Related papers: PI-Net: A Deep Learning Approach to Extract Topolo…

Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…

Convolutional neural networks (CNNs) depend on deep network architectures to extract accurate information for image super-resolution. However, obtained information of these CNNs cannot completely express predicted high-quality images for…

Diffusion models excel at creating visually impressive images but often struggle to generate images with a specified topology. The Betti number, which represents the number of structures in an image, is a fundamental measure in topology.…

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of…

Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…

Skeletonization extracts thin representations from images that compactly encode their geometry and topology. These representations have become an important topological prior for preserving connectivity in curvilinear structures, aiding…

Data-driven modeling of human motions is ubiquitous in computer graphics and computer vision applications, such as synthesizing realistic motions or recognizing actions. Recent research has shown that such problems can be approached by…

We study end-to-end learning strategies for 3D shape inference from images, in particular from a single image. Several approaches in this direction have been investigated that explore different shape representations and suitable learning…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

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…

Visual patterns represent the discernible regularity in the visual world. They capture the essential nature of visual objects or scenes. Understanding and modeling visual patterns is a fundamental problem in visual recognition that has wide…

Hyperspectral images (HSI) have become popular for analysing remotely sensed images in multiple domain like agriculture, medical. However, existing models struggle with complex relationships and characteristics of spectral-spatial data due…

In this paper, we propose a learning-based approach to the task of automatically extracting a "wireframe" representation for images of cluttered man-made environments. The wireframe (see Fig. 1) contains all salient straight lines and their…

Deep learning methods have achieved a lot of success in various applications involving converting wearable sensor data to actionable health insights. A common application areas is activity recognition, where deep-learning methods still…

Meshes are widely used in 3D computer vision and graphics, but their irregular topology poses challenges in applying them to existing neural network architectures. Recent advances in mesh neural networks turn to remeshing and push the…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…