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The minimal path method has proven to be particularly useful and efficient in tubular structure segmentation applications. In this paper, we propose a new minimal path model associated with a dynamic Riemannian metric embedded with an…
Retinal images provide early signs of diabetic retinopathy, glaucoma, and hypertension. These signs can be investigated based on microaneurysms or smaller vessels. The diagnostic biomarkers are the change of vessel widths and angles…
This paper demonstrates the efficacy of a modified U-Net structure for the extraction of vascular tree masks for human fundus photographs. On limited compute resources and training data, the proposed model only slightly underperforms when…
Detection of non-calcified plaques in the coronary tree is a challenging problem due to the nature of comprising substances. Hard plaques are easily discernible in CTA data cloud due to apparent bright behaviour, therefore many approaches…
Tree skeleton plays an important role in tree structure analysis, forest inventory and ecosystem monitoring. However, it is a challenge to extract a skeleton from a tree point cloud with complex branches. In this paper, an automatic and…
Purpose: The mechanics of the mitral valve leaflet as a nonlinear, inelastic and anisotropic soft tissue results from an integrated response of many mathematical/physical indexes' that illustrate the tissue. In the past decade, finite…
We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be…
Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the…
Given a directed graph, G=(V,E), a path query, path(u,v), returns whether there is a directed path from u to v in G, for u,v vertices in V. Given only V, exactly learning all the edges in G using path queries is often impossible, since path…
Anisotropy in crystals plays a pivotal role in many technological applications. For example, anisotropic electronic and thermal transport are thought to be beneficial for thermoelectric applications, while anisotropic mechanical properties…
We present tree extraction in 3D images as a graph refinement task, of obtaining a subgraph from an over-complete input graph. To this end, we formulate an approximate Bayesian inference framework on undirected graphs using mean field…
Dependency trees convey rich structural information that is proven useful for extracting relations among entities in text. However, how to effectively make use of relevant information while ignoring irrelevant information from the…
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent…
Junctions in the retinal vasculature are key points to be able to extract its topology, but they vary in appearance, depending on vessel density, width and branching/crossing angles. The complexity of junction patterns is usually…
Automatic blood vessel extraction from 3D medical images is crucial for vascular disease diagnoses. Existing methods based on convolutional neural networks (CNNs) may suffer from discontinuities of extracted vessels when segmenting such…
Accurate analysis and modeling of renal functions require a precise segmentation of the renal blood vessels. Micro-CT scans provide image data at higher resolutions, making more small vessels near the renal cortex visible. Although…
Pulmonary diseases rank prominently among the principal causes of death worldwide. Curing them will require, among other things, a better understanding of the complex 3D tree-shaped structures within the pulmonary system, such as airways,…
Vertex deletion and edge deletion problems play a central role in Parameterized Complexity. Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the study of edge…
Advancements in cytometry technologies have led to a remarkable increase in the number of markers that can be analyzed simultaneously, presenting significant challenges in data analysis. Traditional approaches, such as dimensional reduction…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…