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.

Money laundering and virtual money: the bitcoin example

Money laundering operations faced multiple changes and become more complex, in line with financial innovation. Often, regulation does not follow that innovation, giving opportunity to take advantage of thes e gaps in less lawful activities. The bitcoin is a virtual currency that has grown significantly, both in value and in volume of transactions, in recent years. The dimension of the phenomenon led to an increasing surveillance from the financial supervisors . We search for evidence of the relationship between money laundering and transactions carried out in bitcoins, the most popular virtual currency at the moment. We analyse the official publications relating the two themes, academic research and the notori ety within the international media. The attitudes toward the bitcoin are diverse, but all share concerns about its future impact. Some sparse evidence indicates that bitcoin may be an opportunity for money laundering, however more data is required.