相关论文: Geodesic Tracking via New Data-driven Connections …
The identification of vascular networks is an important topic in the medical image analysis community. While most methods focus on single vessel tracking, the few solutions that exist for tracking complete vascular networks are usually…
Segmentation of tubular structures in vascular imaging is a well studied task, although it is rare that we try to infuse knowledge of the tree-like structure of the regions to be detected. Our work focuses on detecting the important…
Vascular tracking of angiographic image sequences is one of the most clinically important tasks in the diagnostic assessment and interventional guidance of cardiac disease. However, this task can be challenging to accomplish because of…
Vascular graphs can embed a number of high-level features, from morphological parameters, to functional biomarkers, and represent an invaluable tool for longitudinal and cross-sectional clinical inference. This, however, is only feasible…
The analysis of vessel morphology and connectivity has an impact on a number of cardiovascular and neurovascular applications by providing patient-specific high-level quantitative features such as spatial location, direction and scale. In…
The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…
Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…
We introduce a novel framework for learning vector representations of tree-structured geometric data focusing on 3D vascular networks. Our approach employs two sequentially trained Transformer-based autoencoders. In the first stage, the…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…
We study a data-driven sub-Riemannian (SR) curve optimization model for connecting local orientations in orientation lifts of images. Our model lives on the projective line bundle $\mathbb{R}^{2} \times P^{1}$, with $P^{1}=S^{1}/_{\sim}$…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to…
This paper presents a method for retinal vasculature extraction based on biologically inspired multi-orientation analysis. We apply multi-orientation analysis via so-called invertible orientation scores, modeling the cortical columns in the…
Vessel tracing by modeling vascular structures in 3D medical images with centerlines and radii can provide useful information for vascular health. Existing algorithms have been developed but there are certain persistent problems such as…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
We present a fully automatic, graph-based technique for extracting the retinal vascular topology -- that is, how different vessels are connected to each other -- given a single color fundus image. Determining this connectivity is very…
Quantitative analysis of cardiac motion is crucial for assessing cardiac function. This analysis typically uses imaging modalities such as MRI and Echocardiograms that capture detailed image sequences throughout the heartbeat cycle.…
In image analysis one often encounters spherical images, for instance in retinal imaging. The behavior of the vessels in the retina is an indicator of several diseases. To automate disease diagnosis using retinal images, it is necessary to…
What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold -- requiring a Riemannian…
In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…