Image Based Rendering Using Algebraic Techniques

This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

The Quadric Reference Surface: Theory and Applications

The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.

On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.

Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different starting point. Chemical compositional data, as used in provenance studies on archaeological materials, will be approached from the measurement theory. The results will show, in a very intuitive way that chemical data can only be treated by using the approach developed for compositional data. It will be shown that compositional data analysis is a particular case in projective geometry, when the projective coordinates are in the positive orthant, and they have the properties of logarithmic interval metrics. Moreover, it will be shown that this approach can be extended to a very large number of applications, including shape analysis. This will be exemplified with a case study in architecture of Early Christian churches dated back to the 5th-7th centuries AD

La formación de actividades ilegales en la ciudad de Cartagena a partir de la concentración de la gestión distrital en el sector del turismo. Análisis del periodo : 2002-2006

Colombia durante los últimos años ha intentado cambiar el estigma que tiene, en cuanto a su imagen internacional. Por lo tanto, el país ha tratado de explotar y potenciar las zonas que ha considerado con mayores fortalezas destacándose entre ellas la región de la costa, especialmente la ciudad de Cartagena, permitiéndose el fortalecimiento notable del sector del turismo en esta ciudad. En esa medida, este sector se ha preocupado por mantenerse en una competencia permanente en cuanto a la captación de turistas. Sin embargo, la ciudad de Cartagena se encuentra dentro de una dualidad enmarcada por la desigualdad social que ha polarizado su población. Abriendo paso a la generación actividades que se encuentran determinadas como indeseables. De acuerdo con lo anterior, podría hablarse de que en virtud del turismo se generan unas actividades, que no se encuentran propiamente bajo el marco de lo deseable como en el caso de la prostitución, la venta de estupefacientes y el comercio informal, que sumados a la mala planeación, se han convertido en los mayores problemas que atacan a esta ciudad.

A system to evaluate the accuracy of a visual mosaicking methodology

When underwater vehicles navigate close to the ocean floor, computer vision techniques can be applied to obtain motion estimates. A complete system to create visual mosaics of the seabed is described in this paper. Unfortunately, the accuracy of the constructed mosaic is difficult to evaluate. The use of a laboratory setup to obtain an accurate error measurement is proposed. The system consists on a robot arm carrying a downward looking camera. A pattern formed by a white background and a matrix of black dots uniformly distributed along the surveyed scene is used to find the exact image registration parameters. When the robot executes a trajectory (simulating the motion of a submersible), an image sequence is acquired by the camera. The estimated motion computed from the encoders of the robot is refined by detecting, to subpixel accuracy, the black dots of the image sequence, and computing the 2D projective transform which relates two consecutive images. The pattern is then substituted by a poster of the sea floor and the trajectory is executed again, acquiring the image sequence used to test the accuracy of the mosaicking system

Planar homography: accuracy analysis and applications

Projective homography sits at the heart of many problems in image registration. In addition to many methods for estimating the homography parameters (R.I. Hartley and A. Zisserman, 2000), analytical expressions to assess the accuracy of the transformation parameters have been proposed (A. Criminisi et al., 1999). We show that these expressions provide less accurate bounds than those based on the earlier results of Weng et al. (1989). The discrepancy becomes more critical in applications involving the integration of frame-to-frame homographies and their uncertainties, as in the reconstruction of terrain mosaics and the camera trajectory from flyover imagery. We demonstrate these issues through selected examples

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