Related papers: Geodesic distance on optimally regularized functio…
Optical coherence tomography (OCT) is a non-invasive imaging technique that can produce images of the eye at the microscopic level. OCT image segmentation to localise retinal layer boundaries is a fundamental procedure for diagnosing and…
A key question in modern neuroscience is how cognitive changes in a human brain can be quantified and captured by functional connectomes (FC) . A systematic approach to measure pairwise functional distance at different brain states is…
Person re-identification is challenging due to the large variations of pose, illumination, occlusion and camera view. Owing to these variations, the pedestrian data is distributed as highly-curved manifolds in the feature space, despite the…
Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…
Functional Connectivity (FC) matrices measure the regional interactions in the brain and have been widely used in neurological brain disease classification. However, a FC matrix is neither a natural image which contains shape and texture…
Finding trajectories and discovering motifs that are similar in large datasets is a central problem for a wide range of applications. Solutions addressing this problem usually rely on spatial indexing and on the computation of a similarity…
We establish the equivalence between the regularity (rectifiability) of sets and suitable estimates on the oscillation of the gradient for smooth non-local distance functions. A prototypical example of such a distance was introduced, as…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
Recent neuroimaging studies have shown that functional connectomes are unique to individuals, i.e., two distinct fMRIs taken over different sessions of the same subject are more similar in terms of their connectomes than those from two…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
Data-driven brain parcellations aim to provide a more accurate representation of an individual's functional connectivity, since they are able to capture individual variability that arises due to development or disease. This renders…
Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout physics and engineering -- for instance, in determining…
Fingerprints are widely recognized as one of the most unique and reliable characteristics of human identity. Most modern fingerprint authentication systems rely on contact-based fingerprints, which require the use of fingerprint scanners or…
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical…
Functional connectivity, as estimated using resting state fMRI, has shown potential in bridging the gap between pathophysiology and cognition. However, clinical use of functional connectivity biomarkers is impeded by unreliable estimates of…
We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean…
The Escherization problem involves finding a closed figure that tiles the plane that is most similar to a given goal figure. In Koizumi and Sugihara's formulation of the Escherization problem, the tile and goal figures are represented as…
Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we…
Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…
Despite the potential of federated learning in medical applications, inconsistent imaging quality across institutions-stemming from lower-quality data from a minority of clients-biases federated models toward more common high-quality…