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We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…
We compute the geodesic curvature of logarithmic spirals on surfaces of constant Gaussian curvature. In addition, we show that the asymptotic behavior of the geodesic curvature is independent of the curvature of the ambient surface. We also…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
Text-to-image diffusion models can generate visually stunning images, yet, controlling what appears and how it appears, remains surprisingly difficult, especially when operating solely within the constraints of the text-conditioning space.…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to…
Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are…
Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objects are segmented, selective segmentation is used to isolate specific objects in an image and is of particular…
Generating learning-friendly representations for points in space is a fundamental and long-standing problem in ML. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D/3D…
It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the…
We propose to use deep convolutional neural networks to address the problem of cross-view image geolocalization, in which the geolocation of a ground-level query image is estimated by matching to georeferenced aerial images. We use…
The multi-scale Frangi vesselness filter is an established tool in (retinal) vascular imaging. However, it cannot cope with crossings or bifurcations, since it only looks for elongated structures. Therefore, we disentangle crossing…
Surface reconstruction has been widely studied in computer vision and graphics. However, existing surface reconstruction works struggle to recover accurate scene geometry when the input views are extremely sparse. To address this issue, we…
We construct convex bodies that can be "captured by nets." More precisely, for each dimension $n \geq 2$, we construct a family of Riemannian $n$-spheres, each with a stable geodesic net, which is a stable 1-dimensional integral varifold.…
Cortical surface registration is a fundamental tool for neuroimaging analysis that has been shown to improve the alignment of functional regions relative to volumetric approaches. Classically, image registration is performed by optimizing a…
Retinal image registration plays an important role in the ophthalmological diagnosis process. Since there exist variances in viewing angles and anatomical structures across different retinal images, keypoint-based approaches become the…
Segmentation of retinal vessel images is critical to the diagnosis of retinopathy. Recently, convolutional neural networks have shown significant ability to extract the blood vessel structure. However, it remains challenging to refined…
This work presents a motion planning framework for robotic manipulators that computes collision-free paths directly in image space. The generated paths can then be tracked using vision-based control, eliminating the need for an explicit…
Accurate segmentation of retinal vessels is a basic step in Diabetic retinopathy(DR) detection. Most methods based on deep convolutional neural network (DCNN) have small receptive fields, and hence they are unable to capture global context…
The appearance and structure of blood vessels in retinal images have an important role in diagnosis of diseases. This paper proposes a method for automatic retinal vessel segmentation. In this work, a novel preprocessing based on local…