Related papers: A neuro-mathematical model for geometrical optical…
Computer vision helps machines or computer to see like humans. Computer Takes information from the images and then understands of useful information from images. Gesture recognition and movement recognition are the current area of research…
Confocal quadrics capture (encode) and geometrize spectral properties of symmetric operators. Certain metric-projective properties of confocal quadrics (most of them established in the first half of the XIX$^{\mathrm{th}}$ century) {\it…
Although all members of the ophthalmic community agree that distortion is an aberration affecting the geometry of an image produced by the periphery of an ophthalmic lens, there are several approaches for analyzing and quantifying this…
It is a mystery how the brain decodes color vision purely from the optic nerve signals it receives, with a core inferential challenge being how it disentangles internal perception with the correct color dimensionality from the unknown…
The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the…
With the present and soon-to-be breakthrough of optical interferometry, countless objects shall be within reach of interferometers; yet, most of them are expected to remain only marginally resolved with hectometric baselines. In this paper,…
Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature [5,6] certain simplifying…
Explanation methods aim to make neural networks more trustworthy and interpretable. In this paper, we demonstrate a property of explanation methods which is disconcerting for both of these purposes. Namely, we show that explanations can be…
While there has been substantial progress in learning suitable distance metrics, these techniques in general lack transparency and decision reasoning, i.e., explaining why the input set of images is similar or dissimilar. In this work, we…
Object geometry is key information for robot manipulation. Yet, object reconstruction is a challenging task because cameras only capture partial observations of objects, especially when occlusion occurs. In this paper, we leverage two extra…
Among the most impressive recent applications of neural decoding is the visual representation decoding, where the category of an object that a subject either sees or imagines is inferred by observing his/her brain activity. Even though…
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
The problem of 3D object recognition is of immense practical importance, with the last decade witnessing a number of breakthroughs in the state of the art. Most of the previous work has focused on the matching of textured objects using…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role. We…
We suggest a geometric approach to modeling biochemical processes, aiming at those processes that occur in humans with food sensitivities or chemical sensitivities.