6,646 research outputs found
The double torus as a 2D cosmos: groups, geometry and closed geodesics
The double torus provides a relativistic model for a closed 2D cosmos with
topology of genus 2 and constant negative curvature. Its unfolding into an
octagon extends to an octagonal tessellation of its universal covering, the
hyperbolic space H^2. The tessellation is analysed with tools from hyperbolic
crystallography. Actions on H^2 of groups/subgroups are identified for SU(1,
1), for a hyperbolic Coxeter group acting also on SU(1, 1), and for the
homotopy group \Phi_2 whose extension is normal in the Coxeter group. Closed
geodesics arise from links on H^2 between octagon centres. The direction and
length of the shortest closed geodesics is computed.Comment: Latex, 27 pages, 5 figures (late submission to arxiv.org
Angular variation as a monocular cue for spatial percepcion
Monocular cues are spatial sensory inputs which are picked up exclusively from one eye. They are in majority static features that
provide depth information and are extensively used in graphic art to create realistic representations of a scene. Since the spatial
information contained in these cues is picked up from the retinal image, the existence of a link between it and the theory of direct
perception can be conveniently assumed. According to this theory, spatial information of an environment is directly contained in the
optic array. Thus, this assumption makes possible the modeling of visual perception processes through computational approaches.
In this thesis, angular variation is considered as a monocular cue, and the concept of direct perception is adopted by a computer
vision approach that considers it as a suitable principle from which innovative techniques to calculate spatial information can be
developed.
The expected spatial information to be obtained from this monocular cue is the position and orientation of an object with respect to
the observer, which in computer vision is a well known field of research called 2D-3D pose estimation. In this thesis, the attempt to
establish the angular variation as a monocular cue and thus the achievement of a computational approach to direct perception is
carried out by the development of a set of pose estimation methods. Parting from conventional strategies to solve the pose
estimation problem, a first approach imposes constraint equations to relate object and image features. In this sense, two algorithms
based on a simple line rotation motion analysis were developed. These algorithms successfully provide pose information; however,
they depend strongly on scene data conditions. To overcome this limitation, a second approach inspired in the biological processes
performed by the human visual system was developed. It is based in the proper content of the image and defines a computational
approach to direct perception.
The set of developed algorithms analyzes the visual properties provided by angular variations. The aim is to gather valuable data
from which spatial information can be obtained and used to emulate a visual perception process by establishing a 2D-3D metric
relation. Since it is considered fundamental in the visual-motor coordination and consequently essential to interact with the
environment, a significant cognitive effect is produced by the application of the developed computational approach in environments
mediated by technology. In this work, this cognitive effect is demonstrated by an experimental study where a number of participants
were asked to complete an action-perception task. The main purpose of the study was to analyze the visual guided behavior in
teleoperation and the cognitive effect caused by the addition of 3D information. The results presented a significant influence of the
3D aid in the skill improvement, which showed an enhancement of the sense of presence.Las señales monoculares son entradas sensoriales capturadas exclusivamente por un
solo ojo que ayudan a la percepción de distancia o espacio. Son en su mayoría
características estáticas que proveen información de profundidad y son muy
utilizadas en arte gráfico para crear apariencias reales de una escena. Dado que la
información espacial contenida en dichas señales son extraídas de la retina, la
existencia de una relación entre esta extracción de información y la teoría de
percepción directa puede ser convenientemente asumida. De acuerdo a esta teoría, la
información espacial de todo le que vemos está directamente contenido en el arreglo
óptico. Por lo tanto, esta suposición hace posible el modelado de procesos de
percepción visual a través de enfoques computacionales. En esta tesis doctoral, la
variación angular es considerada como una señal monocular, y el concepto de
percepción directa adoptado por un enfoque basado en algoritmos de visión por
computador que lo consideran un principio apropiado para el desarrollo de nuevas
técnicas de cálculo de información espacial.
La información espacial esperada a obtener de esta señal monocular es la posición y
orientación de un objeto con respecto al observador, lo cual en visión por computador
es un conocido campo de investigación llamado estimación de la pose 2D-3D. En esta
tesis doctoral, establecer la variación angular como señal monocular y conseguir un
modelo matemático que describa la percepción directa, se lleva a cabo mediante el
desarrollo de un grupo de métodos de estimación de la pose. Partiendo de estrategias
convencionales, un primer enfoque implanta restricciones geométricas en ecuaciones
para relacionar características del objeto y la imagen. En este caso, dos algoritmos
basados en el análisis de movimientos de rotación de una línea recta fueron
desarrollados. Estos algoritmos exitosamente proveen información de la pose. Sin
embargo, dependen fuertemente de condiciones de la escena. Para superar esta
limitación, un segundo enfoque inspirado en los procesos biológicos ejecutados por el
sistema visual humano fue desarrollado. Está basado en el propio contenido de la
imagen y define un enfoque computacional a la percepción directa.
El grupo de algoritmos desarrollados analiza las propiedades visuales suministradas
por variaciones angulares. El propósito principal es el de reunir datos de importancia
con los cuales la información espacial pueda ser obtenida y utilizada para emular
procesos de percepción visual mediante el establecimiento de relaciones métricas 2D-
3D. Debido a que dicha relación es considerada fundamental en la coordinación
visuomotora y consecuentemente esencial para interactuar con lo que nos rodea, un
efecto cognitivo significativo puede ser producido por la aplicación de métodos de
L
estimación de pose en entornos mediados tecnológicamente. En esta tesis doctoral, este
efecto cognitivo ha sido demostrado por un estudio experimental en el cual un número
de participantes fueron invitados a ejecutar una tarea de acción-percepción. El
propósito principal de este estudio fue el análisis de la conducta guiada visualmente en
teleoperación y el efecto cognitivo causado por la inclusión de información 3D. Los
resultados han presentado una influencia notable de la ayuda 3D en la mejora de la
habilidad, así como un aumento de la sensación de presencia
Quantitative and Qualitative Measures for the Evaluation of the Superquadric Models
In this paper we discuss the evaluation criteria for superquadric models recovered from the range data. We present arguments to support our belief that both quantitative and qualitative measures are required in order to evaluate a superquadric fit. The concept of superquadric contraction and dilation is introduced and used to derive a novel interpretation of the modified superquadric inside-outside function in terms of contraction/expansion factor. The same concept also gives a close initial guess for the numerical procedure computing the minimum Euclidean distance of a point from a superquadric model. The minimum Euclidean distance map is introduced as a qualitative criterion for interpretation of fit. View-dependent qualitative measures like the contour-difference map and the z-distance map are shown to be essential for the complete evaluation of the models. Analytical solution and techniques for the contour generator on superquadric models are presented. Finally, examples of real objects are given to generate the measures
A moving observer in a three-dimensional world
For many tasks, such as retrieving a previously viewed object, an observer must form a representation of the world at one location and use it at another. A world-based 3D reconstruction of the scene built up from visual information would fulfil this requirement, something computer vision now achieves with great speed and accuracy. However, I argue that it is neither easy nor necessary for the brain to do this. I discuss biologically plausible alternatives, including the possibility of avoiding 3D coordinate frames such as ego-centric and world-based representations. For example, the distance, slant and local shape of surfaces dictate the propensity of visual features to move in the image with respect to one another as the observer’s perspective changes (through movement or binocular viewing). Such propensities can be stored without the need for 3D reference frames. The problem of representing a stable scene in the face of continual head and eye movements is an appropriate starting place for understanding the goal of 3D vision, more so, I argue, than the case of a static binocular observer
- …