Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Annotation taken, in the perspective of criminal and constitutional law, as well as in criminology, to the decision of the portuguese constitutional court, of January 13, 2011 – with respect to the problems of “consent” and “medical act”

1 – Summary of the decision taken by the Portuguese Constitutional Court, of January 13, 2011; 2 – Complete text of the decision of the Portuguese Constitutional Court, of January 13, 2011, Judge Maria João ANTUNES (Reporter), Judge Carlos Pamplona de OLIVEIRA, Judge José Borges SOEIRO, Judge Gil GALVÃO, Judge Rui Manuel Moura RAMOS (President) –in terms of the tribunalconstitucional.pt, August 1, 2011; 3 – Brief annotation to the problem of the “medical act”; 3.1 – Plus some conclusions on the brief annotation to the problem of the “medical act”; 3.2 – Brief annotation to the problem of “consent”– continuation of the previous comments; 4 – Conclusions. It must never be forgotten that “consent” does not stand as the only cause of exclusion of unlawfulness.

A Travel Optimization System for Academic Environments

Carpooling initiated in America in the 1970s due to the oil crisis. However, over the past years, carpooling has increased significantly across the world. Some countries have created a High Occupancy Vehicle (HOV) lane to encourage commuters not to travel alone. In additional, carpool websites has been developed to facilitate the connection between the commuters, making it possible to create a compatible match in a faster and efficient manner. This project focuses on carpooling, especially in an academic environment since younger people are more likely to choose carpool. Initially, an intense research was made to examine carpool studies that occurred all over the world, following with a research of higher education institutes that use carpooling as a transportation mode. Most websites created carpools by targeting people from a specific country. These commuters have different origins and destinations making it more complicated to create compatible matches. The objective of this project is to develop a system helping teachers and students from an academic environment to create carpool matches. This objective makes it easier to create carpools because these students and teachers have the same destination. During the research, it was essential to explore, as many as possible, existing carpool websites that are available across the world. After this analysis, several sketches were made to develop the layout and structure of the web application that’s being implemented throughout the project. Once the layout was established, the development of the web application was initiated. This project had its ups and downs but it accomplished all the necessary requirements. This project can be accessed on the link: http://ipcacarpool.somee.com. Once the website was up and running, a web-based survey was developed to study the reasons that motivate people to consider carpooling as an alternative to driving alone. To develop this survey was used a tool called Survey Planet. This survey contained 408 respondents, which 391 are students and 17 are teachers. This study concludes that a majority of the respondents don’t carpool, however they will consider carpooling if there was a dedicated parking space. A majority of the respondents that carpool initiated less than a year ago, indicating that this mean of transportation is recent.