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Nanostructured materials have recently emerged as a promising approach for material appearance design. Research has mainly focused on creating structural colours by wave interference, leaving aside other important aspects that constitute…
This paper introduces the geodesics of triangulated image object shapes. Both rectilinear and curvilinear triangulations of shapes are considered. The triangulation of image object shapes leads to collections of what are known as nerve…
We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for…
Representation of 2D frame less visual space as neural manifold and its modelling in the frame work of information geometry is presented. Origin of hyperbolic nature of the visual space is investigated using evidences from neuroscience.…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…
Guiding off-screen points of interest (POIs) is a practical way of providing additional information to users of small-screen devices, such as smart devices and head-mounted displays. Popular previous methods involve displaying a primitive…
Image-based 3D object modeling refers to the process of converting raw optical images to 3D digital representations of the objects. Very often, such models are desired to be dimensionally true, semantically labeled with photorealistic…
It is the aim of this paper to transfer to generalised geometry tools employed in the study of semi-Riemannian immersions, specializing at times to semi-Riemannian hypersurfaces. Given an exact Courant algebroid $E \to M$ and an immersion…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
Object detection, a fundamental and challenging problem in computer vision, has experienced rapid development due to the effectiveness of deep learning. The current objects to be detected are mostly rigid solid substances with apparent and…
Rendering realistic human-object interactions (HOIs) from sparse-view inputs is a challenging yet crucial task for various real-world applications. Existing methods often struggle to simultaneously achieve high rendering quality, physical…
We study obstructed deformation problems for two-dimensional residual Galois representations arising from weight~$2$ newforms of level~$N$. Using Poitou-Tate duality, we isolate local and global sources of obstructions and give concrete…
Recently, learning frameworks have shown the capability of inferring the accurate shape, pose, and texture of an object from a single RGB image. However, current methods are trained on image collections of a single category in order to…
Electronic structure calculations are ubiquitous in most branches of chemistry, but all have errors in both energies and equilibrium geometries. Quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. A…
We propose using global orientation from inertial measurements, and the bias it induces on the shape of objects populating the scene, to inform visual 3D reconstruction. We test the effect of using the resulting prior in depth prediction…
Geodesics on Riemannian manifolds are precisely the locally length-minimizing curves, but their explicit description via simple functions is rarely possible. Geodesics of the simplest form, such as lines on Euclidean space and great circles…
In language and vision-language models, hallucination is broadly understood as content generated from a model's prior knowledge or biases rather than from the given input. While this phenomenon has been studied in those domains, it has not…
We study geodesics of the form $\gamma(t)=\pi(\exp(tX)\exp(tY))$, $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces $G/K$, where $\pi:G\rightarrow G/K$ is the natural projection. These curves naturally generalise homogeneous…
Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…
Generating realistic 3D Human-Object Interactions (HOI) is a fundamental task for applications ranging from embodied AI to virtual content creation, which requires harmonizing high-level semantic intent with strict low-level physical…