相关论文: Connectivity Preserving Multivalued Functions in D…

Although the preservation of shape continuity and physiological anatomy is a natural assumption in the segmentation of medical images, it is often neglected by deep learning methods that mostly aim for the statistical modeling of input data…

We define LCL decompositions of the plane and investigate the advantages of using such decompositions in the context of digital topology. We show that discretization schemes based on such decompositions associate, to each LCL tiling of the…

Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…

Real-world networks often benefit from capturing both local and global interactions. Inspired by multi-modal analysis in brain imaging, where structural and functional connectivity offer complementary views of network organization, we…

Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some…

Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…

Two important tasks in the field of Topological Data Analysis are building practical multifiltrations on objects and using TDA to detect the geometry. Motivated by the tasks, we build multiparameter filtrations by operators on images named…

In this paper, we develop novel techniques that can be used to alter the architecture of a neural network, while maintaining the function it represents. Such operations are known as function preserving transforms and have proven useful in…

Functional brain connectivity changes dynamically over time, making its representation challenging for learning on non-Euclidean data. We present a framework that encodes dynamic functional connectivity as an image representation of…

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…

Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…

Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…

We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.

In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…

Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

Multi-view networks are broadly present in real-world applications. In the meantime, network embedding has emerged as an effective representation learning approach for networked data. Therefore, we are motivated to study the problem of…

In this article, we investigate properties of digital H-spaces in the graph theoretic model of digital topology. As in prior work, the results obtained often depend fundamentally on the choice between NP$_1$ and NP$_2$ product adjacencies.…

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…

Variational models are widely used in image segmentation, with various models designed to address different types of images by optimizing specific objective functionals. However, traditional segmentation models primarily focus on the visual…