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Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Humans learn object orientation progressively, from recognizing which way an object faces, to mentally rotating it, to reasoning about orientations between objects. Current vision-language benchmarks largely conflate orientation with…
A Riemannian manifold is called a geodesic orbit manifolds, GO for short, if any geodesic is an orbit of a one-parameter group of isometries. By a result of C.Gordon, a non-flat GO nilmanifold is necessarily a two-step nilpotent Lie group…
We consider the scattering of light in participating media composed of sparsely and randomly distributed discrete particles. The particle size is expected to range from the scale of the wavelength to the scale several orders of magnitude…
Human-Object Interaction (HOI) recognition in videos requires understanding both visual patterns and geometric relationships as they evolve over time. Visual and geometric features offer complementary strengths. Visual features capture…
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…
Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light…
We present numerical experiments regarding the diffraction characteristics and their precompensation arising from changing the macroscopic geometry of a flat HOE into a sphere segment. In particular, we discuss a parametric optimization…
Image-to-image translation (i2i) networks suffer from entanglement effects in presence of physics-related phenomena in target domain (such as occlusions, fog, etc), lowering altogether the translation quality, controllability and…
Accurate geometric surface reconstruction, providing essential environmental information for navigation and manipulation tasks, is critical for enabling robotic self-exploration and interaction. Recently, 3D Gaussian Splatting (3DGS) has…
Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a…
X-ray ptychography allows for large fields to be imaged at high resolution at the cost of additional computational expense due to the large volume of data. Given limited information regarding the object, the acquired data often has an…
Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric. We study the…
We consider the problem of visual imitation learning without human supervision (e.g. kinesthetic teaching or teleoperation), nor access to an interactive reinforcement learning (RL) training environment. We present a geometric perspective…
Predicting realistic ground views from satellite imagery in urban scenes is a challenging task due to the significant view gaps between satellite and ground-view images. We propose a novel pipeline to tackle this challenge, by generating…
Object detection in optical remote sensing images, being a fundamental but challenging problem in the field of aerial and satellite image analysis, plays an important role for a wide range of applications and is receiving significant…
Generative models can produce impressively realistic images. This paper demonstrates that generated images have geometric features different from those of real images. We build a set of collections of generated images, prequalified to fool…
Towards intelligent image editing, object removal should eliminate both the target object and its causal visual artifacts, such as shadows and reflections. However, existing image appearance-based methods either follow strictly mask-aligned…
Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an…
Room geometry is important prior information for implementing realistic 3D audio rendering. For this reason, various room geometry inference (RGI) methods have been developed by utilizing the time-of-arrival (TOA) or…