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.

The host-tourist interaction in a world heritage site: the case of Guimarães

Guimarães, in the northwest of Portugal, is a city of strong symbolic and cultural significance and its nomination by UNESCO as world heritage, in 2001, enlarged its tourism potential. In this paper we present a few results of a survey that envisaged capturing the Guimarães residents’ perceptions of tourism impacts and their attitudes towards tourists. Specifically, one analyzes the type of relationship that exists between some socio-demographic groups and the perceived tourism impacts, as well as their socio-characteristics and the existing level of interaction between residents and tourists. The survey was implemented between January and March 2010 to a convenience sample of 540 inhabitants of the municipality of Guimarães resulting in 400 questionnaires with complete data. For this, we made use of various statistical techniques. Using a factorial analysis, we can conclude that the three factors used explain 52.3% of the variance contained in the original variables obtained from the survey. By another side, using a logit model in the analysis and taking as the dependent variable the frequent or very frequent contact with tourists, we found that only the variables referred to perceived positive impacts of tourism, education and the place of residence in urban areas have shown to be statistically significant. We are aware of the multiple ways the issue of residents’ perceptions and attitudes towards tourism can be approached and of the difficulties to get useful policy-oriented insights. This paper is a step in that trail.