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Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE. DIPOLE is a dimensionality-reduction…
The development of laser scanning techniques has popularized the representation of 3D shapes by triangular meshes with a large number of vertices. Compression techniques dedicated to such meshes have emerged, which exploit the idea that the…
We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an…
Local community detection, the problem of identifying a set of relevant nodes nearby a small set of input seed nodes, is an important graph primitive with a wealth of applications and research activity. Recent approaches include using local…
Change detection typically involves identifying regions with changes between bitemporal images taken at the same location. Besides significant changes, slow changes in bitemporal images are also important in real-life scenarios. For…
We present a novel methodology to jointly perform multi-task learning and infer intrinsic relationship among tasks by an interpretable and sparse graph. Unlike existing multi-task learning methodologies, the graph structure is not assumed…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…
Turbulent flows beneath a free surface play a central role in the Earth system, yet their coupling to observable surface features remains incompletely understood. Recent studies using Direct Numerical Simulations (DNS) have reported strong…
Visual scene decomposition into semantic entities is one of the major challenges when creating a reliable object grasping system. Recently, we introduced a bottom-up hierarchical clustering approach which is able to segment objects and…
The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable…
Robot grasping of desktop object is widely used in intelligent manufacturing, logistics, and agriculture.Although vision-language models (VLMs) show strong potential for robotic manipulation, their deployment in low-level grasping faces key…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
The Reeb space of a smooth function is a topological and combinatoric object and fundamental and important in understanding topological and geometric properties of the manifold of the domain. It is the graph and a topological space endowed…
The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of lines through this…
Role discovery in graphs is an emerging area that allows analysis of complex graphs in an intuitive way. In contrast to other graph prob- lems such as community discovery, which finds groups of highly connected nodes, the role discovery…
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…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…
Graph convolution (GConv) is a widely used technique that has been demonstrated to be extremely effective for graph learning applications, most notably node categorization. On the other hand, many GConv-based models do not quantify the…