Related papers: DisPerSE: robust structure identification in 2D an…

The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in…

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…

We propose the segmentation of noisy datasets into Multiple Inlier Structures with a new Robust Estimator (MISRE). The scale of each individual structure is estimated adaptively from the input data and refined by mean shift, without tuning…

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…

Diffusion speech enhancement on discrete audio codec features gain immense attention due to their improved speech component reconstruction capability. However, they usually suffer from high inference computational complexity due to multiple…

To advance the state of the art in the creation of 3D foundation models, this paper introduces the ConDense framework for 3D pre-training utilizing existing pre-trained 2D networks and large-scale multi-view datasets. We propose a novel…

Dimensionality reduction methods such as UMAP and t-SNE are central tools for visualising high-dimensional data, but their local-neighborhood objectives can preserve sampling noise while distorting global topology. We show that standard…

Measuring the confidence of AI models is critical for safely deploying AI in real-world industrial systems. One important application of confidence measurement is information extraction from scanned documents. However, there exists no…

Diffusion models have recently gained prominence as powerful deep generative models, demonstrating unmatched performance across various domains. However, their potential in multi-sensor fusion remains largely unexplored. In this work, we…

We propose a novel concept of dual and integrated latent topologies (DITTO in short) for implicit 3D reconstruction from noisy and sparse point clouds. Most existing methods predominantly focus on single latent type, such as point or grid…

Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we…

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a…

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a…

Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data…

Detecting arbitrarily shaped clusters in high-dimensional noisy data is challenging for current clustering methods. We introduce SHADE (Structure-preserving High-dimensional Analysis with Density-based Exploration), the first deep…

Accurate segmentation of tubular structures in medical images, such as vessels and airway trees, is crucial for computer-aided diagnosis, radiotherapy, and surgical planning. However, significant challenges exist in algorithm design when…

Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an…

Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…

Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…

Anomaly detection in complex, high-dimensional data, such as UAV sensor readings, is essential for operational safety but challenging for existing methods due to their limited sensitivity, scalability, and inability to capture intricate…