Related papers: Rao distances and Conformal Mapping
Looming, traditionally defined as the relative expansion of objects in the observer's retina, is a fundamental visual cue for perception of threat and can be used to accomplish collision free navigation. In this paper we derive novel…
Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…
Deep metric learning (DML) aims to automatically construct task-specific distances or similarities of data, resulting in a low-dimensional representation. Several significant metric-learning methods have been proposed. Nonetheless, no…
In this paper, we study the problem of continuous 3D shape representations. The majority of existing successful methods are coordinate-based implicit neural representations. However, they are inefficient to render novel views or recover…
The problem of identifying the 3D pose of a known object from a given 2D image has important applications in Computer Vision. Our proposed method of registering a 3D model of a known object on a given 2D photo of the object has numerous…
To autonomously navigate and plan interactions in real-world environments, robots require the ability to robustly perceive and map complex, unstructured surrounding scenes. Besides building an internal representation of the observed scene…
3D object localisation based on a sequence of camera measurements is essential for safety-critical surveillance tasks, such as drone-based wildfire monitoring. Localisation of objects detected with a camera can typically be solved with…
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
Random Projection is a foundational research topic that connects a bunch of machine learning algorithms under a similar mathematical basis. It is used to reduce the dimensionality of the dataset by projecting the data points efficiently to…
We re-examine the notion of relative $(p,\eps)$-approximations, recently introduced in [CKMS06], and establish upper bounds on their size, in general range spaces of finite VC-dimension, using the sampling theory developed in [LLS01] and in…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
Real-time three-dimensional (3D) scene representations serve as one of the building blocks that bolster various innovative applications, e.g., digital manufacturing, Virtual/Augmented/Extended/Mixed Reality (VR/AR/XR/MR), and the metaverse.…
The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest…
Accurate, robust, and real-time LiDAR-based odometry (LO) is imperative for many applications like robot navigation, globally consistent 3D scene map reconstruction, or safe motion-planning. Though LiDAR sensor is known for its precise…
Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…
Creating artistic 3D scenes can be time-consuming and requires specialized knowledge. To address this, recent works such as ARF, use a radiance field-based approach with style constraints to generate 3D scenes that resemble a style image…
Most (3D) multi-object tracking methods rely on appearance-based cues for data association. By contrast, we investigate how far we can get by only encoding geometric relationships between objects in 3D space as cues for data-driven data…
Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets:…
Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy…