, the correctness-by-construction principle of change patterns offers a promising perspective. However, using change patterns for model creation imposes…
The paper studies the relation between critical simplices and persistence diagrams of the \v{C}ech filtration. We show that adding a critical $k$-simplex into the filtration corresponds either to a point in the $k$th persistence diagram or…
Pose transfer refers to the probabilistic image generation of a person with a previously unseen novel pose from another image of that person having a different pose. Due to potential academic and commercial applications, this problem is…
The aim of this paper is to present a method for computation of persistent homology that performs well at large filtration values. To this end we introduce the concept of filtered covers. We show that the persistent homology of a bounded…
Homology decomposition techniques are a powerful tool used in the analysis of the homotopy theory of (classifying) spaces. The associated Bousfield-Kan spectral sequences involve higher derived limits of the inverse limit functor. We study…
One of the main objectives of topological data analysis is the study of discrete invariants for persistence modules, in particular when dealing with multiparameter persistence modules. In many cases, the invariants studied for these…