Related papers: Digital Geometry, a Survey
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
Data augmentation has recently seen increased interest in graph machine learning given its demonstrated ability to improve model performance and generalization by added training data. Despite this recent surge, the area is still relatively…
We present a survey on 4D generation and reconstruction, a fast-evolving subfield of computer graphics whose developments have been propelled by recent advances in neural fields, geometric and motion deep learning, as well as 3D generative…
Recognition of objects using Deep Neural Networks is an active area of research and many breakthroughs have been made in the last few years. The paper attempts to indicate how far this field has progressed. The paper briefly describes the…
Digital topological methods are often used on computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a…
Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial…
Transient imaging has recently made a huge impact in the computer graphics and computer vision fields. By capturing, reconstructing, or simulating light transport at extreme temporal resolutions, researchers have proposed novel techniques…
Image matching, which establishes correspondences between two-view images to recover 3D structure and camera geometry, serves as a cornerstone in computer vision and underpins a wide range of applications, including visual localization, 3D…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
Digital image analysis has made a big advance in many areas of enterprise applications including medicine, industry, and entertainment by assisting the extraction of semantic information from digital images. However, its large computational…
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology…
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…
Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…
This review article is an attempt to survey all recent AI based techniques used to deal with major functions in This review paper presents a comprehensive overview of end-to-end deep learning frameworks used in the context of autonomous…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
Image co-segmentation is important for its advantage of alleviating the ill-pose nature of image segmentation through exploring the correlation between related images. Many automatic image co-segmentation algorithms have been developed in…
Information Geometry has been used to inspire efficient algorithms for stochastic optimization, both in the combinatorial and the continuous case. We give an overview of the authors' research program and some specific contributions to the…