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Geometry Projection is a powerful depth estimation method in monocular 3D object detection. It estimates depth dependent on heights, which introduces mathematical priors into the deep model. But projection process also introduces the error…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

Human-Object Interaction (HOI) aims to identify the pairs of humans and objects in images and to recognize their relationships, ultimately forming $\langle human, object, verb \rangle$ triplets. Under default settings, HOI performance is…

We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity…

The goal of this paper is to study two basic problems of hyperbolic geometry. The first problem is to compare the hyperbolic and Euclidean distances. The second problem is to find hyperbolic counterparts of some basic geometric…

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean…

This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…

Creating virtual models of real spaces and objects is cumbersome and time consuming. This paper focuses on the problem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant…

Operators with continuous spectra naturally arise in spectral theory, quantum mechanics, automorphic forms, and noncommutative geometry. However, analyzing such operators, particularly in the non-selfadjoint setting, remains challenging due…

An object's geocentric pose, defined as the height above ground and orientation with respect to gravity, is a powerful representation of real-world structure for object detection, segmentation, and localization tasks using RGBD images. For…

Artificial intelligence (AI) has transformed imaging inverse problems, from medical diagnostics to Earth observation. Yet deep neural networks can produce hallucinations, realistic-looking but incorrect details, undermining their…

This paper exposes the language of geometric contexts and elementary schemes, which is a functorial formalism to study categories of geometric objects such as schemes, topological manifolds, differential manifolds, analytic manifolds, etc.…

We solve explicitly the geodesic equation for a wide class of (pseudo)-Riemannian homogeneous manifolds (G/H,m), including those with G compact, as well as non-compact semisimple Lie groups, under a simple algebraic condition for the metric…

The reconstruction of gap-free signals from observation data is a critical challenge for numerous application domains, such as geoscience and space-based earth observation, when the available sensors or the data collection processes lead to…

In this article, the ray tracing method is studied beyond the classical geometrical theory. The trajectories are here regarded as geodesics in a Riemannian manifold, whose metric and topological properties are those induced by the…

We propose CG-HOI, the first method to address the task of generating dynamic 3D human-object interactions (HOIs) from text. We model the motion of both human and object in an interdependent fashion, as semantically rich human motion rarely…

We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer…

This paper is a survey of some of the developments in coarse extrinsic geometry since its inception in the work of Gromov. Distortion, as measured by comparing the diameter of balls relative to different metrics, can be regarded as one of…

With the success of deep learning based approaches in tackling challenging problems in computer vision, a wide range of deep architectures have recently been proposed for the task of visual odometry (VO) estimation. Most of these proposed…

Human-object interaction (HOI) detection aims to detect interactions between humans and objects in images. While recent advances have improved performance on existing benchmarks, their evaluations mainly focus on overall prediction accuracy…