Related papers: Learning Significant Persistent Homology Features …

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

In 2D image processing, some attempts decompose images into high and low frequency components for describing edge and smooth parts respectively. Similarly, the contour and flat area of 3D objects, such as the boundary and seat area of a…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…

The matching of 3D shapes has been extensively studied for shapes represented as surface meshes, as well as for shapes represented as point clouds. While point clouds are a common representation of raw real-world 3D data (e.g. from laser…

3D object classification is a crucial problem due to its significant practical relevance in many fields, including computer vision, robotics, and autonomous driving. Although deep learning methods applied to point clouds sampled on CAD…

Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…

3D object recognition has attracted wide research attention in the field of multimedia and computer vision. With the recent proliferation of deep learning, various deep models with different representations have achieved the…

A successful point cloud registration often lies on robust establishment of sparse matches through discriminative 3D local features. Despite the fast evolution of learning-based 3D feature descriptors, little attention has been drawn to the…

In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…

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…

Topological data analysis (TDA) is a rapidly evolving field in applied mathematics and data science that leverages tools from topology to uncover robust, shape-driven insights in complex datasets. The main workhorse is persistent homology,…

We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…

Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are often constrained…

Existing deep learning algorithms for point cloud analysis mainly concern discovering semantic patterns from global configuration of local geometries in a supervised learning manner. However, very few explore geometric properties revealing…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Learning structures of 3D shapes is a fundamental problem in the field of computer graphics and geometry processing. We present a simple yet interpretable unsupervised method for learning a new structural representation in the form of 3D…

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known…

Recent years have witnessed an increased interest in the application of persistent homology, a topological tool for data analysis, to machine learning problems. Persistent homology is known for its ability to numerically characterize the…

Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…