Related papers: Core Bifiltration
Accurate segmentation and classification of nuclei in histology images is critical but challenging due to nuclei heterogeneity, staining variations, and tissue complexity. Existing methods often struggle with limited dataset variability,…
Point cloud processing is a challenging task due to its sparsity and irregularity. Prior works introduce delicate designs on either local feature aggregator or global geometric architecture, but few combine both advantages. We propose…
We propose an extension of the classical union-of-balls filtration of persistent homology: fixing a point $q$, we focus our attention to a ball centered at $q$ whose radius is controlled by a second scale parameter. We discuss an absolute…
Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…
In this paper, we present a novel non-parametric clustering technique. Our technique is based on the notion that each latent cluster is comprised of layers that surround its core, where the external layers, or border points, implicitly…
We introduce a new algorithm to parallelise the computation of persistent homology of 2D alpha complexes. Our algorithm distributes the input point cloud among the cores which then compute a cover based on a rectilinear grid. We show how to…
Hollow-core fibers have demonstrated record performance in applications such as high-power pulse delivery, quantum computing, and sensing. However, their routine use is yet to become reality. A major obstacle is the ability to maintain the…
Persistence modules that decompose into interval modules are important in topological data analysis because we can interpret such intervals as the lifetime of topological features in the data. We can classify the settings in which…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
Face analysis is a core part of computer vision, in which remarkable progress has been observed in the past decades. Current methods achieve recognition and tracking with invariance to fundamental modes of variation such as illumination, 3D…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…
Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
Identify the cells' nuclei is the important point for most medical analyses. To assist doctors finding the accurate cell' nuclei location automatically is highly demanded in the clinical practice. Recently, fully convolutional neural…
We present three multi-scale similarity learning architectures, or DeepSim networks. These models learn pixel-level matching with a contrastive loss and are agnostic to the geometry of the considered scene. We establish a middle ground…
Molecular clouds have complex density structures produced by processes including turbulence and gravity. We propose a triangulation-based method to dissect the density structure of a molecular cloud and study the interactions between dense…
The emergence of generative AI and controllable diffusion has made image-to-image synthesis increasingly practical and efficient. However, when input images exhibit low entropy and sparse, the inherent characteristics of diffusion models…
Recent observations have revealed the presence of small fibres or sub-filaments within larger filaments. We present a numerical fragmentation study of fibrous filaments investigating the link between cores and sub-filaments using…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…