Related papers: Crossing-Preserving Geodesic Tracking on Spherical…
Retinal imaging has emerged as a promising method of addressing this challenge, taking advantage of the unique structure of the retina. The retina is an embryonic extension of the central nervous system, providing a direct in vivo window…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
Metasurface-based optical elements typically manipulate light waves by imparting space-variant changes in the amplitude and phase with a dense array of scattering nanostructures. The highly-localized and low optical-quality-factor (Q) modes…
Scattering can rapidly degrade our ability to form an optical image, to the point where only speckle-like patterns can be measured. Truly non-invasive imaging through a strongly scattering obstacle is difficult, and usually reliant on a…
Motion, measured via optical flow, provides a powerful cue to discover and learn objects in images and videos. However, compared to using appearance, it has some blind spots, such as the fact that objects become invisible if they do not…
In the last 15 years, the segmentation of vessels in retinal images has become an intensively researched problem in medical imaging, with hundreds of algorithms published. One of the de facto benchmarking data sets of vessel segmentation…
Retinal fundus photographs have been used in the diagnosis of many ocular diseases such as glaucoma, pathological myopia, age-related macular degeneration and diabetic retinopathy. With the development of computer science, computer aided…
Retinal fundus photography enhancement is important for diagnosing and monitoring retinal diseases. However, early approaches to retinal image enhancement, such as those based on Generative Adversarial Networks (GANs), often struggle to…
Special curves and surfaces have an important place in mathematics, engineering and other fields of science. Loxodromes are special curves which cut all meridians on the Earth's surface at a constant angle and they are very popular in…
We define a class a metric spaces we call Brownian surfaces, arising as the scaling limits of random maps on general orientable surfaces with a boundary and we study the geodesics from a uniformly chosen random point. These metric spaces…
This paper proposes a non-computational method of counteracting the effect of image degradation introduced by the diffraction phenomenon in lensless microscopy. All the optical images (whether focused by lenses or not) are diffraction…
The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with…
Eye tracking is handled as one of the key technologies for applications that assess and evaluate human attention, behavior, and biometrics, especially using gaze, pupillary, and blink behaviors. One of the challenges with regard to the…
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 $P^{1}=S^{1}/_{\sim}$…
In this work, we utilize image segmentation to visually identify blood vessels in retinal examination images. This process is typically carried out manually. However, we can employ heuristic methods and machine learning to automate or at…
Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key…
In medical image visualization, path tracing of volumetric medical data like CT scans produces lifelike three-dimensional visualizations. Immersive VR displays can further enhance the understanding of complex anatomies. Going beyond the…
Geodesics, which play an important role in spray-Finsler geometry, are integral curves of a spray vector field on a manifold. Some comparison theorems and rigidity issues are established on the completeness of geodesics of a spray or a…
Finding a totally geodesic surface, an embedded surface where the geodesics in the surface are also geodesics in the surrounding manifold, has been a problem of interest in the study of 3-manifolds. This has especially been of interest in…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…