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In this paper, we develop a new approach of spatially supervised recurrent convolutional neural networks for visual object tracking. Our recurrent convolutional network exploits the history of locations as well as the distinctive visual…
Accurate interpretation of street-level imagery is essential for large-scale urban mapping and the creation of Spatial Digital Twin (SDT) environments. This work presents a unified framework for joint 2D-3D segmentation and association that…
We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…
Topological invariants have played a fundamental role in the advancement of theoretical high energy physics. Physicists have used several kinematic techniques to distinguish new physics predictions from the Standard Model (SM) of particle…
Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…
The accurate tracking of live cells using video microscopy recordings remains a challenging task for popular state-of-the-art image processing based object tracking methods. In recent years, several existing and new applications have…
Applying image processing algorithms independently to each frame of a video often leads to undesired inconsistent results over time. Developing temporally consistent video-based extensions, however, requires domain knowledge for individual…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
3D multi-object tracking aims to uniquely and consistently identify all mobile entities through time. Despite the rich spatiotemporal information available in this setting, current 3D tracking methods primarily rely on abstracted…
Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…
Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…
We describe a new spatio-temporal video autoencoder, based on a classic spatial image autoencoder and a novel nested temporal autoencoder. The temporal encoder is represented by a differentiable visual memory composed of convolutional long…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…