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This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…

Multiparameter persistent homology is a generalization of classical persistent homology, a central and widely-used methodology from topological data analysis, which takes into account density estimation and is an effective tool for data…

As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era,…

Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…

Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits certain block-wise missing structures -- specifically, where…

Topological data analysis (TDA) is an expanding field that leverages principles and tools from algebraic topology to quantify structural features of data sets or transform them into more manageable forms. As its theoretical foundations have…

We obtain asymptotically sharp error estimates for the consistency error of the Target Measure Diffusion map (TMDmap) (Banisch et al. 2020), a variant of diffusion maps featuring importance sampling and hence allowing input data drawn from…

Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians…

Three novel applications of computational topology in the field of fusion science are developed. A procedure for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using Vietoris-Rips…

Modern deep neural networks have shown remarkable performance in medical image classification. However, such networks either emphasize pixel-intensity features instead of fundamental anatomical structures (e.g., those encoded by topological…

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…

Controlling structural complexity, particularly the number of holes, remains a fundamental challenge in topology optimization, with significant implications for both theoretical analysis and manufacturability. Most existing approaches rely…

Homology is a tool in topological data analysis which measures the shape of the data. In many cases, these measurements translate into new insights which are not available by other means. To compute homology, we rely on mathematical…

Industrial point cloud segmentation for Digital Twin construction faces a persistent challenge: safety-critical components such as reducers and valves are systematically misclassified. These failures stem from two compounding factors: such…

Time series anomaly detection (TSAD) is a vital yet challenging task, particularly in scenarios where labeled anomalies are scarce and temporal dependencies are complex. Recent anomaly assumption (AA) approaches alleviate the lack of…

Density functions that represent sample data are often multimodal, i.e. they exhibit more than one maximum. Typically this behavior is taken to indicate that the underlying data deserves a more detailed representation as a mixture of…

Self-supervised learning can extract representations of good quality from solely unlabeled data, which is appealing for point cloud videos due to their high labelling cost. In this paper, we propose a contrastive mask prediction (PointCMP)…

Existing point cloud completion methods struggle to balance high-quality reconstruction with computational efficiency. To address this, we propose PPC-MT, a novel parallel framework for point cloud completion leveraging a hybrid…

Signals emitted by LiDAR sensors would often be negatively influenced during transmission by rain, fog, dust, atmospheric particles, scattering of light and other influencing factors, causing noises in point cloud images. To address this…

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…