Related papers: Crossing-Preserving Geodesic Tracking on Spherical…
Automatic segmentation of retinal blood vessels from fundus images plays an important role in the computer aided diagnosis of retinal diseases. The task of blood vessel segmentation is challenging due to the extreme variations in morphology…
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…
Developing efficient vessel-tracking algorithms is crucial for imaging-based diagnosis and treatment of vascular diseases. Vessel tracking aims to solve recognition problems such as key (seed) point detection, centerline extraction, and…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
The accurate visual tracking of a moving object is a human fundamental skill that allows to reduce the relative slip and instability of the object's image on the retina, thus granting a stable, high-quality vision. In order to optimize…
Employing symbolic dynamics for geodesic motion on the tesselated pseudosphere, the so-called Hadamard-Gutzwiller model, we construct extremely long periodic orbits without compromising accuracy. We establish criteria for such long orbits…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
Retinal image-based eye tracking is widely used in ophthalmic imaging and vision science, and is a promising path to deliver higher gaze accuracy than the pupil- and cornea-based approaches commonly used in modern AR/VR devices.…
We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequality for weighted geodesic drawings on $\mathbb S^2$ in a…
This paper provides theoretical and computational developments in statistical shape analysis of shape graphs, and demonstrates them using analysis of complex data from retinal blood-vessel (RBV) networks. The shape graphs are represented by…
In this paper, we address the problem of building dense correspondences between human images under arbitrary camera viewpoints and body poses. Prior art either assumes small motion between frames or relies on local descriptors, which cannot…
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…
Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
Retinal vessel segmentation plays an imaportant role in the field of retinal image analysis because changes in retinal vascular structure can aid in the diagnosis of diseases such as hypertension and diabetes. In recent research, numerous…
Retinal blood vessels structure contains information about diseases like obesity, diabetes, hypertension and glaucoma. This information is very useful in identification and treatment of these fatal diseases. To obtain this information,…
Suppose that the surfaces K0 and Kr are the boundaries of two convex, complete, connected C^2 bodies in R^3. Assume further that the (Euclidean) distance between any point x in Kr and K0 is always r (r > 0). For x in Kr, let {\Pi}(x) denote…
This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…