Related papers: Multimapper: Data Density Sensitive Topological Vi…

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric…

We propose a weakly-supervised multi-view learning approach to learn category-specific surface mapping without dense annotations. We learn the underlying surface geometry of common categories, such as human faces, cars, and airplanes, given…

We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.

Vectorized high-definition (HD) maps contain detailed information about surrounding road elements, which are crucial for various downstream tasks in modern autonomous vehicles, such as motion planning and vehicle control. Recent works…

We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…

Data analysis often concerns not only the space where data come from, but also various types of maps attached to data. In recent years, several related structures have been used to study maps on data, including Reeb spaces, mappers and…

Depth imaging has largely focused on sensor and intrinsics properties. However, the accuracy of acquire pixel is largely dependent on the capture. We propose a new depth estimation and approximation algorithm which takes an arbitrary 3D…

Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm…

Constructing effective representations is a critical but challenging problem in multimedia understanding. The traditional handcraft features often rely on domain knowledge, limiting the performances of exiting methods. This paper discusses…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

In autonomous driving, mapping is critical for motion planning but remains an under-utilized resource for perception tasks such as 3D object detection. Maps can provide robust structural priors of the static environment, helping resolve…

Accurate feature detection is fundamental for various computer vision tasks, including autonomous robotics, 3D reconstruction, medical imaging, and remote sensing. Despite advancements in enhancing the robustness of visual features, no…

Tabular data are central to biomedical research, from liquid biopsy and bulk and single-cell transcriptomics to electronic health records and phenotypic profiling. Unlike images or sequences, however, tabular datasets lack intrinsic spatial…

Visual localization and mapping is the key technology underlying the majority of mixed reality and robotics systems. Most state-of-the-art approaches rely on local features to establish correspondences between images. In this paper, we…

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying…

A significant amount of recent research work has addressed the problem of solving various data management problems in the cloud. The major algorithmic challenges in map-reduce computations involve balancing a multitude of factors such as…

We introduce a deep appearance model for rendering the human face. Inspired by Active Appearance Models, we develop a data-driven rendering pipeline that learns a joint representation of facial geometry and appearance from a multiview…

We present a simple method, CropMix, for the purpose of producing a rich input distribution from the original dataset distribution. Unlike single random cropping, which may inadvertently capture only limited information, or irrelevant…