Related papers: ATOL: Measure Vectorization for Automatic Topologi…

Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…

Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…

Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…

Identifying affordance regions on 3D objects from semantic cues is essential for robotics and human-machine interaction. However, existing 3D affordance learning methods struggle with generalization and robustness due to limited annotated…

In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

Terrain geometry is, in general, non-smooth, non-linear, non-convex, and, if perceived through a robot-centric visual unit, appears partially occluded and noisy. This work presents the complete control pipeline capable of handling the…

Video object detection (VID) has been vigorously studied for years but almost all literature adopts a static accuracy-based evaluation, i.e., average precision (AP). From a robotic perspective, the importance of recall continuity and…

Retinal fundus photography enhancement is important for diagnosing and monitoring retinal diseases. However, early approaches to retinal image enhancement, such as those based on Generative Adversarial Networks (GANs), often struggle to…

Motivated by the challenging segmentation task of pancreatic tubular networks, this paper tackles two commonly encountered problems in biomedical imaging: Topological consistency of the segmentation, and expensive or difficult annotation.…

Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the…

Let P be a distribution with support S. The salient features of S can be quantified with persistent homology, which summarizes topological features of the sublevel sets of the distance function (the distance of any point x to S). Given a…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Obtaining large-scale labeled object detection dataset can be costly and time-consuming, as it involves annotating images with bounding boxes and class labels. Thus, some specialized active learning methods have been proposed to reduce the…

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…

Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…

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…

Recent advances in scanning transmission electron and scanning tunneling microscopies allow researchers to measure materials structural and electronic properties, such as atomic displacements and charge density modulations, at an Angstrom…

Amodal perception, the ability to comprehend complete object structures from partial visibility, is a fundamental skill, even for infants. Its significance extends to applications like autonomous driving, where a clear understanding of…