Related papers: Rao distances and Conformal Mapping
For a given real number $\alpha$, let us place the fractional parts of the points $0, \alpha, 2 \alpha,$ $ \cdots, (N-1) \alpha$ on the unit circle. These points partition the unit circle into intervals having at most three lengths, one…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
The conformal nature of smooth curves in $\mathbb{R}^3$ is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges .…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
The input to the distant representatives problem is a set of $n$ objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
We present a method to reconstruct the three-dimensional trajectory of a moving instance of a known object category in monocular video data. We track the two-dimensional shape of objects on pixel level exploiting instance-aware semantic…
This project was built from a pre-existing architecture that facilitates the planning and automatic execution of drone routes in a known space through a 3D virtual reality environment. Our work consisted in extending this architecture by…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
Event cameras in motion tend to detect object boundaries or texture edges, which produce lines of brightness changes, especially in man-made environments. While lines can constitute a robust intermediate representation that is consistently…
This paper addresses the problem of building augmented metric representations of scenes with semantic information from RGB-D images. We propose a complete framework to create an enhanced map representation of the environment with…
Humans have the remarkable ability to use held objects as tools to interact with their environment. For this to occur, humans internally estimate how hand movements affect the object's movement. We wish to endow robots with this capability.…
The challenge of object categorization in images is largely due to arbitrary translations and scales of the foreground objects. To attack this difficulty, we propose a new approach called collaborative receptive field learning to extract…
We examine length measurement in curved spacetime, based on the 1+3-splitting of a local observer frame. This situates extended objects within spacetime, in terms of a given coordinate which serves as an external reference. The radar metric…
Recently, the robotics community has regained interest in radar-based perception and state estimation. A 2D imaging radar provides dense 360deg information about the environment. Despite the radar antenna's cone of emission and reception,…
2D object proposals, quickly detected regions in an image that likely contain an object of interest, are an effective approach for improving the computational efficiency and accuracy of object detection in color images. In this work, we…
A new equivalence relation, named relation of 'similarity' is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named 'similar' trajectories) are obtained; they have the theoretical…
Learning-based 3D object reconstruction enables single- or few-shot estimation of 3D object models. For robotics, this holds the potential to allow model-based methods to rapidly adapt to novel objects and scenes. Existing 3D reconstruction…
In this paper, the extremal graph with the maximum RRD-value among all the graphs of order n with given cut vertices or edges is characterized. In addition, an upper bounds on the reciprocal degree distance in terms of the number of cut…
Contouring is an indispensable step in Radiotherapy (RT) treatment planning. However, today's contouring software is constrained to only work with a 2D display, which is less intuitive and requires high task loads. Virtual Reality (VR) has…