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

Geometric data pruning methods, while practical for leveraging pretrained models, are fundamentally unstable. Their reliance on extrinsic geometry renders them highly sensitive to latent space perturbations, causing performance to degrade…

The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from…

Three-dimensional (3D) medical image enhancement, including denoising and super-resolution, is critical for clinical diagnosis in CT, PET, and MRI. Although diffusion models have shown remarkable success in 2D medical imaging, scaling them…

Establishing reliable correspondences is essential for registration tasks such as 3D and 2D3D registration. Existing methods commonly leverage geometric or semantic point features to generate potential correspondences. However, these…

Persistent homology is an area within topological data analysis (TDA) that can uncover different dimensional holes (connected components, loops, voids, etc.) in data. The holes are characterized, in part, by how long they persist across…

Continuous diffusion models have demonstrated their effectiveness in addressing the inherent uncertainty and indeterminacy in monocular 3D human pose estimation (HPE). Despite their strengths, the need for large search spaces and the…

Diffusion models (DMs) have revolutionized image generation, producing high-quality images with applications spanning various fields. However, their ability to create hyper-realistic images poses significant challenges in distinguishing…

We present TopoMortar, a brick wall dataset that is the first dataset specifically designed to evaluate topology-focused image segmentation methods, such as topology loss functions. Motivated by the known sensitivity of methods to dataset…

Classical diffusion models typically rely on isotropic Gaussian noise, treating all regions uniformly and overlooking structural information important for high-quality generation. We introduce an edge-preserving diffusion process that…

Image downscaling is one of the key operations in recent display technology and visualization tools. By this process, the dimension of an image is reduced, aiming to preserve structural integrity and visual fidelity. In this paper, we…

4D radar measurements offer an affordable and weather-robust solution for 3D perception. However, the inherent sparsity and noise of radar point clouds present significant challenges for accurate 3D object detection, underscoring the need…

Segmenting curvilinear structures in medical images is essential for analyzing morphological patterns in clinical applications. Integrating topological properties, such as connectivity, improves segmentation accuracy and consistency.…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of…

Topological features such as persistence diagrams and their functional approximations like persistence images (PIs) have been showing substantial promise for machine learning and computer vision applications. This is greatly attributed to…

We introduce a novel offset meshing approach that can robustly handle a 3D surface mesh with an arbitrary geometry and topology configurations, while nicely capturing the sharp features on the original input for both inward and outward…

Visual speech recognition aims to identify the sequence of phonemes from continuous speech. Unlike the traditional approach of using 2D image feature extraction methods to derive features of each video frame separately, this paper proposes…

Scanning Transmission Electron Microscopes (STEMs) acquire 2D images of a 3D sample on the scale of individual cell components. Unfortunately, these 2D images can be too noisy to be fused into a useful 3D structure and facilitating good…

This paper explores the utility of diffusion-based models for anomaly detection, focusing on their efficacy in identifying deviations in both compact and high-resolution datasets. Diffusion-based architectures, including Denoising Diffusion…

In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the category of tame functors. We show how this pseudo-metric can be…